List of top Questions asked in CUET (PG)

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:
Let \(Z^3 = \bar Z\) where Z is a complex number on the unit circle then Z is a solution of _____:
If \(u = x^2 - y^2\) is real part of an analytic function f(z), then f(z) is:
Match List I with List II
LIST I LIST II
A.\(f(z)=z^3\)I.Not analytic any where
B.\(f(z)=\frac{1}{z}\)II.Analytic at Z = 0 only
C.\(f(z)=\bar z\)III.Analytic everywhere
D.\(f(z)=z\bar z\)IV.Not analytic at Z = 0
Choose the correct answer from the options given below:
If\(ƒ(x + iy) = x^3 − 3.xy^2 + ¡\Psi(x,y) \space where \space i= \sqrt{-1}\) and ƒ (x+iy) is an analytic function, then \(\Psi (x, y)\) is: 
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
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:
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?
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 area bounded by the curves y = x2 and y = 4 - x2 is
The set of all points, where the function \(f(x)=\frac{x}{(1+|x|)}\) is differentiable, is
The value of C in Rolle's theorem where \(-\frac{π}{2}\)<C<\(\frac{π}{2}\) and \(f(x)=cos x\) on \([-\frac{π}{2},\frac{π}{2}]\) is equal to :
Which one of the following is harmonic function
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
LIST I LIST II
A.Series \(\displaystyle\sum_{n=1}^{∞} \frac{1}{n^\frac{3}{2}}\) isI.Monotone and 
convergent both
B.Series \(\displaystyle\sum_{n=1}^{∞} \frac{3^n}{n^2}\) isII.\(e^{-2}\)
C.\(\lim\limits_{n \to \infty} (\frac{n+1}{n+2})^{2n+1}\)III.Divergent to ∞
D.sequence \(x_n=1+\frac{1}{2!}+\frac{1}{3!}+…\frac{1}{n!}\) for n∈NIV.Convergent
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
Match List I with List II
LIST I LIST II
A.A square matrix A is said to be symmetric if I.A=A'
B.A square matrix A is said to be skew symmetric ifII.A= -A'
C.If A is any square matrix thenIII.A+A' is a symmetric matrix
D.If A is any square matrix thenIV.A-A' is a skew symmetric matrix
Choose the correct answer from the options given below: