List of top Mathematics Questions asked in CUET (UG)

The radius of a spherical ball is increasing at the rate of 1 m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by:

The absolute maximum value of the function f(x)=sinx + cosx, x \(\in\)[0, \(\pi\)] is:

The value of b for which the function f(x) = sinx - bx + C, where b and e are constants is decreasing for \(x \in R\) is given by

If A = \(\begin{bmatrix}2a & 0& 0\\[0.3em]0& 2a& 0\\[0.3em]0&0 & 2a\\[0.3em] \end{bmatrix}\), then the value of \(|adj A|\)is:

There are two values of a for which the determinant, \(\Delta =\begin{bmatrix}1& -2& 5\\[0.3em]0& a& 1\\[0.3em] 0& 4& 2a\\[0.3em] \end{bmatrix} = 86\), then the sum of these values of a is:

If, A = \(\begin{bmatrix}a& d& l\\[0.3em]b& e& m\\[0.3em]c& f& n\\[0.3em] \end{bmatrix}\)and B = \(\begin{bmatrix}l& m& n\\[0.3em]a& b& c\\[0.3em]d& e& f\\[0.3em]  \end{bmatrix}\), then

If A is a non-identity invertible symmetric matrix, then \(A^{-1}\) is:

If A is a skew-symmetric matrix of order n. then

The value of x given by \(cos (tan ^{-1}x) = sin (cot^{-1} \ \frac{3}{4})\)is:

If \(A= \begin{bmatrix}1 & 0 \\[0.3em]-1 & 5 \\[0.3em] \end{bmatrix}\) and \(I= \begin{bmatrix}1& 0\\[0.3em]0& 1\\[0.3em] \end{bmatrix}\) then the value of k so that \(A^2 = 6A + kI\) is given by:

Le L be the set of all lines in a plane and R be the relation in L. defined as R = {(\(L_1, L_2\)): \(L_1\) is perpendicular to \(L_2\)} then R is:
A) Reflexive
B) Symmetric
C) Neither reflexive nor transitive
D) Transitive
E) Neither reflexive nor symmetric
Choose the correct answer from the options given below:

The solution set of the inequality \(2x + 3y < 4\) is:

Consider the non-empty set consisting of children in a family and a relation R is defined as aRb if a is a brother of b. Then R is:

The corner points of the feasible region determined by the system of linear inequalities are (0,0), (4, 0), (2, 4) and (0.5). If the maximum value of Z = ax + by where a, \(b > 0\) occurs at both (2, 4) and (4.0), then

The value of the expression sin \([cot^{-1}(cos (tan^{-1}1))]\) is:

If \(P(A) = \frac{3}{10}\), \(P(B) = \frac{2}{5}\) and \(P(A \bigcup B) = \frac{3}{5}\), then \(P(B|A)+P(A|B)\) is equal to:

Two cards are drawn without replacement. The probability distribution of number of aces is given by:

The area bounded by x = 1, x = 2, xy = 1 and x-axis is:

If \(e^y(x+2)=10\), then \(\frac{d^2y}{dx^2}\) is equal to:

The general solution of differential equation \(\frac{dy}{dx} - xy = e^{\frac{x^2}{2}}\)

Match List I with List II

List I	List II
\(A.\ [1 + (\frac{dy}{dx})^2] = \frac{d^2y}{dx^2}\)	I. order 2, degree 3
\(B. \ (\frac{d^3y}{dx^2})^2 - 3\frac{d^2y}{dx^2} + 2(\frac{dy}{dx})^4 = y^4\)	II. order 2, degree 1
\(C. \ (\frac{dy}{dx})^2 + (\frac{d^2y}{dx^2})^3 = 0\)	III. order 1, degree 2
\(D.\ (\frac{dy}{dx})^2 + 6y^3 = 0\)	IV. order 3, degree 2

Choose the correct answer from the options given below:

The points on the curve \(\frac{x^2}{9} + \frac{y^2}{16} = 1\) at which the tangents are parallel to x-axis:

The value of the integral \(\int e^x (logx + \frac{1}{x})dx\) is:

The interval on which the function \(f(x)=2x^3 +12x^2 +18x-7\) is decreasing, is:

If, A is a square matrix of order 3 and |A| = -2 then. \(|-2 \ A^{-1}|\) is: