Download NIOS (National Institute of Open Schooling) Class 10 (Secondary) April 2015 211 Maths Question Paper
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
50/HIS/2/211?A 4
2. If
?
?
?
?
?
?
1
9
n
= 81, the value of n is : 1
?????
?
?
?
?
?
?
1
9
n
= 81, ???? n ??? ????? ??? :
(A) ? 2 (B) ? 1
(C) 1 (D) 2
3. Monthly expenditure of a family is 60% of the monthly income. If the family saves
` 6,000 per month, the monthly income of the family (in rupees) is : 1
??? ?????????? ??? ???????? ?????, ???????? ???? ??? 60% ??? ? ????? ???? ?????????? ` 6,000 ??????????? ?????? ??????? ???,
???? ??? ?????????? ??? ???????? ???? (???????? ???) ??? :
(A) 10,000 (B) 12,000
(C) 15,000 (D) 18,000
4. 144 is what percent of 360 ? 1
144, 360 ??? ???????? ?????????? ??? ????????? ??? ?
(A) 250 (B) 100
(C) 40 (D) 4
5. In the figure given below, ? BOD is equal to : 1
?????? ??? ????? ???????? ???, ? BOD ????????? ??? :
(A) x? (B) (90 + x)?
(C) (90 ? x)? (D) (180 ? x)?
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
50/HIS/2/211?A 4
2. If
?
?
?
?
?
?
1
9
n
= 81, the value of n is : 1
?????
?
?
?
?
?
?
1
9
n
= 81, ???? n ??? ????? ??? :
(A) ? 2 (B) ? 1
(C) 1 (D) 2
3. Monthly expenditure of a family is 60% of the monthly income. If the family saves
` 6,000 per month, the monthly income of the family (in rupees) is : 1
??? ?????????? ??? ???????? ?????, ???????? ???? ??? 60% ??? ? ????? ???? ?????????? ` 6,000 ??????????? ?????? ??????? ???,
???? ??? ?????????? ??? ???????? ???? (???????? ???) ??? :
(A) 10,000 (B) 12,000
(C) 15,000 (D) 18,000
4. 144 is what percent of 360 ? 1
144, 360 ??? ???????? ?????????? ??? ????????? ??? ?
(A) 250 (B) 100
(C) 40 (D) 4
5. In the figure given below, ? BOD is equal to : 1
?????? ??? ????? ???????? ???, ? BOD ????????? ??? :
(A) x? (B) (90 + x)?
(C) (90 ? x)? (D) (180 ? x)?
5 50/HIS/2/211?A
6. In a plane, the point equidistant from the vertices of a triangle is called its : 1
(A) Centroid (B) Incentre
(C) Circumcentre (D) Orthocentre
??? ???????? ??? ??????? ??????? ??? ???? ???? ??? ???????????? ??????? ?????????? ??? :
(A) ???????? (B) ????:??????
(C) ??????????? (D) ????? ??????
7. In the figure given below, O is the centre of a circle. If ? AOB = 100?, the value of x
is : 1
?????? ??? ????? ???????? ???, O ?????? ????? ??? ?????? ??????? ??? ? ????? ? AOB = 100?, ???? x ??? ????? ??? :
(A) 50? (B) 120?
(C) 130? (D) 150?
8. If 4 tan A = 3, the value of
2 sin A + cos A
3 sin A ? 2 cos A
is 1
????? 4 tan A = 3, ????
2 sin A + cos A
3 sin A ? 2 cos A
??? ????? ??? :
(A) 20 (B) 10
(C)
15
4
(D)
10
3
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
50/HIS/2/211?A 4
2. If
?
?
?
?
?
?
1
9
n
= 81, the value of n is : 1
?????
?
?
?
?
?
?
1
9
n
= 81, ???? n ??? ????? ??? :
(A) ? 2 (B) ? 1
(C) 1 (D) 2
3. Monthly expenditure of a family is 60% of the monthly income. If the family saves
` 6,000 per month, the monthly income of the family (in rupees) is : 1
??? ?????????? ??? ???????? ?????, ???????? ???? ??? 60% ??? ? ????? ???? ?????????? ` 6,000 ??????????? ?????? ??????? ???,
???? ??? ?????????? ??? ???????? ???? (???????? ???) ??? :
(A) 10,000 (B) 12,000
(C) 15,000 (D) 18,000
4. 144 is what percent of 360 ? 1
144, 360 ??? ???????? ?????????? ??? ????????? ??? ?
(A) 250 (B) 100
(C) 40 (D) 4
5. In the figure given below, ? BOD is equal to : 1
?????? ??? ????? ???????? ???, ? BOD ????????? ??? :
(A) x? (B) (90 + x)?
(C) (90 ? x)? (D) (180 ? x)?
5 50/HIS/2/211?A
6. In a plane, the point equidistant from the vertices of a triangle is called its : 1
(A) Centroid (B) Incentre
(C) Circumcentre (D) Orthocentre
??? ???????? ??? ??????? ??????? ??? ???? ???? ??? ???????????? ??????? ?????????? ??? :
(A) ???????? (B) ????:??????
(C) ??????????? (D) ????? ??????
7. In the figure given below, O is the centre of a circle. If ? AOB = 100?, the value of x
is : 1
?????? ??? ????? ???????? ???, O ?????? ????? ??? ?????? ??????? ??? ? ????? ? AOB = 100?, ???? x ??? ????? ??? :
(A) 50? (B) 120?
(C) 130? (D) 150?
8. If 4 tan A = 3, the value of
2 sin A + cos A
3 sin A ? 2 cos A
is 1
????? 4 tan A = 3, ????
2 sin A + cos A
3 sin A ? 2 cos A
??? ????? ??? :
(A) 20 (B) 10
(C)
15
4
(D)
10
3
50/HIS/2/211?A 6
9. The value of
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
is 1
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
??? ????? ??? :
(A) 0 (B) 1
(C) 2 (D) ? 1
10. The value of sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A is : 1
sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A ??? ????? ??? :
(A) ? 1 (B) 0
(C) 1 (D) 2
11. In the figure given below, ?ABC is right angled at B. Which of the following is true ? 1
?????? ??? ????? ???????? ???, ?ABC ??? ?????? B ?????????? ??? ? ?????????????? ??? ??? ?????? ????? ??? ?
(A) cosec A =
a
c
(B) cosec A =
c
a
(C) cosec A =
a
b
(D) cosec A =
b
a
12. The width of each of five continuous classes in a frequency distribution is 5 and the
lower limit of the lowest (First) class is 10. The upper limit of the highest (last) class
is 1
?????? ?????????????? ??????? ??? ?????? ?????? ?????? ??? ????????? ??? ?????????? 5 ??? ????? ??????? ??????? (???????) ????? ??? ??????
?????? 10 ??? ? ??????? ?????? (???????) ????? ??? ?????? ?????? ??? :
(A) 15 (B) 20
(C) 30 (D) 35
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
50/HIS/2/211?A 4
2. If
?
?
?
?
?
?
1
9
n
= 81, the value of n is : 1
?????
?
?
?
?
?
?
1
9
n
= 81, ???? n ??? ????? ??? :
(A) ? 2 (B) ? 1
(C) 1 (D) 2
3. Monthly expenditure of a family is 60% of the monthly income. If the family saves
` 6,000 per month, the monthly income of the family (in rupees) is : 1
??? ?????????? ??? ???????? ?????, ???????? ???? ??? 60% ??? ? ????? ???? ?????????? ` 6,000 ??????????? ?????? ??????? ???,
???? ??? ?????????? ??? ???????? ???? (???????? ???) ??? :
(A) 10,000 (B) 12,000
(C) 15,000 (D) 18,000
4. 144 is what percent of 360 ? 1
144, 360 ??? ???????? ?????????? ??? ????????? ??? ?
(A) 250 (B) 100
(C) 40 (D) 4
5. In the figure given below, ? BOD is equal to : 1
?????? ??? ????? ???????? ???, ? BOD ????????? ??? :
(A) x? (B) (90 + x)?
(C) (90 ? x)? (D) (180 ? x)?
