List of top Questions asked in CUET (PG)

Where is the karuṇā in Buddha’s teachings?

“By nirvāṇa only kleśāvaraṇa is destroyed, not jñeyāvaraṇa” — whose theory was this?

He is a Buddhist logician.

Saṃyuktanikāya is in which Piṭaka of Tripiṭakas?

“A Buddhist monk can’t get a category of Buddha in spite of getting the position of Arhat” — whose concept was this?

“Ultimate cessation of suffering is the nirvāṇa” — whose concept is this?

This is an important text in the Abhidharma theory of Sarvāstivādins.

The particular integral of differential equation \( \frac{d^2y}{dx^2} + 2\frac{dy}{dx} + y = e^{-x}\log x \) is:

Match List-I with List-II

\[ \begin{array}{|l|l|} \hline \textbf{List-I (Curve)} & \textbf{List-II (Orthogonal trajectory)} \\ \hline (A) \; xy = c & (I) \; \tfrac{y^2}{2} + x^2 = c \\ (B) \; e^x + e^{-y} = c & (II) \; y(y^2 + 3x^2) = c \\ (C) \; y^2 = cx & (III) \; y^2 - x^2 = 2c \\ (D) \; x^2 - y^2 = cx & (IV) \; e^y - e^{-x} = c \\ \hline \end{array} \]
Choose the correct answer from the options given below:

The integral equation corresponding to the boundary value problem \[ \frac{d^2y}{dx^2} + \lambda y(x) = 0; \quad y(0) = 0; \quad y(1) = 0 \] is

where \[ k(x,t) = \begin{cases} t(1-x), & \text{if } t < x \\ x(1-t), & \text{if } t > x \end{cases} \]

The general solution of differential equation \( \frac{d^2y}{dx^2} + 9y = \cos(3x) \) is:

The Laplace transform of \( \cos\sqrt{t} \) is:

Which one of the following statement is not correct?

Let \( \vec{F} \) be the vector valued function and f be a scalar function. Let \( \nabla = \hat{i}\frac{\partial}{\partial x} + \hat{j}\frac{\partial}{\partial y} + \hat{k}\frac{\partial}{\partial z} \) then,
(A) div (grad f) = \( \nabla^2 f \)
(B) curl curl \( \vec{F} \) = grad curl \( \vec{F} \) - \( \nabla^2 \vec{F} \)
(C) div curl \( \vec{F} \) = \( \vec{0} \)
(D) curl grad f = \( \vec{0} \)
(E) div (\(f\vec{F}\)) = f div \( \vec{F} \) + (grad f) \( \times \vec{F} \)
Choose the correct answer from the options given below:

The directional derivative of \( \nabla \cdot (\nabla f) \) at the point (1, -2, 1) in the direction of the normal to the surface \( xy^2z = 3x + z^2 \) where \( f = 2x^3y^2z^4 \) and \( \nabla = \hat{i}\frac{\partial}{\partial x} + \hat{j}\frac{\partial}{\partial y} + \hat{k}\frac{\partial}{\partial z} \) is

The value of \( \oint_S \vec{F} \cdot d\vec{s} \) where \( \vec{F} = 4x\hat{i} - 2y^2\hat{j} + z^2\hat{k} \) taken over the cylinder \( x^2+y^2=4, z=0 \) and \( z=3 \) is:

The surface area of the plane \(x + 2y + 2z = 12\) cut off by \(x=0, y=0\) and \(x^2+y^2=16\) is

If R is a closed region in the xy-plane bounded by a simple closed curve C and if M(x, y) and N(x, y) are continuous functions of x and y having continuous derivative in R, then

The value of \( \int_2^3 \vec{A} \cdot \frac{d\vec{A}}{dt} dt \) if \( \vec{A}(2) = 2\hat{i} - \hat{j} + 2\hat{k} \) and \( \vec{A}(3) = 4\hat{i} - 2\hat{j} + 3\hat{k} \) is

Match List-I with List-II

\[ \begin{array}{|l|l|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; P \text{ and } Q \text{ are two perpendicular forces, acting at a point} & (I) \; R = |P - Q| \\ (B) \; P \text{ and } Q \text{ are equal, forces acting at a point at an angle } \alpha & (II) \; R = P + Q \\ (C) \; P \text{ and } Q \text{ are acting at a point in same direction} & (III) \; R = 2P \cos(\tfrac{\alpha}{2}) \\ (D) \; P \text{ and } Q \text{ are acting at a point in opposite direction} & (IV) \; R = \sqrt{P^2 + Q^2} \\ \hline \end{array} \]
Choose the correct answer from the options given below:

Two forces acting at a point of a body are equilibrium if and only if they
(A) are equal in magnitude
(B) have same direction
(C) have opposite direction
(D) act along the same straight line
(E) are not equal in magnitude but have same direction
Choose the correct answer from the options given below:

If three forces of magnitudes 8 newtons, 5 newtons and 4 newtons acting a point are in equilibrium, then the angle between the two smaller forces is

If two stones are thrown vertically upwards with their velocities in the ratio 2:5, then the ratio of the maximum heights attained by the stones is

Match List-I with List-II

\[ \begin{array}{|l|l|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; \dfrac{y^2}{36} - \dfrac{x^2}{16} = 1 & (I) \; \text{Eccentricity is } 2\sqrt{2} \\ (B) \; 7x^2 + 12xy - 2y^2 - 2x + 4y - 7 = 0 & (II) \; \text{Eccentricity is } \tfrac{3}{2} \\ (C) \; 7x^2 - y^2 = 224 & (III) \; \text{Eccentricity is } \tfrac{\sqrt{13}}{3} \\ (D) \; \dfrac{x^2}{16} - \dfrac{y^2}{20} = \dfrac{1}{9} & (IV) \; \text{Asymptotes are } y = \pm \tfrac{3}{2}x \\ \hline \end{array} \]

Match List-I with List-II

\[ \begin{array}{|l|l|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; 9x^2 - 12xy + 4y^2 - 74x - 98y + 324 = 0 & (I) \; \text{Hyperbola} \\ (B) \; 12x^2 + 7xy - 12y^2 + 10x + 55y - 125 = 0 & (II) \; \text{A pair of straight lines} \\ (C) \; x^2 + 3xy + 2y^2 + x + y = 0 & (III) \; \text{Ellipse} \\ (D) \; 5x^2 + y^2 - 30x + 1 = 0 & (IV) \; \text{Parabola} \\ \hline \end{array} \]
Choose the correct answer from the options given below: