List of top Questions asked in CUET (PG)

Consider the linear mapping F: R2 →R2 defined by F(x, y) = (3x+4y, 2x-5y) and following bases of R2: E= {e1, e2} = {(1, 0), (0, 1)} and S = {u1, u2} = {(1, 2), (2, 3)}. Then the matrix A representing F relative to the basis E is:
In a group G, if a5 = e, aba-1 = b2 for a, b ∈ G then o(b) is equal to:
Which one of the following statements is wrong.
Which one of the following is wrong?
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
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) =
Let f: R→R such that f(1) =3 and f'(1) = 6. Then \(\lim\limits_{x\rightarrow0}\left(\frac{f(1+x)}{f(1)}\right)^{1/x}\)equals
The integrating factor of the differential equation \(\frac{dy}{dx}=\frac{x^3+y^3}{xy^2}\)is
The order of the permutation\(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\   2 & 4 & 6 & 5 & 1 & 3 \end{pmatrix}\)is
If λ1,λ2,λ3 are the given values of the matrix \(\begin{bmatrix}   -2 & 2 & -3 \\   2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}\), then λ12+λ22+λ32 is equal to
The minimum distance of the point (3, 4, 12) from the sphere x2 + y2 + z2 = 1 is
If \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then
The function f(z) defined by \(f(z)= \begin{cases}     \frac{Re(z)}{z}       & z\neq0\\     0  & z=0   \end{cases}\)then which one of the following is true?
The volume generated by the revolution of the cardiod r = a(1-cosθ) about x-axis 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 given series \(\frac{x}{1.3}+\frac{x^2}{2.4}+\frac{x^3}{3.5}+......,(x\gt0)\)is convergent in the interval
Which one of the following is not correct?
The general solution of \((D^2+6D+9)y=\frac{e^{-3x}}{x^2}\), where \(D\equiv \frac{d}{dx}\) is
(given that c1 and c2 are arbitrary constants)
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
If W is a subspace of R3, where W = {(a, b, c): a+b+c = 0}, then dim W is equal to
The dimension of the general solution space W of the homogeneous system
x1+2x2-3x3+2x4-4x5=0
2x1+4x2-5x3+x4-6x5 = 0
5x1+10x2-13x3+4x4-16x5= 0
If A=\(\begin{bmatrix} 1 & 2 & 0 & -1\\   2 & 6 & -3 & -3\\  3 & 10 & -6 & -5 \end{bmatrix}\), then which one of the following is true?
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 \(x^2\frac{d^2y}{dx^2}-2x\frac{dy}{dx}-4y=x^4\), then particular integral (P.I) of the given differential equation is
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?