List of top Mathematics Questions asked in CUET (PG)

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 average of 5 consecutive odd positive integers is 9. Then sum of smallest and greatest number is

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

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:

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

Which one of the following is 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

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

A single 6-sided dice is rolled, then the probability of getting an odd number is

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

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

Which of the following is incorrect?

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

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?

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

The minimum distance of the point (3, 4, 12) from the sphere x² + y² + z² = 1 is

Which one of the following statements is wrong.

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

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

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