Question Paper Name: B PLANNING AND B ARCH 6th Jan 2020 Shift 2 Set 2
Subject Name: B PLANNING AND B ARCH
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Creation Date: 2020-01-06 20:31:58
Duration: 210
Total Marks: 500
Display Marks: Yes
B PLANNING AND B ARCH
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Group Number : 1
Group Id : 40503612
Group Maximum Duration : 0
Group Minimum Duration : 210
Show Attended Group? : No
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Edit Attended Group? : No
Break time: 0
Group Marks: 500
Is this Group for Examiner?: No
Mathematics
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Section Id : 4056
Section Number : 1
Section type : Online
Mandatory or Optional: Mandatory
Number of Questions: 25
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Number of Questions to be attempted: 25
Section Marks: 100
Sub-Section Number: 1
Sub-Section Id: 40503651
Question Shuffling Allowed : Yes
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Question Number : 1 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
If A = {1, 2, 3, 4}, then the number of
functions on the set A, which are not
one - one, is:
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Options:
1. 232
3. 248
4. 256
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Question Number : 1 Question Type : MCQ Option Shuffling: Yes
Correct Marks: 4 Wrong Marks : 1
? A = {1,2,3,4} ?, ? ? A ? ? ?
? ? ? ? ? ?, ? :
Options:
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1. 232
2. 240
3. 248
4. 256
Question Number: 1 Question Type: MCQ Option Shuffling : Yes
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Correct Marks: 4 Wrong Marks : 1
? A = {1, 2, 3, 4} ?, ? ?-? ? ? ?
? A ? ? ? ? ?
Options:
1. 232
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2. 240
4. 256
Question Number: 2 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
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The sum of the values of x satisfying the
equation, vx (vx-4)-3vx-2+6=0
(x=0), is:
Options:
1. 26
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2. 25
3. 10
4. 8
Question Number: 2 Question Type: MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
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? vx (vx-4)-3vx-2+6=0
(x=0) ? ? ? ? x ? ? ? ?
? :
Options:
1. 26
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2. 25
4. 8
Question Number: 2 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
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?vx (vx-4)-3vx-2+6=0 (x=0)
? ? ? x ? ? ? ?
?.
Options:
1. 26
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2. 25
3. 10
4. 8
Question Number: 3 Question Type: MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
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If m be the least value of
|z-3+i4|/2+|z-5-i2|/2, z?C attained at
z = z0, then the ordered pair (z0, m) is equal
to:
Options:
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1. (v13, 10)
2. (v17, 20)
4. (v13, 20)
Question Number: 3 Question Type : MCQ Option Shuffling: Yes
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Correct Marks: 4 Wrong Marks : 1
? z = z0 ? |z-3+i4|/2+|z-5-i2|/2, z?C
? ? ? ? ? m ?, ? ? ?
(z0, m) ? ? :
Options:
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1. (v13, 10)
2. (v17, 20)
3. (v17, 10)
4. (v13, 20)
Question Number: 3 Question Type: MCQ Option Shuffling: Yes
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Correct Marks : 4 Wrong Marks : 1
? z=zo ? |z - 3 + i4|/2+|z - 5 - i2|/2,
ze C ? ? ? m ? ? ?, ? ?
? ( zo, m) = .
Options:
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1. (v13, 10)
2. (v17, 20)
4. (v13, 20)
Question Number : 4 Question Type : MCQ Option Shuffling : Yes
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Correct Marks : 4 Wrong Marks : 1
If for some c < 0, the quadratic equation,
2cx²-2(2c-1)x+3c²+2=0 has two distinct
1 1
real roots, and , then the value of the
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a b
1+ a 1 1
determinant, 1 1+ b 1 is:
1 1 1+ c
Options:
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1. 2
2. 0
4
3. 3
4. 1
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Question Number: 4 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
? ? c < 0 ? ? ? ?
2cx²-2(2c-1)x+3c²+2 = 0 ? ? ? ?
1 1 ?, ? ?
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? ?
a b
1+ a 1 1
1 1+ b 1 ? ? ? :
1 1 1+ c
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Options:
2. 0
4
3. 3
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4. 1
Question Number : 4 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
? ? c < 0 ? ? ?
