List of top Mathematics Questions asked in CUET (PG)

If W is a subspace of R³, where W = {(a, b, c): a+b+c = 0}, then dim W is equal to

The average of 5 consecutive odd positive integers is 9. Then sum of smallest and greatest number is

The orthogonal trajectories of the family of curves y = \(ax^3\) is

The general solution of differential equation \(\frac{d^2y}{dx^2}+9y=sin^3x\) is
(given that c₁ and c₂ are arbitrary constants)

The solution of (x² -√2y) dx + (y² - √2x) dy = 0 is given by

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)

The sequence is

Given below are two statements
Statement I: Every cyclic group is abelian
Statement II: (Z,+) is a cyclic group with 1 and -1 as the only generators
In the light of the above statements, choose the most appropriate answer from the options given below

In a group G, if a⁵ = e, aba^-1 = b² for a, b ∈ G then o(b) is equal to:

The order of 16 in \((\mathbb{Z}_{24}, +_{24})\) is:

Which one of the following is correct :-

If 2.5x=0.05 y, then find the value of \((\frac{y-x}{y+x}).\)

The minimum distance of the point (3, 4, 12) from the sphere x² + y² + z² = 1 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?

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

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

Let f : Z→ \(Z_2\), be a homomorphism of groups defined by
\(f(a) =   \begin{cases}    0,  & \quad \text{if } a \text{ is even}\\     1,  & \quad \text{if } a \text{ is odd}   \end{cases}\)

then Kerf 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

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:

The surface area of the cylinder \(x^2+z^2 = 4\) inside the cylinder \(x^2 + y^2 = 4\) is:

Integrating factors of the equation y (2xy + e^x) dx - e^x dy = 0 is :

The orthogonal trajectory of the cardioid r = a(1+cos θ), a being the parameter is:

Given below are two statements:
Statement I : If x²y" - 2xy' - 4y = x⁴, then \(C.F.=\frac{C_1}{x}+C_2x^4\)
Statement II: If (D²-8D+15) y = 0, then auxiliary equation has equal roots.
In the light of the above statements, choose the correct answer from the options given below

If \(\vec{A} =(3x^2+6y)\hat{i}—14yz\hat{j} +20xz^2\hat{k}\), then the line integral \(\int\limits_{C} \vec{A}.d\bar{r}\) from (0.0, 0) to (1, 1.1), along the curve C ;x=t, y=t². z=t³ is: