List of top Mathematics Questions asked in CUET (PG)

Which one of the following is wrong?
Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x7} where x7 denotes multiplication moduls 7?
The number of common tangents that can be drawn to the circle x2+y2-4x-6y-3=0 and x2+y2+2x+2y+1=0 is
The area of the region bounded by the curve x2=4y and the straight line x = 4y - 2 is
The Value of \(lim_{n\rightarrow \infty }\bigg[\frac{2}{1}\bigg(\frac{3}{2}\bigg)^2\bigg(\frac{4}{3}\bigg)^3.....\bigg(\frac{n+1}{n}\bigg)^n\bigg]^{\frac{1}{n}}is\)
The point (-1, 2, 7, 6) lies in which of the following half spaces corresponding to hyperplane 2x1+3x2+4x3+5x4 = 6
The surface area of the sphere x2 + y2 + z2 = 9 lying inside the cylinder x2 + y2 = 3y is
In the neighborhood of z = 1, the function f(z) has a power series expansion of the form f(z) = 1+(1-z)+(1-z)2 + .... then f(z) is
If W is a subspace of R3, where W = {(a, b, c): a+b+c = 0}, then dim W is equal to
The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4 × 4 symmetric positive definite matrix is
If f is twice differentiable function such that f''(x) = - f(x) and f'(x) = g(x), h(x) = [f(x)]2+[g(x)]2 and h(5)=11, then h(10) =
A single 6-sided dice is rolled, then the probability of getting an odd number is
If \(\overrightarrow F=y^2\hat{i}+xy\hat{j}+xz\hat{k}\) and C is the bounding curve of the hemisphere x2+y2+z2=9,z>0, oriented in the positive direction, then value of \(\int\limits_C \overrightarrow F\cdot d\hat{r}\) is
The minimum distance of the point (3, 4, 12) from the sphere x2 + y2 + z2 = 1 is
If \(\vec{a},\vec{b},\vec{c}\) are non-coplanar unit vectors such that \(\vec{a}\times(\vec{b}\times \vec{c})=\frac{(\vec{b}+\vec{c})}{\sqrt2}\) then the angle between a and b is
If the solution of \(x\frac{dy}{dx}+y=x^3y^6\) is \(\frac{1}{y^\alpha x^\beta}=\frac{\gamma}{2x^2}+C\), then value of \(\alpha+\beta+\gamma\) is
If \(\overrightarrow F=2z\hat{i}-x\hat{j}+y\hat{k}\) and Vis the region bounded by the surface x=0,y=0,x=2,y=4,z=x2,z=2, then value of \(\iiint\limits_V\overrightarrow FdV\)is
The solution x1 = 1, x2 = 1, x3 = 0 and z = 3 to the system of equations
x1+x2+x3=2
x1+x2-x3=2
x1,x2,x3≥0
which minimizes z = x1 + 2x2 + 3x3 is
If \(x^2\frac{d^2y}{dx^2}-2x\frac{dy}{dx}-4y=x^4\), then particular integral (P.I) of the given differential equation is
The value of \(\int\limits_C \frac{\sin\pi z^2+\cos\pi z^2}{(z-1)(z-2)}dz\), where C is the circle |z|=3 is
The volume generated by the revolution of the cardiod r = a(1-cosθ) about x-axis is
If f(x) satisfies the conditions of Rolle's theorem in [1, 2] and f(x) is continuous in [1, 2], then \(\int_1^2f'(x)dx\) is equal to
Let f(z) = u + iv be an analytic function, where u = x3-3xy2 +3x2 -3y2, then the imaginary part v of f(z) is
With the help of suitable transform of the independent variable, the differential equation
\(x\frac{d^2y}{dx^2}+\frac{2dy}{dx}=6x+\frac{1}{x}\) reduces to the form:
If f: R2→R2 is a function defined as \(f(x,y) =   \begin{cases}   \frac{x}{\sqrt{x^2+y^2}},      & x\neq0,y\neq0\\     2,  & x=0,y=0   \end{cases}\)then, which of the following is correct?