2cx²-2(2c-1)x + 3c²+2 = 0 ? ? ? ?
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1 1 ?, ? ?
?
a b
1+ a 1 1
1 1+ b 1 ? ? =
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1 1 1+ c
Options:
1. 2
2. 0
4
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3. 3
4. 1
Question Number : 5 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
Let A = [x 2y] ; x, y ? R.
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[-1 y]
1 0
If AAT = [ ] (a ? R), then a + y² is
0 a
equal to :
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Options:
1. 1
2. v2 - 1
3. 2
4. v2
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Question Number : 5 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
x 2y
? A = [ ] ; x, y?R ? ?
-1 y
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1 0
AAT = [ ] (a? R) ?, ? a + y² ? ?
0 a
? :
Options:
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1. 1
2. v2 - 1
3. 2
Question Number: 5 Question Type : MCQ Option Shuffling: Yes
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Correct Marks : 4 Wrong Marks : 1
x 2y
? A = [ ] ; x, y ? R. ?
-1 y
1 0
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AAT = [ ] (a ? R) ?, ?
0 a
a + y² = .
Options:
1. 1
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2. v2 - 1
3. 2
4. v2
Question Number : 6 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
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Let Sn denote the sum of the first n terms of
an A.P., a1, a2, a3, ..., an. If a5 + a9 = 1 and
S9 = 6, then which one of the following is
not true?
Options:
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13
1. S13 =
2
2. a13 = 0
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4. S6 = 19/2
Question Number : 6 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
? S1, ? ? a1, a2, a3, ..., an ? ?
n ? ? ? ? ? ? ? a5+ag = 1 ?
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S9 = 6 ?, ? ? ? ? ? ? ? ? ? ?
Options:
13
1. S13 =
2
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2. a13 = 0
3. a5+ag = 1
4. S6 = 19/2
Question Number: 6 Question Type: MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
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? S ? ? ? ? (A.P.) a1, a7, a3, ..…, an
? ? n ? ? ? ?. ? as + ag = 1
? S, = 6 ?, ? ? ? ? ?
Options:
13
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1. S13 =
2
3. a5+ag = 1
4. S6 = 19/2
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Question Number : 7 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
9 9
If S (r+3) °C, = a(3/2) + ß, then
r=1
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2
a + ß is equal to :
Options:
1. 2
2. 9
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3. 3
4. 6
Question Number : 7 Question Type : MCQ Option Shuffling: Yes
Correct Marks: 4 Wrong Marks : 1
9 9
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? S (r+3) °C, = a(3/2) + ß ?, ?
r=1
2
a + ß ? ? ? :
Options:
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1. 2
3. 3
4. 6
Question Number : 7 Question Type : MCQ Option Shuffling: Yes
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Correct Marks : 4 Wrong Marks : 1
9 9
? S (r+3) °C, = a(3/2) + ß ?, ?
r=1
2
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a+ß= .
Options:
1. 2
2. 9
3. 3
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4. 6
Question Number : 8 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
Let a function, f: (-1, 3) ? R be defined
as f(x) = min{x[x], x[x]-2+2}, where [x]
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denotes the greatest integer=x. Then fis:
Options:
neither continuous nor differentiable
1. at exactly 3 points.
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continuous at two points and not
2. differentiable at 3 points.
neither continuous nor differentiable
3. at exactly two points.
not continuous at only one point and
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4. not differentiable at three points.
Question Number: 8 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
? ? ? f: (-1, 3) ? R,
f(x) = min{x[x], [x[x] - 2 +2} ? ? ?,
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? [x], ? ? = x ? ? ?, ? f :
Options:
? ? ? ? ? ? ? ? ? ? ?
1. ? ?
? ? ? ? ? ? ? ? ?
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2. ? ? ? ?
? ? ? ? ? ? ? ? ? ? ?
3. ? ?
? ? ? ? ? ? ? ? ?
4. ? ? ? ? ?
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Question Number: 8 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
f(x) = min{x[x], [x[x] - 2 + 2} ? ?
?, ? [x] ? ? ? ? =x ?, ? f
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? :
Options:
? 3 ? ? ? ? ? ?
1. ? ? ?.
? ? ? ? ? ? 3 ?
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2. ? ? ?.