5 50/HIS/2/211?A
6. In a plane, the point equidistant from the vertices of a triangle is called its : 1
(A) Centroid (B) Incentre
(C) Circumcentre (D) Orthocentre
??? ???????? ??? ??????? ??????? ??? ???? ???? ??? ???????????? ??????? ?????????? ??? :
(A) ???????? (B) ????:??????
(C) ??????????? (D) ????? ??????
7. In the figure given below, O is the centre of a circle. If ? AOB = 100?, the value of x
is : 1
?????? ??? ????? ???????? ???, O ?????? ????? ??? ?????? ??????? ??? ? ????? ? AOB = 100?, ???? x ??? ????? ??? :
(A) 50? (B) 120?
(C) 130? (D) 150?
8. If 4 tan A = 3, the value of
2 sin A + cos A
3 sin A ? 2 cos A
is 1
????? 4 tan A = 3, ????
2 sin A + cos A
3 sin A ? 2 cos A
??? ????? ??? :
(A) 20 (B) 10
(C)
15
4
(D)
10
3
50/HIS/2/211?A 6
9. The value of
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
is 1
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
??? ????? ??? :
(A) 0 (B) 1
(C) 2 (D) ? 1
10. The value of sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A is : 1
sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A ??? ????? ??? :
(A) ? 1 (B) 0
(C) 1 (D) 2
11. In the figure given below, ?ABC is right angled at B. Which of the following is true ? 1
?????? ??? ????? ???????? ???, ?ABC ??? ?????? B ?????????? ??? ? ?????????????? ??? ??? ?????? ????? ??? ?
(A) cosec A =
a
c
(B) cosec A =
c
a
(C) cosec A =
a
b
(D) cosec A =
b
a
12. The width of each of five continuous classes in a frequency distribution is 5 and the
lower limit of the lowest (First) class is 10. The upper limit of the highest (last) class
is 1
?????? ?????????????? ??????? ??? ?????? ?????? ?????? ??? ????????? ??? ?????????? 5 ??? ????? ??????? ??????? (???????) ????? ??? ??????
?????? 10 ??? ? ??????? ?????? (???????) ????? ??? ?????? ?????? ??? :
(A) 15 (B) 20
(C) 30 (D) 35
7 50/HIS/2/211?A
13. Mode of the data, 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 is : 1
?????????? 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 ??? ????????? ??? :
(A) 20 (B) 18
(C) 15 (D) 14
14. Observe the histogram given below. How many students have the height 145 cm and
above ? 1
?????? ???? ???? ??????????? ???? ?????? ??? ??????? ? ???????? ???????????? ??? ???????? 145 ?????? ??? ?????? ?????? ??? ?
(A) 15 (B) 10
(C) 23 (D) 11
OR / ??????
(For Visually Impaired Learners Only)
(??????? ?????? ??????????? ???????????? ??? ????)
For drawing a frequency polygon of a continuous frequency distribution, we plot the
points whose ordinates are the frequencies of the respective classes and abscissa are
respectively :
(A) class mark of the classes (B) lower limits of classes
(C) upper limits of classes (D) upper limits of preceding classes
?????? ?????? ?????????????? ??????? ??? ???? ?????????????? ?????????? ???????? ??? ????, ???? ??? ??????? ?????????? ??????? ???, ????????
??????????? ??????? ?????? ??? ???????????????? ??????? ??? ????? ????? ???????: ??? :
(A) ?????? ??? ????? ?????? (B) ?????? ??? ?????? ????????
(C) ?????? ??? ??????? ???????? (D) ???????? ????? ??? ??????? ????????
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
50/HIS/2/211?A 4
2. If
?
?
?
?
?
?
1
9
n
= 81, the value of n is : 1
?????
?
?
?
?
?
?
1
9
n
= 81, ???? n ??? ????? ??? :
(A) ? 2 (B) ? 1
(C) 1 (D) 2
3. Monthly expenditure of a family is 60% of the monthly income. If the family saves
` 6,000 per month, the monthly income of the family (in rupees) is : 1
??? ?????????? ??? ???????? ?????, ???????? ???? ??? 60% ??? ? ????? ???? ?????????? ` 6,000 ??????????? ?????? ??????? ???,
???? ??? ?????????? ??? ???????? ???? (???????? ???) ??? :
(A) 10,000 (B) 12,000
(C) 15,000 (D) 18,000
4. 144 is what percent of 360 ? 1
144, 360 ??? ???????? ?????????? ??? ????????? ??? ?
(A) 250 (B) 100
(C) 40 (D) 4
5. In the figure given below, ? BOD is equal to : 1
?????? ??? ????? ???????? ???, ? BOD ????????? ??? :
(A) x? (B) (90 + x)?
(C) (90 ? x)? (D) (180 ? x)?
5 50/HIS/2/211?A
6. In a plane, the point equidistant from the vertices of a triangle is called its : 1
(A) Centroid (B) Incentre
(C) Circumcentre (D) Orthocentre
??? ???????? ??? ??????? ??????? ??? ???? ???? ??? ???????????? ??????? ?????????? ??? :
(A) ???????? (B) ????:??????
(C) ??????????? (D) ????? ??????
7. In the figure given below, O is the centre of a circle. If ? AOB = 100?, the value of x
is : 1
?????? ??? ????? ???????? ???, O ?????? ????? ??? ?????? ??????? ??? ? ????? ? AOB = 100?, ???? x ??? ????? ??? :
(A) 50? (B) 120?
(C) 130? (D) 150?
8. If 4 tan A = 3, the value of
2 sin A + cos A
3 sin A ? 2 cos A
is 1
????? 4 tan A = 3, ????
2 sin A + cos A
3 sin A ? 2 cos A
??? ????? ??? :
(A) 20 (B) 10
(C)
15
4
(D)
10
3
50/HIS/2/211?A 6
9. The value of
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
is 1
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
??? ????? ??? :
(A) 0 (B) 1
(C) 2 (D) ? 1
10. The value of sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A is : 1
sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A ??? ????? ??? :
(A) ? 1 (B) 0
(C) 1 (D) 2
11. In the figure given below, ?ABC is right angled at B. Which of the following is true ? 1
?????? ??? ????? ???????? ???, ?ABC ??? ?????? B ?????????? ??? ? ?????????????? ??? ??? ?????? ????? ??? ?
(A) cosec A =
a
c
(B) cosec A =
c
a
(C) cosec A =
a
b
(D) cosec A =
b
a
12. The width of each of five continuous classes in a frequency distribution is 5 and the
lower limit of the lowest (First) class is 10. The upper limit of the highest (last) class
is 1
?????? ?????????????? ??????? ??? ?????? ?????? ?????? ??? ????????? ??? ?????????? 5 ??? ????? ??????? ??????? (???????) ????? ??? ??????
?????? 10 ??? ? ??????? ?????? (???????) ????? ??? ?????? ?????? ??? :
(A) 15 (B) 20
(C) 30 (D) 35
7 50/HIS/2/211?A
13. Mode of the data, 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 is : 1
?????????? 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 ??? ????????? ??? :
(A) 20 (B) 18
(C) 15 (D) 14
14. Observe the histogram given below. How many students have the height 145 cm and
above ? 1
?????? ???? ???? ??????????? ???? ?????? ??? ??????? ? ???????? ???????????? ??? ???????? 145 ?????? ??? ?????? ?????? ??? ?
(A) 15 (B) 10
(C) 23 (D) 11
OR / ??????
(For Visually Impaired Learners Only)
(??????? ?????? ??????????? ???????????? ??? ????)
For drawing a frequency polygon of a continuous frequency distribution, we plot the
points whose ordinates are the frequencies of the respective classes and abscissa are
respectively :
(A) class mark of the classes (B) lower limits of classes
(C) upper limits of classes (D) upper limits of preceding classes
?????? ?????? ?????????????? ??????? ??? ???? ?????????????? ?????????? ???????? ??? ????, ???? ??? ??????? ?????????? ??????? ???, ????????
??????????? ??????? ?????? ??? ???????????????? ??????? ??? ????? ????? ???????: ??? :
(A) ?????? ??? ????? ?????? (B) ?????? ??? ?????? ????????
(C) ?????? ??? ??????? ???????? (D) ???????? ????? ??? ??????? ????????
50/HIS/2/211?A 8
15. Median of first 10 prime numbers is : 1
??????? ???? ??????? ?????????? ??? ???????? ??? :
(A) 11 (B) 12
(C) 13 (D) 14
16. Rationalise the denominator of the following : 2
?????? ??? ???? ??? ???????????????? ??????? :
11 ? 5
11 + 5
17. Multiply x
2
+
2
3
x +
5
6
by x ?
7
4
. 2
x
2
+
2
3
x +
5
6
???? x ?
7
4
??? ?????? ??????? ?
18. A certain sum of money at simple interest amounts to ` 1,300 in 4 years and to
` 1,525 in 7 years. Find the sum of money. 2
?????? ?????? ?????????? ?????? ???? 4 ?????? ??? ` 1,300 ????? 7 ?????? ??? ` 1,525 ???? ?????? ??? ? ?????? ????? ??????? ?
19. D is any point on the base BC of a ?ABC. If AB > AC, then prove that AB > AD. 2
?ABC ??? ??????? BC ???? ?????? ??????? D ??? ? ????? AB > AC, ???? ????? ??????? ??? AB > AD ?
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
50/HIS/2/211?A 4
2. If
?
?
?
?
?
?
1
9
n
= 81, the value of n is : 1
?????
?
?
?
?
?
?
1
9
n
= 81, ???? n ??? ????? ??? :
(A) ? 2 (B) ? 1
(C) 1 (D) 2
3. Monthly expenditure of a family is 60% of the monthly income. If the family saves
` 6,000 per month, the monthly income of the family (in rupees) is : 1
??? ?????????? ??? ???????? ?????, ???????? ???? ??? 60% ??? ? ????? ???? ?????????? ` 6,000 ??????????? ?????? ??????? ???,
???? ??? ?????????? ??? ???????? ???? (???????? ???) ??? :
(A) 10,000 (B) 12,000
(C) 15,000 (D) 18,000
4. 144 is what percent of 360 ? 1
144, 360 ??? ???????? ?????????? ??? ????????? ??? ?
(A) 250 (B) 100
(C) 40 (D) 4
5. In the figure given below, ? BOD is equal to : 1
?????? ??? ????? ???????? ???, ? BOD ????????? ??? :
(A) x? (B) (90 + x)?
(C) (90 ? x)? (D) (180 ? x)?
5 50/HIS/2/211?A
6. In a plane, the point equidistant from the vertices of a triangle is called its : 1
(A) Centroid (B) Incentre
(C) Circumcentre (D) Orthocentre
??? ???????? ??? ??????? ??????? ??? ???? ???? ??? ???????????? ??????? ?????????? ??? :
(A) ???????? (B) ????:??????
(C) ??????????? (D) ????? ??????
7. In the figure given below, O is the centre of a circle. If ? AOB = 100?, the value of x
is : 1
?????? ??? ????? ???????? ???, O ?????? ????? ??? ?????? ??????? ??? ? ????? ? AOB = 100?, ???? x ??? ????? ??? :
(A) 50? (B) 120?
(C) 130? (D) 150?
8. If 4 tan A = 3, the value of
2 sin A + cos A
3 sin A ? 2 cos A
is 1
????? 4 tan A = 3, ????
2 sin A + cos A
3 sin A ? 2 cos A
??? ????? ??? :
(A) 20 (B) 10
(C)
15
4
(D)
10
3
50/HIS/2/211?A 6
9. The value of
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
is 1
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
??? ????? ??? :
(A) 0 (B) 1
(C) 2 (D) ? 1
10. The value of sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A is : 1
sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A ??? ????? ??? :
(A) ? 1 (B) 0
(C) 1 (D) 2
11. In the figure given below, ?ABC is right angled at B. Which of the following is true ? 1
?????? ??? ????? ???????? ???, ?ABC ??? ?????? B ?????????? ??? ? ?????????????? ??? ??? ?????? ????? ??? ?
(A) cosec A =
a
c
(B) cosec A =
c
a
(C) cosec A =
a
b
(D) cosec A =
b
a
12. The width of each of five continuous classes in a frequency distribution is 5 and the
lower limit of the lowest (First) class is 10. The upper limit of the highest (last) class
is 1
?????? ?????????????? ??????? ??? ?????? ?????? ?????? ??? ????????? ??? ?????????? 5 ??? ????? ??????? ??????? (???????) ????? ??? ??????
?????? 10 ??? ? ??????? ?????? (???????) ????? ??? ?????? ?????? ??? :
(A) 15 (B) 20
(C) 30 (D) 35
7 50/HIS/2/211?A
13. Mode of the data, 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 is : 1
?????????? 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 ??? ????????? ??? :
(A) 20 (B) 18
(C) 15 (D) 14
14. Observe the histogram given below. How many students have the height 145 cm and
above ? 1
?????? ???? ???? ??????????? ???? ?????? ??? ??????? ? ???????? ???????????? ??? ???????? 145 ?????? ??? ?????? ?????? ??? ?
(A) 15 (B) 10
(C) 23 (D) 11
OR / ??????
(For Visually Impaired Learners Only)
(??????? ?????? ??????????? ???????????? ??? ????)
For drawing a frequency polygon of a continuous frequency distribution, we plot the
points whose ordinates are the frequencies of the respective classes and abscissa are
respectively :
(A) class mark of the classes (B) lower limits of classes
(C) upper limits of classes (D) upper limits of preceding classes
?????? ?????? ?????????????? ??????? ??? ???? ?????????????? ?????????? ???????? ??? ????, ???? ??? ??????? ?????????? ??????? ???, ????????
??????????? ??????? ?????? ??? ???????????????? ??????? ??? ????? ????? ???????: ??? :
(A) ?????? ??? ????? ?????? (B) ?????? ??? ?????? ????????
(C) ?????? ??? ??????? ???????? (D) ???????? ????? ??? ??????? ????????
50/HIS/2/211?A 8
15. Median of first 10 prime numbers is : 1
??????? ???? ??????? ?????????? ??? ???????? ??? :
(A) 11 (B) 12
(C) 13 (D) 14
16. Rationalise the denominator of the following : 2
?????? ??? ???? ??? ???????????????? ??????? :
11 ? 5
11 + 5
17. Multiply x
2
+
2
3
x +
5
6
by x ?
7
4
. 2
x
2
+
2
3
x +
5
6
???? x ?
7
4
??? ?????? ??????? ?
18. A certain sum of money at simple interest amounts to ` 1,300 in 4 years and to
` 1,525 in 7 years. Find the sum of money. 2
?????? ?????? ?????????? ?????? ???? 4 ?????? ??? ` 1,300 ????? 7 ?????? ??? ` 1,525 ???? ?????? ??? ? ?????? ????? ??????? ?
19. D is any point on the base BC of a ?ABC. If AB > AC, then prove that AB > AD. 2
?ABC ??? ??????? BC ???? ?????? ??????? D ??? ? ????? AB > AC, ???? ????? ??????? ??? AB > AD ?
9 50/HIS/2/211?A
20. PAB is a secant to the circle from a point P outside the circle. PAB passes through the
centre of the circle and PT is a tangent. If PT = 8 cm and OP = 10 cm, find the radius
of the circle. 2
?????? ????? ??? ??????? ?????? ??????? P ??? PAB ????? ??? ??? ??????? ??? ????? ???? ????? ??? ?????? ??????? O ??? ????????
?????? ??? ? PT ????? ??? ?????? ?????? ??? ? ????? PT = 8 ?????? ????? OP = 10 ??????, ???? ????? ??? ??????? ?????
??????? ?
21. If the length of a chord of a circle is 16 cm and the distance of the chord from the
centre is 6 cm, find the radius of the circle. 2
????? ??? ????? ??? ??? ?????? ??? ???????? 16 ?????? ????? ??? ?????? ??? ?????? ??? ?????? 6 ?????? ???, ???? ????? ??? ???????
????? ??????? ?
22. Find the coordinates of the point on x?axis equidistant from the points (2, 5) and
(3, 4). 2
x-??? ???? ??? ??????? ??? ???????????? ????? ??????? ???? ?????????? (2, 5) ????? (3, 4) ??? ??????? ?????? ???? ???? ?
23. Find the perimeter and area of the sector of a circle of radius 9 cm with central angle
35?. 2
9 ?????? ??????? ?????? ????? ??? ??? ??????????? ??? ?????????? ????? ????????? ????? ??????? ???????? ????????? ?????? 35?
??? ?
24. Find the area of a rhombus whose side is of the length 5 m and one of its diagonals is
of length 8 m. 2
??? ????? ??????????????? ??? ????????? ????? ??????? ???????? ?????? ??? ???????? 5 ??????? ????? ??? ???????? ??? ????????
8 ??????? ??? ?
25. Prove that : 2
????? ??????? ??? :
1 ? cos A
1 + cos A
= (cosec A ? cot A)
2
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
50/HIS/2/211?A 4
2. If
?
?
?
?
?
?
1
9
n
= 81, the value of n is : 1
?????
?
?
?
?
?
?
1
9
n
= 81, ???? n ??? ????? ??? :
(A) ? 2 (B) ? 1
(C) 1 (D) 2
3. Monthly expenditure of a family is 60% of the monthly income. If the family saves
` 6,000 per month, the monthly income of the family (in rupees) is : 1
??? ?????????? ??? ???????? ?????, ???????? ???? ??? 60% ??? ? ????? ???? ?????????? ` 6,000 ??????????? ?????? ??????? ???,
???? ??? ?????????? ??? ???????? ???? (???????? ???) ??? :
(A) 10,000 (B) 12,000
(C) 15,000 (D) 18,000
4. 144 is what percent of 360 ? 1
144, 360 ??? ???????? ?????????? ??? ????????? ??? ?
(A) 250 (B) 100
(C) 40 (D) 4
5. In the figure given below, ? BOD is equal to : 1
?????? ??? ????? ???????? ???, ? BOD ????????? ??? :
(A) x? (B) (90 + x)?
(C) (90 ? x)? (D) (180 ? x)?
5 50/HIS/2/211?A
6. In a plane, the point equidistant from the vertices of a triangle is called its : 1
(A) Centroid (B) Incentre
(C) Circumcentre (D) Orthocentre
??? ???????? ??? ??????? ??????? ??? ???? ???? ??? ???????????? ??????? ?????????? ??? :
(A) ???????? (B) ????:??????
(C) ??????????? (D) ????? ??????
7. In the figure given below, O is the centre of a circle. If ? AOB = 100?, the value of x
is : 1
?????? ??? ????? ???????? ???, O ?????? ????? ??? ?????? ??????? ??? ? ????? ? AOB = 100?, ???? x ??? ????? ??? :
(A) 50? (B) 120?
(C) 130? (D) 150?
8. If 4 tan A = 3, the value of
2 sin A + cos A
3 sin A ? 2 cos A
is 1
????? 4 tan A = 3, ????
2 sin A + cos A
3 sin A ? 2 cos A
??? ????? ??? :
(A) 20 (B) 10
(C)
15
4
(D)
10
3
50/HIS/2/211?A 6
9. The value of
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
is 1
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
??? ????? ??? :
(A) 0 (B) 1
(C) 2 (D) ? 1
10. The value of sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A is : 1
sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A ??? ????? ??? :
(A) ? 1 (B) 0
(C) 1 (D) 2
11. In the figure given below, ?ABC is right angled at B. Which of the following is true ? 1
?????? ??? ????? ???????? ???, ?ABC ??? ?????? B ?????????? ??? ? ?????????????? ??? ??? ?????? ????? ??? ?
(A) cosec A =
a
c
(B) cosec A =
c
a
(C) cosec A =
a
b
(D) cosec A =
b
a
12. The width of each of five continuous classes in a frequency distribution is 5 and the
lower limit of the lowest (First) class is 10. The upper limit of the highest (last) class
is 1
?????? ?????????????? ??????? ??? ?????? ?????? ?????? ??? ????????? ??? ?????????? 5 ??? ????? ??????? ??????? (???????) ????? ??? ??????
?????? 10 ??? ? ??????? ?????? (???????) ????? ??? ?????? ?????? ??? :
(A) 15 (B) 20
(C) 30 (D) 35
7 50/HIS/2/211?A
13. Mode of the data, 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 is : 1
?????????? 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 ??? ????????? ??? :
(A) 20 (B) 18
(C) 15 (D) 14
14. Observe the histogram given below. How many students have the height 145 cm and
above ? 1
?????? ???? ???? ??????????? ???? ?????? ??? ??????? ? ???????? ???????????? ??? ???????? 145 ?????? ??? ?????? ?????? ??? ?
(A) 15 (B) 10
(C) 23 (D) 11
OR / ??????
(For Visually Impaired Learners Only)
(??????? ?????? ??????????? ???????????? ??? ????)
For drawing a frequency polygon of a continuous frequency distribution, we plot the
points whose ordinates are the frequencies of the respective classes and abscissa are
respectively :
(A) class mark of the classes (B) lower limits of classes
(C) upper limits of classes (D) upper limits of preceding classes
?????? ?????? ?????????????? ??????? ??? ???? ?????????????? ?????????? ???????? ??? ????, ???? ??? ??????? ?????????? ??????? ???, ????????
??????????? ??????? ?????? ??? ???????????????? ??????? ??? ????? ????? ???????: ??? :
(A) ?????? ??? ????? ?????? (B) ?????? ??? ?????? ????????
(C) ?????? ??? ??????? ???????? (D) ???????? ????? ??? ??????? ????????
50/HIS/2/211?A 8
15. Median of first 10 prime numbers is : 1
??????? ???? ??????? ?????????? ??? ???????? ??? :
(A) 11 (B) 12
(C) 13 (D) 14
16. Rationalise the denominator of the following : 2
?????? ??? ???? ??? ???????????????? ??????? :
11 ? 5
11 + 5
17. Multiply x
2
+
2
3
x +
5
6
by x ?
7
4
. 2
x
2
+
2
3
x +
5
6
???? x ?
7
4
??? ?????? ??????? ?
18. A certain sum of money at simple interest amounts to ` 1,300 in 4 years and to
` 1,525 in 7 years. Find the sum of money. 2
?????? ?????? ?????????? ?????? ???? 4 ?????? ??? ` 1,300 ????? 7 ?????? ??? ` 1,525 ???? ?????? ??? ? ?????? ????? ??????? ?
19. D is any point on the base BC of a ?ABC. If AB > AC, then prove that AB > AD. 2
?ABC ??? ??????? BC ???? ?????? ??????? D ??? ? ????? AB > AC, ???? ????? ??????? ??? AB > AD ?
9 50/HIS/2/211?A
20. PAB is a secant to the circle from a point P outside the circle. PAB passes through the
centre of the circle and PT is a tangent. If PT = 8 cm and OP = 10 cm, find the radius
of the circle. 2
?????? ????? ??? ??????? ?????? ??????? P ??? PAB ????? ??? ??? ??????? ??? ????? ???? ????? ??? ?????? ??????? O ??? ????????
?????? ??? ? PT ????? ??? ?????? ?????? ??? ? ????? PT = 8 ?????? ????? OP = 10 ??????, ???? ????? ??? ??????? ?????
??????? ?
21. If the length of a chord of a circle is 16 cm and the distance of the chord from the
centre is 6 cm, find the radius of the circle. 2
????? ??? ????? ??? ??? ?????? ??? ???????? 16 ?????? ????? ??? ?????? ??? ?????? ??? ?????? 6 ?????? ???, ???? ????? ??? ???????
????? ??????? ?
22. Find the coordinates of the point on x?axis equidistant from the points (2, 5) and
(3, 4). 2
x-??? ???? ??? ??????? ??? ???????????? ????? ??????? ???? ?????????? (2, 5) ????? (3, 4) ??? ??????? ?????? ???? ???? ?
23. Find the perimeter and area of the sector of a circle of radius 9 cm with central angle
35?. 2
9 ?????? ??????? ?????? ????? ??? ??? ??????????? ??? ?????????? ????? ????????? ????? ??????? ???????? ????????? ?????? 35?
??? ?
24. Find the area of a rhombus whose side is of the length 5 m and one of its diagonals is
of length 8 m. 2
??? ????? ??????????????? ??? ????????? ????? ??????? ???????? ?????? ??? ???????? 5 ??????? ????? ??? ???????? ??? ????????
8 ??????? ??? ?
25. Prove that : 2
????? ??????? ??? :
1 ? cos A
1 + cos A
= (cosec A ? cot A)
2
50/HIS/2/211?A 10
26. Three years ago Atul?s age was four times Parul?s age. After 5 years from now, Atul?s
age will be twice Parul?s age. Find their present ages. 4
????? ????? ??????, ?????? ??? ????? ??????? ??? ????? ??? ????? ?????? ??? ? ???? ??? 5 ????? ????????? ?????? ??? ?????
??????? ??? ????? ??? ????????? ??????? ? ?????? ????? ??????? ??? ?????????? ????? ????? ??????? ?
27. Find the 50
th
term and sum of first 50 terms of the A.P 11,16, 21, 26, ?.. 4
?????????? ??????? 11, 16, 21, 26, ............... ??? 50???? ???? ???? ??????? 50 ?????? ??? ?????? ????? ??????? ?
28. A cooler is available for ` 3,400 cash or ` 2,000 as cash down payment followed by
five equal monthly instalments. If the rate of interest charged under the instalment
plan is 30% per annum, find the amount of each instalment. 4
??? ??????? ` 3,400 ?????? ?????????? ?????? ` 2,000 ???????? ?????????? ????? ?????? ????? ?????? ??????? ???????? ????????
??? ???????? ??? ? ????? ??? ?????? ????????? ??? ????????? ???? ?????? ?????? ?????? ??? ???? 30% ???????? ???, ???? ?????????
?????? ??? ???? ?????? ?????? ?????? ??? ??????? ??????? ?
29. Prove that the parallelograms on equal (or same) bases and between the same parallels
are equal in area. 4
????? ??????? ??? ??????? ??????? (??? ??? ??? ???????) ????? ???? ?????????? ????????? ??? ????? ????? ?????????? ???????????
????????? ??? ??????? ??????? ??? ?
30. ABC is a triangle right angled at C. If CD, the length of perpendicular from C on AB
is p, BC = a, AC = b and AB = c, then prove that
1
p
2
=
1
a
2
+
1
b
2
. 4
ABC ??? ???????? ??? ???????? ? C = 90? ? ????? CD, ?????? C ??? AB ???? ?????? ??? ????? ??? ???????? p ??? ?????
BC = a, AC = b ????? AB = c ????, ???? ????? ??????? ???
1
p
2
=
1
a
2
+
1
b
2
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
50/HIS/2/211?A 4
2. If
?
?
?
?
?
?
1
9
n
= 81, the value of n is : 1
?????
?
?
?
?
?
?
1
9
n
= 81, ???? n ??? ????? ??? :
(A) ? 2 (B) ? 1
(C) 1 (D) 2
3. Monthly expenditure of a family is 60% of the monthly income. If the family saves
` 6,000 per month, the monthly income of the family (in rupees) is : 1
??? ?????????? ??? ???????? ?????, ???????? ???? ??? 60% ??? ? ????? ???? ?????????? ` 6,000 ??????????? ?????? ??????? ???,
???? ??? ?????????? ??? ???????? ???? (???????? ???) ??? :
(A) 10,000 (B) 12,000
(C) 15,000 (D) 18,000
4. 144 is what percent of 360 ? 1
144, 360 ??? ???????? ?????????? ??? ????????? ??? ?
(A) 250 (B) 100
(C) 40 (D) 4
5. In the figure given below, ? BOD is equal to : 1
?????? ??? ????? ???????? ???, ? BOD ????????? ??? :
(A) x? (B) (90 + x)?
(C) (90 ? x)? (D) (180 ? x)?
5 50/HIS/2/211?A
6. In a plane, the point equidistant from the vertices of a triangle is called its : 1
(A) Centroid (B) Incentre
(C) Circumcentre (D) Orthocentre
??? ???????? ??? ??????? ??????? ??? ???? ???? ??? ???????????? ??????? ?????????? ??? :
(A) ???????? (B) ????:??????
(C) ??????????? (D) ????? ??????
7. In the figure given below, O is the centre of a circle. If ? AOB = 100?, the value of x
is : 1
?????? ??? ????? ???????? ???, O ?????? ????? ??? ?????? ??????? ??? ? ????? ? AOB = 100?, ???? x ??? ????? ??? :
(A) 50? (B) 120?
(C) 130? (D) 150?
8. If 4 tan A = 3, the value of
2 sin A + cos A
3 sin A ? 2 cos A
is 1
????? 4 tan A = 3, ????
2 sin A + cos A
3 sin A ? 2 cos A
??? ????? ??? :
(A) 20 (B) 10
(C)
15
4
(D)
10
3
50/HIS/2/211?A 6
9. The value of
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
is 1
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
??? ????? ??? :
(A) 0 (B) 1
(C) 2 (D) ? 1
10. The value of sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A is : 1
sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A ??? ????? ??? :
(A) ? 1 (B) 0
(C) 1 (D) 2
11. In the figure given below, ?ABC is right angled at B. Which of the following is true ? 1
?????? ??? ????? ???????? ???, ?ABC ??? ?????? B ?????????? ??? ? ?????????????? ??? ??? ?????? ????? ??? ?
(A) cosec A =
a
c
(B) cosec A =
c
a
(C) cosec A =
a
b
(D) cosec A =
b
a
12. The width of each of five continuous classes in a frequency distribution is 5 and the
lower limit of the lowest (First) class is 10. The upper limit of the highest (last) class
is 1
?????? ?????????????? ??????? ??? ?????? ?????? ?????? ??? ????????? ??? ?????????? 5 ??? ????? ??????? ??????? (???????) ????? ??? ??????
?????? 10 ??? ? ??????? ?????? (???????) ????? ??? ?????? ?????? ??? :
(A) 15 (B) 20
(C) 30 (D) 35
7 50/HIS/2/211?A
13. Mode of the data, 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 is : 1
?????????? 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 ??? ????????? ??? :
(A) 20 (B) 18
(C) 15 (D) 14
14. Observe the histogram given below. How many students have the height 145 cm and
above ? 1
?????? ???? ???? ??????????? ???? ?????? ??? ??????? ? ???????? ???????????? ??? ???????? 145 ?????? ??? ?????? ?????? ??? ?
(A) 15 (B) 10
(C) 23 (D) 11
OR / ??????
(For Visually Impaired Learners Only)
(??????? ?????? ??????????? ???????????? ??? ????)
For drawing a frequency polygon of a continuous frequency distribution, we plot the
points whose ordinates are the frequencies of the respective classes and abscissa are
respectively :
(A) class mark of the classes (B) lower limits of classes
(C) upper limits of classes (D) upper limits of preceding classes
?????? ?????? ?????????????? ??????? ??? ???? ?????????????? ?????????? ???????? ??? ????, ???? ??? ??????? ?????????? ??????? ???, ????????
??????????? ??????? ?????? ??? ???????????????? ??????? ??? ????? ????? ???????: ??? :
(A) ?????? ??? ????? ?????? (B) ?????? ??? ?????? ????????
(C) ?????? ??? ??????? ???????? (D) ???????? ????? ??? ??????? ????????
50/HIS/2/211?A 8
15. Median of first 10 prime numbers is : 1
??????? ???? ??????? ?????????? ??? ???????? ??? :
(A) 11 (B) 12
(C) 13 (D) 14
16. Rationalise the denominator of the following : 2
?????? ??? ???? ??? ???????????????? ??????? :
11 ? 5
11 + 5
17. Multiply x
2
+
2
3
x +
5
6
by x ?
7
4
. 2
x
2
+
2
3
x +
5
6
???? x ?
7
4
??? ?????? ??????? ?
18. A certain sum of money at simple interest amounts to ` 1,300 in 4 years and to
` 1,525 in 7 years. Find the sum of money. 2
?????? ?????? ?????????? ?????? ???? 4 ?????? ??? ` 1,300 ????? 7 ?????? ??? ` 1,525 ???? ?????? ??? ? ?????? ????? ??????? ?
