List of top Mathematics Questions asked in CUET (PG)

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 :-

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

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

Which of the following is incorrect?

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

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

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

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

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

Which one of the following is wrong?

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

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

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

Given below are two statements
Statement I: Draw back in Lagrange's method of undetermined multipliers is that nature of stationary point cannot be determined
Statement II: \(\displaystyle\sum_{n=1}^{∞} (-1)^{n-1}\frac{1}{n\sqrt n}\)convergent
In the light of the above statements, choose the correct answer from the options given below

If \(\int\int_R(x + y) dydx = A\), where R is the region bounded by x = 0, x = 2, y = x, y = x+2, then \(\frac{A}{12}\) is equal to:

If\(\int\limits_0^{1+i}(x^2 -iy) dz = α + iβ\) along the path \(y = x\), then value of \(α– β\) is:

Evaluate the integral\(\oint\limits_C\frac{dz}{(z^2+4)^2},C:|z-i|=2\)

The surface area of the cylinder \(x^2+z^2 = 4\) inside the cylinder \(x^2 + y^2 = 4\) is:

A scalar potential \(\Psi\) has the gradient defined as  \(\nabla\Psi=yz\hat{i}+xz\hat{j}+xy\hat{k}\). The value of the integral \(\int_c\nabla\Psi.d\overrightarrow{r}\) on the curve \(\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}\), where curve C: x=t, y = t², z = 3t² (1 ≤ t ≤ 3) is:

Integrating factors of the equation y (2xy + e^x) dx - e^x dy = 0 is :