List of top Mathematics Questions asked in CUET (PG)

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

The area of region bounded by the curve y²=x, the y-axis and between y = 2 and y = 4 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

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Equation 5x-7y+z=11, 6x-8y-z=15 and 3x+2y-6z=7, then the system is consistent and has infinitely many solutions.
Reasons (R): If D=0 then the 3 linear equations is consistent and has infinitely many solutions if D₁ = D₂ = D₃=0.
In the light of the above Statements, choose the correct answer from the options given below :

Which of the following is incorrect?

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

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

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:

The infinite series $\displaystyle\sum_{n=1}^{∞} (1+\frac{1}{n})^{-n^2}$ is:

The infinite series $\displaystyle\sum_{n=1}^{∞} \frac{3^n}{4^{n+2}}$ is:

Match List I with List II

Choose the correct answer from the options given below:

The value of $\lim\limits_{n \to \infty} \frac{1}{n} [1+2^{\frac{1}{2}}+3^{\frac{1}{3}}+...n^{\frac{1}{n}}]$ is

If $f(x,y)=x^2+y^2+6x+12$, then minimum value of f is:

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

Which one of the following is harmonic function

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

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

The solution of the Linear Programming Problem
maximize Z = 107x + y
subject to constraints x + y ≤2
-3x + y ≥ 3
x, y ≥ 0 is

Let A =$\begin{bmatrix}2&3\\4&-1\end{bmatrix}$ then the matrix B that represents the linear operator A relative to the basis
S = {$u_1,u_2$}=${[1, 3]^T, [2, 5]^T}$, is:

Which one of the following is a cyclic group?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The given vector $\vec{F}=(y^2-z^2+3yz-2x)\hat{i} +(3xz+2xy)\hat{j}+(3xy-2xz+2z)\hat{k}$ is solenoidal
Reason R: A vector $\vec{F}$ is said to be solenoidal if div $\vec{F}$ = 0
In the light of the above statements, choose the correct answer from the options given below :

If the curl of vector $\vec{A} = (2xy-3yz)\hat{i} +(x^2+axz −4z^2)\hat{j}-(3xy+byz)\hat{k}$ is zero, then a + b is equal to :

For what value(s) of k the set of vectors {(1, k, 5), (1, -3, 2), (2, -1, 1)} form a basis in R³ ?

The work done by the force $\overrightarrow F = (x^2-y^2)\hat{i} + (x+y)\hat{j}$ in moving a particle along the closed path C containing the curves x + y = 0, x²+ y² = 16 and y = x in the first and fourth quadrant is