19. D is any point on the base BC of a ?ABC. If AB > AC, then prove that AB > AD. 2
?ABC ??? ??????? BC ???? ?????? ??????? D ??? ? ????? AB > AC, ???? ????? ??????? ??? AB > AD ?
9 50/HIS/2/211?A
20. PAB is a secant to the circle from a point P outside the circle. PAB passes through the
centre of the circle and PT is a tangent. If PT = 8 cm and OP = 10 cm, find the radius
of the circle. 2
?????? ????? ??? ??????? ?????? ??????? P ??? PAB ????? ??? ??? ??????? ??? ????? ???? ????? ??? ?????? ??????? O ??? ????????
?????? ??? ? PT ????? ??? ?????? ?????? ??? ? ????? PT = 8 ?????? ????? OP = 10 ??????, ???? ????? ??? ??????? ?????
??????? ?
21. If the length of a chord of a circle is 16 cm and the distance of the chord from the
centre is 6 cm, find the radius of the circle. 2
????? ??? ????? ??? ??? ?????? ??? ???????? 16 ?????? ????? ??? ?????? ??? ?????? ??? ?????? 6 ?????? ???, ???? ????? ??? ???????
????? ??????? ?
22. Find the coordinates of the point on x?axis equidistant from the points (2, 5) and
(3, 4). 2
x-??? ???? ??? ??????? ??? ???????????? ????? ??????? ???? ?????????? (2, 5) ????? (3, 4) ??? ??????? ?????? ???? ???? ?
23. Find the perimeter and area of the sector of a circle of radius 9 cm with central angle
35?. 2
9 ?????? ??????? ?????? ????? ??? ??? ??????????? ??? ?????????? ????? ????????? ????? ??????? ???????? ????????? ?????? 35?
??? ?
24. Find the area of a rhombus whose side is of the length 5 m and one of its diagonals is
of length 8 m. 2
??? ????? ??????????????? ??? ????????? ????? ??????? ???????? ?????? ??? ???????? 5 ??????? ????? ??? ???????? ??? ????????
8 ??????? ??? ?
25. Prove that : 2
????? ??????? ??? :
1 ? cos A
1 + cos A
= (cosec A ? cot A)
2
50/HIS/2/211?A 10
26. Three years ago Atul?s age was four times Parul?s age. After 5 years from now, Atul?s
age will be twice Parul?s age. Find their present ages. 4
????? ????? ??????, ?????? ??? ????? ??????? ??? ????? ??? ????? ?????? ??? ? ???? ??? 5 ????? ????????? ?????? ??? ?????
??????? ??? ????? ??? ????????? ??????? ? ?????? ????? ??????? ??? ?????????? ????? ????? ??????? ?
27. Find the 50
th
term and sum of first 50 terms of the A.P 11,16, 21, 26, ?.. 4
?????????? ??????? 11, 16, 21, 26, ............... ??? 50???? ???? ???? ??????? 50 ?????? ??? ?????? ????? ??????? ?
28. A cooler is available for ` 3,400 cash or ` 2,000 as cash down payment followed by
five equal monthly instalments. If the rate of interest charged under the instalment
plan is 30% per annum, find the amount of each instalment. 4
??? ??????? ` 3,400 ?????? ?????????? ?????? ` 2,000 ???????? ?????????? ????? ?????? ????? ?????? ??????? ???????? ????????
??? ???????? ??? ? ????? ??? ?????? ????????? ??? ????????? ???? ?????? ?????? ?????? ??? ???? 30% ???????? ???, ???? ?????????
?????? ??? ???? ?????? ?????? ?????? ??? ??????? ??????? ?
29. Prove that the parallelograms on equal (or same) bases and between the same parallels
are equal in area. 4
????? ??????? ??? ??????? ??????? (??? ??? ??? ???????) ????? ???? ?????????? ????????? ??? ????? ????? ?????????? ???????????
????????? ??? ??????? ??????? ??? ?
30. ABC is a triangle right angled at C. If CD, the length of perpendicular from C on AB
is p, BC = a, AC = b and AB = c, then prove that
1
p
2
=
1
a
2
+
1
b
2
. 4
ABC ??? ???????? ??? ???????? ? C = 90? ? ????? CD, ?????? C ??? AB ???? ?????? ??? ????? ??? ???????? p ??? ?????
BC = a, AC = b ????? AB = c ????, ???? ????? ??????? ???
1
p
2
=
1
a
2
+
1
b
2
11 50/HIS/2/211?A
31. An observer standing 40 m away from a building observes that the angle of elevation
of the top and bottom of a flagstaff, which is surmounted on the building are 60? and
45? respectively. Find the height of the building and the length of the flagstaff.
( 3 = 1.732) 4
??? ???????? ?????? ?????? ??? 40 ??????? ??? ?????? ???? ?????? ???????? ???? ???????? ??? ??? ??? ?????? ???, ???? ??? ?????? ????
????? ????? ???, ?????? ???? ????? ?????????? ??? ???????? ?????? ???????: 60? ???? 45? ??? ? ?????? ??? ???????? ????? ??????
??? ???????? ????? ??????? ? ( 3 = 1.732)
32. If the mean of the following data is 17.45, find the value of P. 4
????? ?????? ?????????? ??? ?????? 17.45 ???, ???? P ??? ????? ????? ??????? ?
X
i
15 16 17 18 19 20
F
i
3 8 10 P 5 4
33. A pair of dice is thrown once. Find the probability of getting 4
(i) same number on both dice
(ii) sum of the numbers appearing on dice as 9.
???? ??????? ???? ??? ????? ??? ????? ?????? ?????? ??? ? ?????? ???? ??????? ??????? ??? ???????????? ????? ??????? :
(i) ???????? ??????? ???? ??? ??? ???????
(ii) ???????? ??????? ???? ??????? ?????????? ??? ?????? 9
34. Check whether the roots of the quadratic equation
x
x + 1
+
x + 1
x
=
34
15
(x ? 0, 1) are
real or not. If yes, find the roots. 6
?????? ??????? ??? ???????? ???????????
x
x + 1
+
x + 1
x
=
34
15
(x ? 0, 1) ??? ????? ??????????? ??? ?????? ????? ?
????? ????, ???? ????? ????? ??????? ?
FirstRanker.com - FirstRanker's Choice
This Question Paper consists of 36 questions and 12 printed pages.
??? ??????-???? ??? 36 ?????? ???? 12 ???????? ?????? ??? ?
Roll No.
?????????????
MATHEMATICS
???????
(211)
Day and Date of Examination ????????????????????????
(???????? ??? ????? ?? ?????????)
Signature of Invigilators 1. ??????????????
(???????????? ??? ??????????)
2. ??????????????
General Instructions :
1. Candidate must write his/her Roll Number on the first page of the Question Paper.
2. Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also
check to see that the questions are in sequential order.
3. For the objective type of questions, you have to choose any one of the four alternatives given in
the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the answer-book given
to you.
4. All the question including objective type questions are to be answered within the allotted time
and no separate time limit is fixed for answering objective type questions.
5. Making any identification mark in the answer-book or writing roll number anywhere other than
the specified places will lead to disqualification of the candidate.
6. Write your Question Paper Code No. 50/HIS/2, Set A on the answer-book.
7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided in
the answer-book.
(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
Code No.
?????? ???.
50/HIS/2
SET/????? A
50/HIS/2/211-A
50/HIS/2/211?A 2
????????? ????????? :
1. ??????????? ??????-???? ??? ??????? ?????? ???? ?????? ????????????? ?????? ?????? ?
2. ???????? ??????-???? ???? ?????? ??? ??? ??????-???? ??? ????? ???????? ????? ???????? ??? ?????? ??? ??????? ??? ???????? ??????? ?????? ??? ???????
?????? ????? ??? ? ??? ????? ??? ?????? ??? ???? ??? ??? ?????? ???????? ???? ??? ??? ?
3. ???????????? ???????? ??? ???????? ????? ?????????? (A), (B), (C) ????? (D) ??? ??? ?????? ??? ????? ???????? ??? ????? ??? ???? ?????-
?????????? ??? ???? ????? ????? ??????? ?
4. ???????????? ???????? ??? ?????-????? ????? ???????? ??? ????? ???????????? ?????? ??? ??????? ??? ?????? ??? ? ???????????? ???????? ??? ???? ?????
??? ?????? ????? ?????? ??????? ?
5. ?????-?????????? ??? ?????????-?????? ???????? ?????? ????????? ???????? ??? ?????????? ????? ??? ????????????? ???????? ???? ??????????? ????
???????? ?????????? ????????? ?
6. ?????? ?????-?????????? ???? ??????-???? ??? ?????? ??????? 50/HIS/2, ????? A ?????? ?
7. (??) ??????-???? ??????? ???????/????????? ??? ??? ? ????? ???, ????? ???? ?????? ???? ?????? ??? ???? ?????? ??? ?????? ??? ????? ??? ??????? ??? :
?????????, ???????, ?????, ?????????, ????????, ???????, ???????????, ????????, ?????????, ????????, ????????, ???????????, ?????????, ???????????,
?????????, ?????????, ?????????, ????????? ????? ??????? ?
???????? ?????-?????????? ??? ???? ??? ??????? ??? ?????? ??? ???? ????? ?????? ??? ????? ????? ????? ??? ?
(??) ????? ???? ??????? ???? ????????? ??? ?????????? ?????? ???? ?????? ??? ????? ???????? ??? ???? ?????? ???? ????????? ??? ??????? ??????
??????????/??????????? ??? ????????????? ??????? ??????? ??????? ?
3 50/HIS/2/211?A
MATHEMATICS
???????
(211)
Time : 2
1
2
Hours ] [ Maximum Marks : 85
?????? : 2
1
2
?????? ] [ ????????? : 85
Note : (i) Question Numbers (1-15) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices, (A), (B), (C) and (D) are
provided, of which only one is correct. You have to select the correct alternative
and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D)
as the case may be.
(ii) Question Numbers (16-25) carry 2 marks each.
(iii) Question Numbers (26-33) carry 4 marks each.
(iv) Question Numbers (34-36) carry 6 marks each.
(v) All questions are compulsory.
???????? : (i) ?????? ??????? (1-15) ???? ?????????????? ?????? (Multiple Choice Question) ??? ? ????????? ?????? ???
???? ??? ??? ? ????????? ?????? ??? ????? ???????? (A), (B), (C) ????? (D) ?????? ????? ???, ???????? ??? ??????? ???
????? ??? ? ???????? ????? ???????? ???????? ??? ????? ????????? ?????? ??? ????? ?????? ?????-?????????? ??? (A), (B),
(C) ?????? (D) ?????? ??? ??????? ????, ????????? ????????? ??? ?
(ii) ?????? ??????? (16-25) ???? ????????? ?????? ??? 2 ???? ??? ?
(iii) ?????? ??????? (26-33) ???? ????????? ?????? ??? 4 ???? ??? ?
(iv) ?????? ??????? (34-36) ???? ????????? ?????? ??? 6 ???? ??? ?
(v) ????? ?????? ?????????? ??? ?
1. Which of the following is not a rational number ? 1
?????????????? ??? ??? ?????? ?????????? ??????? ????? ??? ?
(A) 3 (B)
5
?7
(C)
?
?
?
?
?
?
2
3
2
(D) (2)
?
50/HIS/2/211?A 4
2. If
?
?
?
?
?
?
1
9
n
= 81, the value of n is : 1
?????
?
?
?
?
?
?
1
9
n
= 81, ???? n ??? ????? ??? :
(A) ? 2 (B) ? 1
(C) 1 (D) 2
3. Monthly expenditure of a family is 60% of the monthly income. If the family saves
` 6,000 per month, the monthly income of the family (in rupees) is : 1
??? ?????????? ??? ???????? ?????, ???????? ???? ??? 60% ??? ? ????? ???? ?????????? ` 6,000 ??????????? ?????? ??????? ???,
???? ??? ?????????? ??? ???????? ???? (???????? ???) ??? :
(A) 10,000 (B) 12,000
(C) 15,000 (D) 18,000
4. 144 is what percent of 360 ? 1
144, 360 ??? ???????? ?????????? ??? ????????? ??? ?
(A) 250 (B) 100
(C) 40 (D) 4
5. In the figure given below, ? BOD is equal to : 1
?????? ??? ????? ???????? ???, ? BOD ????????? ??? :
(A) x? (B) (90 + x)?
(C) (90 ? x)? (D) (180 ? x)?
5 50/HIS/2/211?A
6. In a plane, the point equidistant from the vertices of a triangle is called its : 1
(A) Centroid (B) Incentre
(C) Circumcentre (D) Orthocentre
??? ???????? ??? ??????? ??????? ??? ???? ???? ??? ???????????? ??????? ?????????? ??? :
(A) ???????? (B) ????:??????
(C) ??????????? (D) ????? ??????
7. In the figure given below, O is the centre of a circle. If ? AOB = 100?, the value of x
is : 1
?????? ??? ????? ???????? ???, O ?????? ????? ??? ?????? ??????? ??? ? ????? ? AOB = 100?, ???? x ??? ????? ??? :
(A) 50? (B) 120?
(C) 130? (D) 150?
8. If 4 tan A = 3, the value of
2 sin A + cos A
3 sin A ? 2 cos A
is 1
????? 4 tan A = 3, ????
2 sin A + cos A
3 sin A ? 2 cos A
??? ????? ??? :
(A) 20 (B) 10
(C)
15
4
(D)
10
3
50/HIS/2/211?A 6
9. The value of
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
is 1
cos
2
36? + cos
2
54? ? 1
sin
2
63? + sin
2
27?
??? ????? ??? :
(A) 0 (B) 1
(C) 2 (D) ? 1
10. The value of sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A is : 1
sin
4
A + cos
4
A + 2sin
2
A ? cos
2
A ??? ????? ??? :
(A) ? 1 (B) 0
(C) 1 (D) 2
11. In the figure given below, ?ABC is right angled at B. Which of the following is true ? 1
?????? ??? ????? ???????? ???, ?ABC ??? ?????? B ?????????? ??? ? ?????????????? ??? ??? ?????? ????? ??? ?
(A) cosec A =
a
c
(B) cosec A =
c
a
(C) cosec A =
a
b
(D) cosec A =
b
a
12. The width of each of five continuous classes in a frequency distribution is 5 and the
lower limit of the lowest (First) class is 10. The upper limit of the highest (last) class
is 1
?????? ?????????????? ??????? ??? ?????? ?????? ?????? ??? ????????? ??? ?????????? 5 ??? ????? ??????? ??????? (???????) ????? ??? ??????
?????? 10 ??? ? ??????? ?????? (???????) ????? ??? ?????? ?????? ??? :
(A) 15 (B) 20
(C) 30 (D) 35
7 50/HIS/2/211?A
13. Mode of the data, 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 is : 1
?????????? 15, 14, 19, 20, 14, 15, 14, 18, 14, 15, 17, 14, 18 ??? ????????? ??? :
(A) 20 (B) 18
(C) 15 (D) 14
14. Observe the histogram given below. How many students have the height 145 cm and
above ? 1
?????? ???? ???? ??????????? ???? ?????? ??? ??????? ? ???????? ???????????? ??? ???????? 145 ?????? ??? ?????? ?????? ??? ?
(A) 15 (B) 10
(C) 23 (D) 11
OR / ??????
(For Visually Impaired Learners Only)
(??????? ?????? ??????????? ???????????? ??? ????)
For drawing a frequency polygon of a continuous frequency distribution, we plot the
points whose ordinates are the frequencies of the respective classes and abscissa are
respectively :
(A) class mark of the classes (B) lower limits of classes
(C) upper limits of classes (D) upper limits of preceding classes
?????? ?????? ?????????????? ??????? ??? ???? ?????????????? ?????????? ???????? ??? ????, ???? ??? ??????? ?????????? ??????? ???, ????????
??????????? ??????? ?????? ??? ???????????????? ??????? ??? ????? ????? ???????: ??? :
(A) ?????? ??? ????? ?????? (B) ?????? ??? ?????? ????????
(C) ?????? ??? ??????? ???????? (D) ???????? ????? ??? ??????? ????????
