List of top Questions asked in CUET (PG)

In a group G, if a⁵ = e, aba^-1 = b² for a, b ∈ G then o(b) is equal to:

Which one of the following statements is wrong.

Which one of the following is wrong?

If W is a subspace of R³, where W = {(a, b, c): a+b+c = 0}, then dim W is equal to

Which of the following is incorrect?

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

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

Let \(F: R^4 → R^3\) 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

In the neighborhood of z = 1, the function f(z) has a power series expansion of the form f(z) = 1+(1-z)+(1-z)² + .... then f(z) is

The function f(z) defined by \(f(z)= \begin{cases}     \frac{Re(z)}{z}       & z\neq0\\     0  & z=0   \end{cases}\)then which one of the following is true?

Which one of the following is not correct?

A rectangular box open at the top is to have volume of 32 cubic feets. The minimum outer surface area of the box is

If 2.5x=0.05 y, then find the value of \((\frac{y-x}{y+x}).\)

The Value of \(lim_{n\rightarrow \infty }\bigg[\frac{2}{1}\bigg(\frac{3}{2}\bigg)^2\bigg(\frac{4}{3}\bigg)^3.....\bigg(\frac{n+1}{n}\bigg)^n\bigg]^{\frac{1}{n}}is\)

Let f: R→R such that f(1) =3 and f'(1) = 6. Then \(\lim\limits_{x\rightarrow0}\left(\frac{f(1+x)}{f(1)}\right)^{1/x}\)equals

Let f : Z→ \(Z_2\), be a homomorphism of groups defined by
\(f(a) =   \begin{cases}    0,  & \quad \text{if } a \text{ is even}\\     1,  & \quad \text{if } a \text{ is odd}   \end{cases}\)

then Kerf is : 

The order of the permutation\(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\   2 & 4 & 6 & 5 & 1 & 3 \end{pmatrix}\)is

The order of the given permutation \(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6& 7&8&9 \\2 &4& 6 &1 &7&3& 8&9 &5  \end{pmatrix}\) is:

The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?

If the matrices \(\left(\begin{matrix} 1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   -1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   i & 0 \\   0 & 0  \end{matrix}\right) and \left(\begin{matrix}   -i & 0 \\   0 & 0  \end{matrix}\right)\) form a group with respect to matrix multiplication, then which one of the following statements about the groups, thus formed is correct?

Consider the linear mapping F: R² →R² defined by F(x, y) = (3x+4y, 2x-5y) and following bases of R²: E= {e₁, e₂} = {(1, 0), (0, 1)} and S = {u₁, u₂} = {(1, 2), (2, 3)}. Then the matrix A representing F relative to the basis E is:

If λ₁,λ₂,λ₃ are the given values of the matrix \(\begin{bmatrix}   -2 & 2 & -3 \\   2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}\), then λ₁²+λ₂²+λ₃² is equal to

The dimension of the general solution space W of the homogeneous system
x₁+2x₂-3x₃+2x₄-4x₅=0
2x₁+4x₂-5x₃+x₄-6x₅ = 0
5x₁+10x₂-13x₃+4x₄-16x₅= 0

If A=\(\begin{bmatrix} 1 & 2 & 0 & -1\\   2 & 6 & -3 & -3\\  3 & 10 & -6 & -5 \end{bmatrix}\), then which one of the following is true?

If f: R²→R² is a function defined as \(f(x,y) =   \begin{cases}   \frac{x}{\sqrt{x^2+y^2}},      & x\neq0,y\neq0\\     2,  & x=0,y=0   \end{cases}\)then, which of the following is correct?