List of top Mathematics Questions asked in CUET (PG)

The function \( f(z) = |z|^2 \) is differentiable, at

If G is a cyclic group of order 12, then the order of Aut(G) is:

The value of the integral \( \iint_R (x+y) \,dy\,dx \) in the region R bounded by \( x=0, x=2, y=x, y=x+2 \), is

If \( \vec{F} \) be the force and C is a non-closed arc, then \( \int_C \vec{F} \cdot d\vec{r} \) represents:

Let \( f(x) = |x| + |x-1| + |x+1| \) be a function defined on \( \mathbb{R} \), then \( f(x) \) is:

Let f be a continuous function on \(\mathbb{R}\) and \( F(x) = \int_{x-2^{x+2} f(t) dt \), then F'(x) is}

Which one of the following mathematical structure forms a group?

The orthogonal trajectory of the cardioid \( r = a(1 - \cos\theta) \), where 'a' is an arbitrary constant is:

For the given linear programming problem,
Minimum Z = 6x + 10y
subject to the constraints
\( x \ge 6 \); \( y \ge 2 \); \( 2x+y \ge 10 \); \( x,y \ge 0 \),
the redundant constraints are:

If C is a triangle with vertices (0,0), (1,0) and (1,1) which are oriented counter clockwise, then \( \oint_C 2xydx + (x^2+2x)dy \) is equal to:

Which of the following function is discontinuous at every point of \(\mathbb{R}\)?

For any Linear Programming Problem (LPP), choose the correct statement:
A. There exists only finite number of basic feasible solutions to LPP
B. Any convex combination of k - different optimum solution to a LPP is again an optimum solution to the problem
C. If a LPP has feasible solution, then it also has a basic feasible solution
D. A basic solution to AX = b is degenerate if one or more of the basic variables vanish

The solution of the differential equation \( (xy^3 + y)dx + (2x^2y^2 + 2x + 2y^4)dy = 0 \) is:

Consider the following: Let f(z) be a complex valued function defined on a subset \( S \subset \mathbb{C} \) of complex numbers. Then which of the following are correct?
A. The order of a zero of a polynomial equals to the order of its first non-vanishing derivative at that zero of the polynomial
B. Zeros of non-zero analytic function are isolated
C. Zeros of f(z) are obtained by equating the numerator to zero if there is no common factor in the numerator and the denominator of f(z)
D. Limit points of zeros of an analytic function is an isolated essential singularity

Maximize \( Z = 2x+3y \), subject to the constraints:
\( x+y \le 2 \)
\( 2x+y \le 3 \)
\( x,y \ge 0 \)

If α and β are the roots of a quadratic equation x²+αx + β=0 where β≠0, then what is the value of α + β?

A triangle can have:

The sum of two digits no. is 10, on reversing the digits of a number the number is decrease by 36. Find the number.

Find the sum of two consecutive numbers in which four times are first number is 12 more than the thrice of the second number

Find the sum of following hexadecimal numbers (7CA)₁₆+ (4B2)₁₆ =?

Given below are two statements:
Statement I: For n ≥1, we have \(\frac{1}{1·2}+\frac{1}{2·3}+\frac{1}{3·4}+.....+\frac{1}{n(n+1)}=\frac{n^2}{n+1}\)
Statement II: (1+x)ⁿ ≥ (1+nx) for all natural number n, where x > -1.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Sum of n terms of series 1²+3²+5²+... to n terms is \(\frac{n}{3}(4n^2-1)\).
Reasons (R): Sum of the squares of first a natural numbers 1², 2², 3²,....,n² is \(\frac{n(n+1)(2n+1)}6\).
In the light of the above Statements, choose the correct answer from the options given below: