List of top Mathematics Questions asked in CUET (PG)

Which one of the following statements is wrong.

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

If \(\vec{a},\vec{b},\vec{c}\) are non-coplanar unit vectors such that \(\vec{a}\times(\vec{b}\times \vec{c})=\frac{(\vec{b}+\vec{c})}{\sqrt2}\) then the angle between a and b is

if \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) are three non-coplanar vectors, then \((\vec{a}+\vec{b}+\vec{c}) [(\vec{a}+\vec{b})\times(\vec{a}+\vec{c})]\) equal to

The variance of a series of numbers 2, 3, 11 and x is 12.25. Find the value of x.

If A, G, H be respectively, the A.M., G.M., and H.M. of three positive numbers a, b, c; then the equation whose roots are these numbers is given by

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

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 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 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?

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

Let f(z) = u + iv be an analytic function, where u = x³-3xy² +3x² -3y², then the imaginary part v of f(z) 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

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

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

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

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

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 volume generated by the revolution of the cardioid \(r = a(1-\cosθ)\) about its axis is:

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

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

The orthogonal trajectory of the cardioid r = a(1+cos θ), a being the parameter is:

Given below are two statements:
Statement I : If x²y" - 2xy' - 4y = x⁴, then \(C.F.=\frac{C_1}{x}+C_2x^4\)
Statement II: If (D²-8D+15) y = 0, then auxiliary equation has equal roots.
In the light of the above statements, choose the correct answer from the options given below

If \(\vec{A} =(3x^2+6y)\hat{i}—14yz\hat{j} +20xz^2\hat{k}\), then the line integral \(\int\limits_{C} \vec{A}.d\bar{r}\) from (0.0, 0) to (1, 1.1), along the curve C ;x=t, y=t². z=t³ is: