List of top Questions asked in CUET (PG)

If the curl of vector \(\vec{A} = (2xy-3yz)\hat{i} +(x^2+axz −4z^2)\hat{j}-(3xy+byz)\hat{k}\) is zero, then a + b is equal to :

Match List I with List II

List I		List II
A.	Φ=y2,∇Φ at (1, 1, 1)	I.	\(\hat{i}\)
B.	Φ=x,∇Φ at (1, -1, 2)	II.	\(-6\hat{k}\)
C.	Φ=2x3,∇Φ at (0, 1, 2)	III.	\(2\hat{j}\)
D.	Φ=3z2,∇Φ at (1, 2, -1)	IV.	\(\vec{0}\)

Choose the correct answer from the options given below:

A. vector \(\vec{V}\) is said to be solenoidal if div \(\vec{V} = 0\)
B. Vector \(\vec{F}\) is said to be irrotational if curl \(\vec{F} = \vec{0}\)
C. If \(\vec{F}\) represents the force acting on a particle along are AB, then total work done \(\int^{B}_A \vec{F}\times \vec{dr}\)
D. Volume integral \(\int \int\limits_{V} \int \vec{F}\times dV\)
choose the correct answer from the options given below

The region represented by the inequation system x,y≥o, y ≥5,x+y≥3 is

The maximum value of Z = x + 2y subjected to the constraints x+2y≥100, 2x-y≤0,2x + y≤ 200,x≥ 0, y≥0, is:

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

From the given system of constraints
A. 3x+5y≤90
B. x + 2y≤30
C. 2x + y≤30
D. x≥0, y≥0
The redundant constraint is :

If a right circular cylinder a height 14cm is increased in a sphere of radius 8cm then volume of the cylinder (in cm³)- (use π = \(\frac{22}{7}\)).

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 solution of the Linear Programming Problem
maximize Z = 107x + y
subject to constraints x + y ≤2
-3x + y ≥ 3
x, y ≥ 0 is

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

For what value(s) of k the set of vectors {(1, k, 5), (1, -3, 2), (2, -1, 1)} form a basis in R³ ?

Evaluate the integral\(\oint\limits_C\frac{dz}{(z^2+4)^2},C:|z-i|=2\)

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

Which one of the following is a cyclic group?

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:

The work done by the force \(\overrightarrow F = (x^2-y^2)\hat{i} + (x+y)\hat{j}\) in moving a particle along the closed path C containing the curves x + y = 0, x²+ y² = 16 and y = x in the first and fourth quadrant is

Let \(\overrightarrow V\) be a vector field and f be a scalar point function, then curl \((f\overrightarrow V)\) is equivalent to________.

Let S be a piecewise smooth surface of the sphere x² + y² + z² = 16, z> 0, bounded by a simple closed curve C. Let \(\overrightarrow V= (3x-y)\hat{i}-2yz^2\hat{j}-2y^2z\hat{k}\) be a vector field which is continuous and has continuous first order partial derivatives in a domain which contains S. Then the value of \(\int\int(\nabla\times\overrightarrow V).\hat{n}dA\), where \(\hat{n}\) the unit normal vector to S is:

The all values of z, such that
√2 sin z = coshβ + isinħβ, where β is real, are

The solution of the differential equation
{x⁴+6x²+2(x+y)} dx-xdy=0
subject to the condition y(1)=0 is

Which of the following statement is not correct?

Let A and B be 2 × 2 matrices, then which of the following is correct?

Let f (x) be defined on [0, 3] by \(f(x) =   \begin{cases}     x,\text{if x is a rational number}       \\  3-x\text{, if x is an irrational number}   \end{cases}\) Then f(x) is continuous in the interval at:

If A is symmetric real valued matrix of dimension 2022, then eigenvalues of A are