Download JNU 2020 Mathematics (Matm) Registered Photo Exam Day Photo Previous Question Paper || Jawaharlal Nehru University (JNU) Last 10 Years Question Paper
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Roll No:
Application No:
Registered Photo
Exam Day Photo
Name:
Exam Date: 07-Oct-2020
Exam Time: 09:00-12:00
Examination: 1. Course Code - M.A./M.Sc./M.C.A.
2. Field of Study - Mathematics (MATM)
SECTION 1 - PART I
Question No.1 (Question Id - 4)
Which of the following is a compact subset of ?
(A)
(Correct Answer)
(B)
(C)
(D)
Question No.2 (Question Id - 10)
Let G be an abelian group of order 16. Which of the following is true ?
(A)
There exists g G such that order of g is 8.
(B)
If there exists a subgroup H of G of order 8, then there exists g G with order 8.
(C)
If there exists g G with order 8, then G is cyclic.
(D)
There is a one-to-one group homomorphism : G Sm for some m 1. (Correct
Answer)
Question No.3 (Question Id - 8)
Consider the system of linear equations :
3x + y - z =
- x + 2y + 5z =
4x + z = 7
For which and does this system have a unique solution ?
(A)
For no , there is a unique solution.
(B)
is unique but can be arbitrary.
(C)
and are both unique.
(D)
For all , there is a unique solution. (Correct Answer)
Question No.4 (Question Id - 6)
(A)
(B)
(Correct Answer)
(C)
(D)
Question No.5 (Question Id - 1)
Let X, Y and Z be finite sets and let f : X Y and g : Y Z be maps.
Which of the following assertions is always true ?
(A)
If gof is a bijection, then both g and f are bijections.
(B)
If g is one to one, then gof is also one to one.
(C)
If f is onto, then gof is also onto.
(D)
If gof is onto, then |Z| |Y|, where |A| denotes the number of elements in any finite set
A.
(Correct Answer)
Question No.6 (Question Id - 9)
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Consider the following subsets of 3 :
X = {(x, y, z) 3 : x 0, y 0, z 0}
Y = {(x, y, z) 3 : 3x + y = 2, y + z = 0}
Z = {(x, y, z) 3 : x2 + 2xy + y2 = 0}
W = {(x, y, z) 3 : x + y + z = 0, 4x + 3y - z = 0}
Which of the above are vector subspaces of 3 ?
(A)
X, Y, Z and W
(B)
Only W
(C)
Only Z and W (Correct Answer)
(D)
Only X and W
Question No.7 (Question Id - 7)
(A)
(Correct Answer)
(B)
(C)
(D)
Question No.8 (Question Id - 3)
(A)
lim sup an = 1 and lim inf an = -1. (Correct Answer)
(B)
lim sup an = 1 and lim inf an = 1.
(C)
lim sup an = -1 and lim inf an = -1.
(D)
lim sup an = - 1 and lim inf an = 1.
Question No.9 (Question Id - 2)
(A)
(B)
(C)
(Correct
Answer)
(D)
Question No.10 (Question Id - 5)
(A)
A, B and C only
(B)
A, B and D only (Correct Answer)
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(C)
A and C only
(D)
B and C only
SECTION 2 - PART II
Question No.1 (Question Id - 12)
(A)
A only
(B)
A and B only (Correct Answer)
(C)
B and C only
(D)
D only
Question No.2 (Question Id - 23)
(A)
N is not a subgroup of G.
(B)
N is a subgroup of G, but N is not normal.
(C)
N is a subgroup of G and the number of cosets of N in G is finite.
(D)
N is a subgroup of G and there are infinitely many cosets of N in G. (Correct Answer)
Question No.3 (Question Id - 22)
Let G be a group in which every element other than identity has order 2. Then, which of the following
statements is necessarily true ?
(A)
G must be finite and abelian.
(B)
G can be infinite, but G must be abelian. (Correct Answer)
(C)
G is not necessarily abelian, but it must be finite.
(D)
G may be non-abelian as well as infinite.
Question No.4 (Question Id - 18)
(A)
(Correct Answer)
(B)
(C)
(D)
Question No.5 (Question Id - 21)
Let A M4x3(), B M3x4() and C M4x5(). Consider the following assertions :
A. The matrix ABC cannot have rank equal to 4.
B. AB can have rank 3 but BC cannot have rank 4.
C. ABC and BA can have ranks at most 3.
D. Rank of AB must be less than or equal to rank of BC.
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Which of the above is/are correct statements ?
(A)
Only A
(B)
Only D
(C)
A, B and C only (Correct Answer)
(D)
B, C and D only
Question No.6 (Question Id - 16)
(A)
- log2
(B)
- 2 log2
(C)
1 - 2 log2 (Correct Answer)
(D)
1 - 3 log2
Question No.7 (Question Id - 17)
(A)
A only
(B)
A and C only (Correct Answer)
(C)
A, B and C only
(D)
A, B and D only
Question No.8 (Question Id - 13)
(A)
A and C only
(B)
B and D only (Correct Answer)
(C)
D only
(D)
B only
Question No.9 (Question Id - 19)
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(A)
(B)
3R5
(C)
(D)
(Correct Answer)
Question No.10 (Question Id - 14)
(A)
B and D only (Correct Answer)
(B)
B, C and D only
(C)
A, C and D only
(D)
A and D only
Question No.11 (Question Id - 11)
Let X = {(x, y) 2 : x2 + y2 = 1}, Y = {(x, y) 2 : x = y} and
Z = {(x, y) 2 : y = - x}. Consider the following assertions :
A. X U Y U Z is an equivalence relation on .
B. X U Y is a reflexive relation on but not symmetric.
C. X U Y is an equivalence relation on .
D. Y U Z is an equivalence relation on .
Which of the above assertions are correct ?
(A)
A and B only
(B)
A, B and D only
(C)
A and D only (Correct Answer)
(D)
A, C and D only
Question No.12 (Question Id - 20)
Let V be a finite dimensional vector space over with dim V 2. Fix a non-zero vector v0 V.
Consider the following assertions :
A. There is a unique basis of V containing v0.
B. There exist infinitely many bases of V containing v0.
C. There is a unique injective linear map T : V V such that T(v0) = v0.
D. There exist infinitely many linear isomorphisms T : V V such that
T(v0) = v0.
Which of the above assertions is/are correct ?
(A)
A only
(B)
C only
(C)
A and C only
(D)
B and D only (Correct Answer)
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Question No.13 (Question Id - 15)
(A)
one
(B)
two (Correct Answer)
(C)
more than 2 but finitely many
(D)
infinitely many
Question No.14 (Question Id - 24)
For which of the following n does n! have 2020 trailing zeros at the end ?
(A)
n = 8097 (Correct Answer)
(B)
n = 8085
(C)
n = 8080
(D)
n = 10100
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This post was last modified on 21 January 2021