List of top Mathematics Questions asked in CUET (PG)

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 -

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 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:

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 :

If \(\int \int\limits_{R} \int xyz\ dxdydz=\frac{m}{n}\) where, m,n, are coprime and R:0≤x≤1,1≤ y ≤2, 2 ≤ z ≤3 , then m.n is equal to:

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

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

Match List I with List II

Choose the correct answer from the options given below:

The natural domain of definition of the function f(z) = \(\frac{1}{1-|z|^2}\) is ________.

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

Which one of the following is harmonic function

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

The area bounded by the curves y = x² and y = 4 - x² is

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

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:

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 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:

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:

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

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:

Let f (x) be defined on [0, 3] by \(f(x) =   \begin{cases}     x,\text{if x is a rational number}       \\  3-x\text{, if x is an irrational number}   \end{cases}\) Then f(x) is continuous in the interval at: