List of top Mathematics Questions asked in CUET (PG)

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

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

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

The maximum value of Z = x + 2y subjected to the constraints x+2y≥100, 2x-y≤0,2x + y≤ 200,x≥ 0, y≥0, is:

If there is no feasible region in LPP, then the problem has:

From the given system of constraints
A. 3x+5y≤90
B. x + 2y≤30
C. 2x + y≤30
D. x≥0, y≥0
The redundant constraint is :

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

The region represented by the inequation system x,y≥o, y ≥5,x+y≥3 is

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

A. f(z) is analytic then \(U_x=V_y,U_y=-V_x\)
B. Polar C-R equation is \(U_r=\frac{1}{r} V_o,U_o=-rV_r\)
C. Two curves are said to be orthogonal to each other, when they intersect at acute angle at each of their points of intersection
D. \(\int_c \frac{dz}{z-1}=2πi\) where \(C:|z-1|=\frac{1}{2}\)
choose the correct answer from the options given below:

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

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?

Let \(Z^3 = \bar Z\) where Z is a complex number on the unit circle then Z is a solution of _____:

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

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

If a right circular cylinder a height 14cm is increased in a sphere of radius 8cm then volume of the cylinder (in cm³)- (use π = \(\frac{22}{7}\)).

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 -