List of top Mathematics Questions asked in CUET (PG)

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

The volume of the cylindrical column standing on the area common to the parabolas \(y^2 = x\), \(x^2 = y\) and cut off by the surface \(z = 12+y-x^2\) is:

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

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

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

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

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:

A. Suppose U and W are finite-dimensional subspace of a vector space V, then \(dim (U+W) = dim U + dim W – dim (U∩W)\)
B. let \(V=R^3\),W = {(a,b,c:a≥0)}, then W is a subspace of V
C. If u =(1,2),v=(3,-5), then u and v are linearly independent
D. (1,1,1) and (1,0,1) form a basis of \(R^3\)
choose the most appropriate answer from the options given below

The general solution of the differential equation y"+y = 6sin x is:

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 -

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:

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

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

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 :

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

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

Given below are two statements
Statement I: If \(x=\frac{1}{3}(2u + v)\) and \(y =\frac{1}{3}(u − v)\), then \(dxdy=\frac{-1}{3}\ dudv\)
Statement II: Area in Polar Co-ordinater \(\int\limits^{\theta_1}_{\theta_1} \int\limits^{r_2}_{r_1} rd\theta dr\)
In the light of the above statements, choose the correct answer from the options given below:

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:

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:

Which of the following set is convex?

The function

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

The set of all points, where the function \(f(x)=\frac{x}{(1+|x|)}\) is differentiable, is

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

The solution of the differential equation \(\frac{dy}{dx}+y=3e^xy^3\) is :