CUET UG Mathematics · Paper 3

The least value of $f(x) = x^3 - 12x$, $x \in [0, 3]$ is

$\int \frac{\sec^2(\log x)}{x}\,dx$ is equal to

If $\begin{vmatrix} -1 & -2 & 5 \\ -2 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = -86$, then the sum of all possible values of $a$ is

The sum of the order and the degree of the differential equation $\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{3/2} = 5\frac{d^2y}{dx^2}$ is

Evaluate $\int \frac{dx}{x^2 - 5x + 6}$ by splitting the integrand into partial fractions.

Find the area, in square units, enclosed between the x-axis and the curve $y = x^2 - 4x + 3$.

A relation $R$ on the set $A = \{1, 2, 3\}$ defined as $R = \{(1, 1), (2, 2), (1, 2)\}$ is

If $|\vec{a}| = 8$, $|\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 12$, then the value of $|\vec{a} \cdot \vec{b}|$ is

The function $f(x) = x^4 - 2x^2$ is strictly decreasing on

The area (in square units) of the smaller region cut off from the circle $x^2 + y^2 = 4$ by the line $x = 1$ is

$\frac{dy}{dx} = F(x, y)$ will be a homogeneous differential equation for which of the following functions?

I. $F(x, y) = 3x + 2y$

II. $F(x, y) = \sin\frac{y}{x} + \log y - \log x$

III. $F(x, y) = e^{y/x} + 1$

IV. $F(x, y) = \sqrt{x^2 + y^2} - y$

In what ratio must a grocer mix two varieties of tea worth ₹60 per kg and ₹65 per kg so that by selling the mixture at ₹68.20 per kg the gain is 10%?

An investment of ₹40,000 grows to ₹62,500 in 2 years. The compound annual growth rate (CAGR) is

If $x$ is a real number such that $-5 < 2 - 3x \le 8$, then

A curve is defined implicitly by $x^2 + xy + y^2 = 7$. What is the slope of its tangent at the point $(1, 2)$?

For the given values 23, 32, 40, 47, 58, 33, 42, the 5-yearly moving averages are

The mean and the variance of a binomial distribution are 4 and 3 respectively. Then $P(X \ge 1)$ is

A trust wants to award a prize of ₹R at the end of every year forever. It invests ₹2,50,000 now in a fund that earns 8% per annum compounded half-yearly. The largest possible value of R is