50/HIS/2/211?A 8
15. Median of first 10 prime numbers is : 1
??????? ???? ??????? ?????????? ??? ???????? ??? :
(A) 11 (B) 12
(C) 13 (D) 14
16. Rationalise the denominator of the following : 2
?????? ??? ???? ??? ???????????????? ??????? :
11 ? 5
11 + 5
17. Multiply x
2
+
2
3
x +
5
6
by x ?
7
4
. 2
x
2
+
2
3
x +
5
6
???? x ?
7
4
??? ?????? ??????? ?
18. A certain sum of money at simple interest amounts to ` 1,300 in 4 years and to
` 1,525 in 7 years. Find the sum of money. 2
?????? ?????? ?????????? ?????? ???? 4 ?????? ??? ` 1,300 ????? 7 ?????? ??? ` 1,525 ???? ?????? ??? ? ?????? ????? ??????? ?
19. D is any point on the base BC of a ?ABC. If AB > AC, then prove that AB > AD. 2
?ABC ??? ??????? BC ???? ?????? ??????? D ??? ? ????? AB > AC, ???? ????? ??????? ??? AB > AD ?
9 50/HIS/2/211?A
20. PAB is a secant to the circle from a point P outside the circle. PAB passes through the
centre of the circle and PT is a tangent. If PT = 8 cm and OP = 10 cm, find the radius
of the circle. 2
?????? ????? ??? ??????? ?????? ??????? P ??? PAB ????? ??? ??? ??????? ??? ????? ???? ????? ??? ?????? ??????? O ??? ????????
?????? ??? ? PT ????? ??? ?????? ?????? ??? ? ????? PT = 8 ?????? ????? OP = 10 ??????, ???? ????? ??? ??????? ?????
??????? ?
21. If the length of a chord of a circle is 16 cm and the distance of the chord from the
centre is 6 cm, find the radius of the circle. 2
????? ??? ????? ??? ??? ?????? ??? ???????? 16 ?????? ????? ??? ?????? ??? ?????? ??? ?????? 6 ?????? ???, ???? ????? ??? ???????
????? ??????? ?
22. Find the coordinates of the point on x?axis equidistant from the points (2, 5) and
(3, 4). 2
x-??? ???? ??? ??????? ??? ???????????? ????? ??????? ???? ?????????? (2, 5) ????? (3, 4) ??? ??????? ?????? ???? ???? ?
23. Find the perimeter and area of the sector of a circle of radius 9 cm with central angle
35?. 2
9 ?????? ??????? ?????? ????? ??? ??? ??????????? ??? ?????????? ????? ????????? ????? ??????? ???????? ????????? ?????? 35?
??? ?
24. Find the area of a rhombus whose side is of the length 5 m and one of its diagonals is
of length 8 m. 2
??? ????? ??????????????? ??? ????????? ????? ??????? ???????? ?????? ??? ???????? 5 ??????? ????? ??? ???????? ??? ????????
8 ??????? ??? ?
25. Prove that : 2
????? ??????? ??? :
1 ? cos A
1 + cos A
= (cosec A ? cot A)
2
50/HIS/2/211?A 10
26. Three years ago Atul?s age was four times Parul?s age. After 5 years from now, Atul?s
age will be twice Parul?s age. Find their present ages. 4
????? ????? ??????, ?????? ??? ????? ??????? ??? ????? ??? ????? ?????? ??? ? ???? ??? 5 ????? ????????? ?????? ??? ?????
??????? ??? ????? ??? ????????? ??????? ? ?????? ????? ??????? ??? ?????????? ????? ????? ??????? ?
27. Find the 50
th
term and sum of first 50 terms of the A.P 11,16, 21, 26, ?.. 4
?????????? ??????? 11, 16, 21, 26, ............... ??? 50???? ???? ???? ??????? 50 ?????? ??? ?????? ????? ??????? ?
28. A cooler is available for ` 3,400 cash or ` 2,000 as cash down payment followed by
five equal monthly instalments. If the rate of interest charged under the instalment
plan is 30% per annum, find the amount of each instalment. 4
??? ??????? ` 3,400 ?????? ?????????? ?????? ` 2,000 ???????? ?????????? ????? ?????? ????? ?????? ??????? ???????? ????????
??? ???????? ??? ? ????? ??? ?????? ????????? ??? ????????? ???? ?????? ?????? ?????? ??? ???? 30% ???????? ???, ???? ?????????
?????? ??? ???? ?????? ?????? ?????? ??? ??????? ??????? ?
29. Prove that the parallelograms on equal (or same) bases and between the same parallels
are equal in area. 4
????? ??????? ??? ??????? ??????? (??? ??? ??? ???????) ????? ???? ?????????? ????????? ??? ????? ????? ?????????? ???????????
????????? ??? ??????? ??????? ??? ?
30. ABC is a triangle right angled at C. If CD, the length of perpendicular from C on AB
is p, BC = a, AC = b and AB = c, then prove that
1
p
2
=
1
a
2
+
1
b
2
. 4
ABC ??? ???????? ??? ???????? ? C = 90? ? ????? CD, ?????? C ??? AB ???? ?????? ??? ????? ??? ???????? p ??? ?????
BC = a, AC = b ????? AB = c ????, ???? ????? ??????? ???
1
p
2
=
1
a
2
+
1
b
2
11 50/HIS/2/211?A
31. An observer standing 40 m away from a building observes that the angle of elevation
of the top and bottom of a flagstaff, which is surmounted on the building are 60? and
45? respectively. Find the height of the building and the length of the flagstaff.
( 3 = 1.732) 4
??? ???????? ?????? ?????? ??? 40 ??????? ??? ?????? ???? ?????? ???????? ???? ???????? ??? ??? ??? ?????? ???, ???? ??? ?????? ????
????? ????? ???, ?????? ???? ????? ?????????? ??? ???????? ?????? ???????: 60? ???? 45? ??? ? ?????? ??? ???????? ????? ??????
??? ???????? ????? ??????? ? ( 3 = 1.732)
32. If the mean of the following data is 17.45, find the value of P. 4
????? ?????? ?????????? ??? ?????? 17.45 ???, ???? P ??? ????? ????? ??????? ?
X
i
15 16 17 18 19 20
F
i
3 8 10 P 5 4
33. A pair of dice is thrown once. Find the probability of getting 4
(i) same number on both dice
(ii) sum of the numbers appearing on dice as 9.
???? ??????? ???? ??? ????? ??? ????? ?????? ?????? ??? ? ?????? ???? ??????? ??????? ??? ???????????? ????? ??????? :
(i) ???????? ??????? ???? ??? ??? ???????
(ii) ???????? ??????? ???? ??????? ?????????? ??? ?????? 9
34. Check whether the roots of the quadratic equation
x
x + 1
+
x + 1
x
=
34
15
(x ? 0, 1) are
real or not. If yes, find the roots. 6
?????? ??????? ??? ???????? ???????????
x
x + 1
+
x + 1
x
=
34
15
(x ? 0, 1) ??? ????? ??????????? ??? ?????? ????? ?
????? ????, ???? ????? ????? ??????? ?
50/HIS/2/211?A 12
35. Construct a triangle ABC in which AB + BC + CA = 9.5 cm, ? ABC = 60? and
? ACB = 45?. 6
??? ???????? ABC ??? ??????? ??????? ???????? AB + BC + CA = 9.5 ??????, ? ABC = 60? ?????
? ACB = 45?
OR / ??????
(For Visually Impaired Learners Only)
(??????? ?????? ??????????? ???????????? ??? ????)
Write the steps of construction to construct a triangle ABC in which AB = 6 cm,
BC = 4 cm and median CD = 3.5 cm.
??? ????? ???????? ABC ??? ??????? ??? ???? ??????? ??? ???? ??????? ???????? AB = 6 ??????, BC = 4 ?????? ?????
?????????? CD = 3.5 ?????? ?
36. The diameter of a solid hemisphere is 42 cm. Find its volume, curved surface area
and total surface area. 6
??? ?????? ??????????? ??? ?????? 42 ?????? ??? ? ??? ??????????? ??? ????????, ????? ????????? ????????? ???? ????? ?????????
????????? ????? ??????? ?
______________
50/HIS/2/211-A
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This post was last modified on 22 January 2020