List of top Questions asked in CUET (PG)

The general solution of differential equation \(\frac{d^2y}{dx^2}+9y=sin^3x\) is
(given that c₁ and c₂ are arbitrary constants)

The solution of (x² -√2y) dx + (y² - √2x) dy = 0 is given by

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)

The sequence is

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

Which one of the following is correct :-

If f(x) satisfies the conditions of Rolle's theorem in [1, 2] and f(x) is continuous in [1, 2], then \(\int_1^2f'(x)dx\) is equal to

The volume generated by the revolution of the cardiod r = a(1-cosθ) about x-axis is

The value of \(\int\limits_C \frac{\sin\pi z^2+\cos\pi z^2}{(z-1)(z-2)}dz\), where C is the circle |z|=3 is

The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4 × 4 symmetric positive definite matrix is

Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x₇} where x₇ denotes multiplication moduls 7?

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