List of top Mathematics Questions asked in CUET (PG)

Double integral \(\int\limits_0^2\int\limits_0^{\sqrt{2x-x^2}}\frac{xdydx}{\sqrt{x^2+y^2}}\) equals:

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

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: 

If \(\int\int_R(x + y) dydx = A\), where R is the region bounded by x = 0, x = 2, y = x, y = x+2, then \(\frac{A}{12}\) is equal to:

The volume generated by the revolution of the cardioid \(r = a(1-\cosθ)\) about its axis is:

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

Match List I with List II

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 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:

Which one of the following is harmonic function

If \(u = x^2 - y^2\) is real part of an analytic function f(z), then f(z) is:

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

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

Given below are two statements
Statement I: Draw back in Lagrange's method of undetermined multipliers is that nature of stationary point cannot be determined
Statement II: \(\displaystyle\sum_{n=1}^{∞} (-1)^{n-1}\frac{1}{n\sqrt n}\)convergent
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 \(\lim\limits_{n \to \infty} \frac{1}{n} [1+2^{\frac{1}{2}}+3^{\frac{1}{3}}+...n^{\frac{1}{n}}]\) 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 :

Match List I with List II

Choose the correct answer from the options given below:

If \(u=sin^{-1}[\frac{x+y}{\sqrt{x}+\sqrt{y}}]\) and \(x^2u_{xx}+2xyu_{xy}+y^2u_{yy}=-\frac{sinucos2u}{m^2cos^3u}\) then, m is equal to

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:

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

The function

is continuous at (0,0), then k is equal to:

Let \(F: R^4 → R^3\) be the linear mapping defined by:
F(x,y,z,t)=(x-y+z+t, 2x-2y+3z+4t, 3x-3y+4z+5t), then nullity (F) equals