List of top Mathematics Questions asked in CUET (PG)

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

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

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

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

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?

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 :

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 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

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

Given below are two statements
Statement I: If f(z) = u + iv is an analytic function, then u and v are both harmonic function.
Statement II: If f (z) is analytic within and on a closed curve C, and if a is any point within C, then \(f(a)=\frac{1}{2πi}\int_c\frac{f(z)}{z-a}dz\)
In the light of the above statements, choose the most appropriate answer from the options given below

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

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:

Given below are two statements
Statement I: In cylindrical co-ordinates, \(Volume = \int \int\limits_{V} \int rdrdødz \)
Statement II: In spherical polar Co-ordinates, \(Volume = \int \int\limits_{V} \int r^2\ \cos\theta\ drd\theta d\phi\)
In the light of the above statements, choose the correct answer from the options given below :

Match List I with List II

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:

If \(\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}\) and \(r=\sqrt{x^2+y^2+z^2}\), then grad \((\frac{1}{r})\) is equal to :

The integral \(\int\limits_0^1\int\limits_0^x(x^2+ y^2) dy dx\) is:

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