CUET-PG SERIES Mathematics
Vector Space
15 previous year questions.
Volume: 15 Ques
Yield: Medium
High-Yield Trend
15
2023 Chapter Questions 15 MCQs
01
PYQ 2023
medium
mathematics ID: cuet-pg-
Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x7} where x7 denotes multiplication moduls 7?
1
3 and 4
2
3 and 5
3
4 and 5
4
3,4 and 5
02
PYQ 2023
easy
mathematics ID: cuet-pg-
In a group G, if a5 = e, aba-1 = b2 for a, b ∈ G then o(b) is equal to:
1
30
2
32
3
31
4
25
03
PYQ 2023
medium
mathematics ID: cuet-pg-
Which one of the following statements is wrong.
1
The centre of a group G is a subgroup of G.
2
The union of two subgroups is always a subgroup.
3
If G is a finite group and H is a subgroup of G then o(H) divides o(G).
4
HK is a subgroup of G iff HK = KH.
04
PYQ 2023
medium
mathematics ID: cuet-pg-
Which one of the following is wrong?
1
The set Z of integers forms a group with respect to the usual addition of integers.
2
Let G be the set {1, -1}. Then it forms a group under multiplication
3
Set of all non-zero complex numbers forms a group under multiplication.
4
The set Q of rational numbers forms a group with respect to the usual multiplication of rational numbers.
05
PYQ 2023
medium
mathematics ID: cuet-pg-
If W is a subspace of R3, where W = {(a, b, c): a+b+c = 0}, then dim W is equal to
1
2
2
3
3
1
4
0
06
PYQ 2023
medium
mathematics ID: cuet-pg-
Which of the following is incorrect?
1
Z is a subring of the ring of rational numbers
2
Q is a subring of the ring of real numbers
3
C is a subring of the ring of real numbers
4
Set E of even integers is a subring of the ring of integers
07
PYQ 2023
medium
mathematics ID: cuet-pg-
Given below are two statements
Statement I: Every cyclic group is abelian
Statement II: (Z,+) is a cyclic group with 1 and -1 as the only generators
In the light of the above statements, choose the most appropriate answer from the options given below
Statement I: Every cyclic group is abelian
Statement II: (Z,+) is a cyclic group with 1 and -1 as the only generators
In the light of the above statements, choose the most appropriate answer from the options given below
1
Both Statement I and Statement II are correct
2
Both Statement I and Statement II are incorrect
3
Statement I is correct but statement II is incorrect
4
Statement I is incorrect but statement II is correct
08
PYQ 2023
medium
mathematics ID: cuet-pg-
Given below are two statements
Statement I: Let G a finite group and H a subgroup of G. Then, the order of H is a divisor of the order of G. That is, |H| divides |G|
Statement II: Let a be an element in a finite group G. Then, O(a) divides |G|
In the light of the above statements, choose the most appropriate answer from the options given below
Statement I: Let G a finite group and H a subgroup of G. Then, the order of H is a divisor of the order of G. That is, |H| divides |G|
Statement II: Let a be an element in a finite group G. Then, O(a) divides |G|
In the light of the above statements, choose the most appropriate answer from the options given below
1
Both Statement I and Statement II are true
2
Both Statement I and Statement II are false
3
Statement I is true but statement II is false
4
Statement I is false but statement II is true
09
PYQ 2023
medium
mathematics ID: cuet-pg-
Let be the linear mapping defined by:
F(x,y,z,t)=(x-y+z+t, 2x-2y+3z+4t, 3x-3y+4z+5t), then nullity (F) equals
F(x,y,z,t)=(x-y+z+t, 2x-2y+3z+4t, 3x-3y+4z+5t), then nullity (F) equals
1
0
2
1
3
2
4
3
10
PYQ 2023
medium
mathematics ID: cuet-pg-
If and are the 3-dimensional subspaces of the 4-dimensional vector space, then the smallest possible dimension of is
1
One
2
Two
3
Three
4
Four
11
PYQ 2023
medium
mathematics ID: cuet-pg-
A. Suppose U and W are finite-dimensional subspace of a vector space V, then
B. let ,W = {(a,b,c:a≥0)}, then W is a subspace of V
C. If u =(1,2),v=(3,-5), then u and v are linearly independent
D. (1,1,1) and (1,0,1) form a basis of
choose the most appropriate answer from the options given below
B. let ,W = {(a,b,c:a≥0)}, then W is a subspace of V
C. If u =(1,2),v=(3,-5), then u and v are linearly independent
D. (1,1,1) and (1,0,1) form a basis of
choose the most appropriate answer from the options given below
1
A, C Only
2
A, D Only
3
B, C Only
4
B, D Only
12
PYQ 2023
medium
mathematics ID: cuet-pg-
If and , then grad is equal to :
1
2
3
4
13
PYQ 2023
medium
mathematics ID: cuet-pg-
If is irrotational, where a, b and c are constant, then a2 + b2 + c2 is equal to :
1
5
2
7
3
19
4
21
14
PYQ 2023
medium
mathematics ID: cuet-pg-
The directional derivative of Φ(x,y,z) = x2yz+4xz2 at (1, -2, 1) in the direction of is
1
2
3
4
15
PYQ 2023
medium
mathematics ID: cuet-pg-
Let U and W are distinct 4-dimensional subspaces of a vector space V of dimension 6. Consider the following statements:
A. The dimension of U ∩ W is either 2 or 3.
B. The dimension of U + W is either 5 or 6.
C. The dimension of U ∩ W is always greater than 4.
D. The dimension of U + W is always greater than 4.
Choose the correct answer from the options given below:
A. The dimension of U ∩ W is either 2 or 3.
B. The dimension of U + W is either 5 or 6.
C. The dimension of U ∩ W is always greater than 4.
D. The dimension of U + W is always greater than 4.
Choose the correct answer from the options given below:
1
A. B and D only
2
A, B and C only
3
B, C and D only
4
C and D only
About Vector Space - CUET-PG
Vector Space is a vital chapter for CUET-PG aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
Frequently Asked Questions
Why focus on Vector Space PYQs?
Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.
How to best use this analysis?
Review the topic breakdown to see which sub-topics within Vector Space carry the most weight. Then, tackle the questions iteratively to solidify your understanding.