? ? ? ? ? ? ? ?
3. ? ? ?.
? ? ? ? ? ? ? ?
4. ? ? ? ?.
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Question Number : 9 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
lim {loge (ex(x-1)_ex(1-x))
x?1
loge (4x(x-1))} is equal to:
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Options:
1. 1
2. -loge 2
3. -2loge 2
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Question Number: 9 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
lim {loge (ex(x-1)_ex(1-x))
x?1
loge (4x(x-1))} ? ? :
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Options:
1. 1
2. -loge 2
3. -2loge 2
4. 1-loge 2
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Question Number : 9 Question Type : MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
lim {loge (ex(x-1)_ex(1-x))
x?1
loge (4x(x-1))} = .
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Options:
1. 1
2. -loge 2
3. -2loge 2
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Question Number : 10 Question Type : MCQ Option Shuffling : Yes
Correct Marks: 4 Wrong Marks : 1
The function f(x) = ex+1 (4x²-16x+11)
is:
Options:
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5 1
1. increasing in (-8,-) U ( , 8)
2 2
2. increasing in (-8, -2) U (2, 8)
5 1
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3. decreasing in (-8,-) U ( , 8)
2 2
1
4. decreasing in (-8, ) U ( , 8)
2 2
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Question Number : 10 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
? f(x) = ex+1 (4x²-16x+11) :
Options:
5 1
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1. (-8,-) U ( , 8) ? ? ?
2 2
2. (-8,-2) U (2, 8) ? ? ?
5 1
3. (-8,-) U ( , 8) ? ? ?
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2 2
4. (-8, 1/2) U (5/2, 8) ? ? ?
Question Number : 10 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
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? f(x) = ex+1 (4x²-16x+11) ? :
Options:
1 5
1. (-8, -) U ( , 8) ? ? ?.
2 2
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2. (-8, -2) U (2, 8) ? ? ?.
1 5
3. (-8, -) U ( , 8) ? ? ?.
2 2
1 5
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4. (-8, ) U ( , 8) ? ? ?.
2 2
Question Number: 11 Question Type: MCQ Option Shuffling: Yes
Correct Marks : 4 Wrong Marks : 1
The area (in sq. units) of the region
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1 p
{(x, y): = y = sinx, 0 = x = } is :
2
Options:
p
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1. v3-
3
p
2. 3-
3
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4. v3-p/6
Question Number : 11 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
? {(x, y): 1/2 = y = sin x, 0 = x = p}
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? ? (? ? ?) ? :
Options:
p
1. v3-
3
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p
2. 3-
3
2p
3. 3-
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3
p
4. v3-
6
Question Number : 11 Question Type : MCQ Option Shuffling : Yes
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Correct Marks : 4 Wrong Marks : 1
? {(x, y) : 1/2 = y = sinx, 0 = x = p
? ? (?. ?) ?.
Options:
p
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1. v3-
3
Question Number : 12 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
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If x = x(y) is the solution of the differential
equation, ydx(x+2y²) dy = 0, with
x( - p) = p², then x is equal to :
Options:
1. 2y²-p²
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2. -2y²+3p?
3. -y²-2?
4. 2y²+ p?
Question Number : 12 Question Type : MCQ Option Shuffling : Yes
Correct Marks: 4 Wrong Marks : 1
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? x = x(y), ? ?
ydx(x+2y²)dy=0, x()=², ? ? ?,
? x ? ? :
Options:
1. 2y²-p²
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3. -?²-2?
4. 2y²+ ?
Question Number : 12 Question Type : MCQ Option Shuffling : Yes
Correct Marks : 4 Wrong Marks : 1
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? x=x (y) ? ? ? ?
ydx(x+2y²) dy = 0 ? ? ?, ?
x(-p) = p², ù x= .
Options:
1. 2y²-p²
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2. -2y²+3p?
3. -?²-2?
4. 2y²+ ?
Question Number : 13 Question Type : MCQ Option Shuffling : Yes
Correct Marks: 4 Wrong Marks : 1
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A ray of light is projected from the origin
at angle of 60° with the positive direction
of x-axis towards the line, y = 2, which gets
reflected from the point (a, 2). Then the
distance of the reflected ray of light from
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the point (2, 2) is:
Options:
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