List of top Questions asked in CUET (PG)

The general solution of \((D^2+6D+9)y=\frac{e^{-3x}}{x^2}\), where \(D\equiv \frac{d}{dx}\) is
(given that c₁ and c₂ are arbitrary constants)

If \(\overrightarrow F=2z\hat{i}-x\hat{j}+y\hat{k}\) and Vis the region bounded by the surface x=0,y=0,x=2,y=4,z=x²,z=2, then value of \(\iiint\limits_V\overrightarrow FdV\)is

If \(\overrightarrow F=y^2\hat{i}+xy\hat{j}+xz\hat{k}\) and C is the bounding curve of the hemisphere x²+y²+z²=9,z>0, oriented in the positive direction, then value of \(\int\limits_C \overrightarrow F\cdot d\hat{r}\) is

If W is a subspace of R³, where W = {(a, b, c): a+b+c = 0}, then dim W 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 the solution of \(x\frac{dy}{dx}+y=x^3y^6\) is \(\frac{1}{y^\alpha x^\beta}=\frac{\gamma}{2x^2}+C\), then value of \(\alpha+\beta+\gamma\) is

If \(x^2\frac{d^2y}{dx^2}-2x\frac{dy}{dx}-4y=x^4\), then particular integral (P.I) of the given differential equation is

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?

If \(u=cos^{-1}\frac{x+y}{\sqrt{x}+\sqrt{y}}\), then the value of \(x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}\) is

The extreme points of the set \({(x, y); |x|≤2,|y|≤2}\) are

The point (-1, 2, 7, 6) lies in which of the following half spaces corresponding to hyperplane 2x₁+3x₂+4x₃+5x₄ = 6

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

The orthogonal trajectories of the family of curves y = \(ax^3\) is

The sequence is

With the help of suitable transform of the independent variable, the differential equation
\(x\frac{d^2y}{dx^2}+\frac{2dy}{dx}=6x+\frac{1}{x}\) reduces to the form:

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 16 in \((\mathbb{Z}_{24}, +_{24})\) is:

Which one of the following is correct :-

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:

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

The rank of matrix A = \(\begin{bmatrix} 1&3&1&-2&-3\\1&4&3&-1&-4\\2&3&-4&-7&-3\\3&8&1&-7&-8 \end{bmatrix}\)