List of top Mathematics Questions asked in CUET (PG)

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
Statement I: If \(x=\frac{1}{3}(2u + v)\) and \(y =\frac{1}{3}(u − v)\), then \(dxdy=\frac{-1}{3}\ dudv\)
Statement II: Area in Polar Co-ordinater \(\int\limits^{\theta_1}_{\theta_1} \int\limits^{r_2}_{r_1} rd\theta dr\)
In the light of the above statements, choose the correct answer from the options given below:

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 :

The value of \(∫_c \frac{3z^2+7z+1}{z+1} dz\), where C is the circle |z|=\(\frac{1}{2}\) is:

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

If \(\vec{F} = (x+2y+az)\hat{i} + (bx −3y-z)\hat{j}+(4x+cy+2z)\hat{k}\) is irrotational, where a, b and c are constant, then a² + b² + c² is equal to :

The volume of the cylindrical column standing on the area common to the parabolas \(y^2 = x\), \(x^2 = y\) and cut off by the surface \(z = 12+y-x^2\) is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The integral \(\int\limits_c\frac{z^2+6z+2}{z-2} dz = 0\), where C is the circle |z|=3
Reason R: If there is no pole inside and on the contour C, then the value of the integral of the function along C is zero
In the light of the above statements, choose the correct answer from the options given below

Let U and W are distinct 4-dimensional subspaces of a vector space V of dimension 6. Consider the following statements:
A. The dimension of U ∩ W is either 2 or 3.
B. The dimension of U + W is either 5 or 6.
C. The dimension of U ∩ W is always greater than 4.
D. The dimension of U + W is always greater than 4.
Choose the correct answer from the options given below:

The directional derivative of Φ(x,y,z) = x²yz+4xz² at (1, -2, 1) in the direction of \(2\hat{i}-\hat{j}-2\hat{k}\) is

The value of the integral \(∮_c \frac{dz}{3-\bar z}, C:|z|=1\) is

The value of double integal \(\int\limits_0^∞\int\limits_0^xe^{-xy} ydydx\) is equal to:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The integral \(\int \int \int (x^2+y^2+z^2)dxdydz\) taken over the volume enclosed by the sphere x²+ y²+z² = 1 is \(\frac{4\pi}{5}\)
Reason R: \(\int^{1}_{0}\int^{1}_{0}x\ dxdy=\frac{1}{2}\)
In the light of the above statements, choose the most appropriate answer from the options given below:

If particular Integral (P.I) of \((D^2-4D+4)y=x^3e^{2x}\) is \(e^{mx}\frac{x^n}{20}\), then m²+n² is equal to:

Given below are two statements
Statement I: If A = \(\begin{bmatrix}2 &2\\ 1& 3\end{bmatrix}\) then sum of eigenvalues of A is 3.
Statement II: If \(λ\) is an eigenvalue of \(T\), where \(T\) is invertible linear operator, then \(λ^{-1}\) is an eigenvalue of \(T^{-1}\)
In the light of the above statements, choose the correct answer from the options given below

Consider the following linear equations:-
3x+7y+z=0
5x+9y-z=0
9x+13y+kz=0
For what values of k the above system of equations has an infinite number of solutions -

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

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:

The solution of the differential equation \(\frac{dy}{dx}+y=3e^xy^3\) is :

The general solution of the differential equation y"+y = 6sin x is:

The general solution of the differential equation \(2x^2 \frac{d^2y}{dx^2}=x\frac{dy}{dx}-6y=0\) is :

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