CUET UG Mathematics — Calculus previous year questions with solutions.
The area of the region bounded by the parabola $y^2 = x$ and the straight line $2y = x$ is
The function $f(x) = x^3 + 3x^2 + 4x + 4$, $x \in \mathbb{R}$ (set of real numbers) :
The demand function for a commodity is $p = 35 - 2x - x^2$, then the consumer's surplus at equilibrium price $p_0 = 20$ is
The real valued function $f(x) = 12x^\frac{4}{3} - 6x^\frac{1}{3}, x \in [-8, 8]$ has absolute maximum value equal to
$\int \frac{x}{(x-1)(x-2)} dx$ is equal to ( where $C$ is a constant of integration)
$\int_0^1 tan^{-1}\left(\frac{2x-1}{1+x-x^2}\right)dx$ is equal to
If $f(x) = |x| + |x - 5|$, then which of the following statements are TRUE? (A) f is a continuous function every where (B) f is a continuous function except $x = 5$ and $x = 0$ (C) f is a continuous function except $x = 0$ but not differentiable at $x = 5$ (D) f is a continuous function everywhere but not differentiable at $x = 0$ and $x = 5$ Choose the correct answer from the options given below:
The area (in square units) of the region enclosed between the lines $x + y = 2$, $x = 0$, $x = 3$ and $x$-axis is equal to
The area of the region bounded by the curve $y = x + 1$, $x = axis$ and the lines $x = 2$ and $x = 3$ is
For the differential equation $(x + y)dy + (x - y)dx = 0$, which of the following is/are correct? (A) Differential equation is homogeneous (B) Order of differential equation is 1 (C) Integrating factor of differential equation is $e^x$ (D) Degree of the equation is not defined Choose the **correct** answer from the options given below:
Interval in which the function $f$ given by $f(x) = \tan x - 4x$, $x \in (0, \frac{\pi}{2})$ is strictly decreasing is
If $\int \frac{x^4}{x-2}dx = px + qx^2 + rx^3 + sx^4 + t\log |x - 2| + C$, where C is an arbitrary constant and p, q, r, s, t are real numbers, then the correct arrangement of p, q, r, s, t is:
The value of $\int \frac{(x^4 - x)^{1/4}}{x^5} dx$ is equal to (where C is an arbitrary constant)
The particular solution of the differential equation $\log\left(\frac{dy}{dx}\right)= 3x + 4y$ satisfying $y = 0$ when $x = 0$ is:
The area (in Sq. units) of the region bounded by $y = -2$, $y = 2$, $x = y^3$ and $x = 0$ is equal to
The rate of change of the area of a circle with respect to its radius $r$, when $r = 3$cm, is:
If $y^{1/m} + y^{-1/m} = 2x$, then the value of $(x^2 - 1)\frac{d^2y}{dx^2} + x\frac{dy}{dx}$ is:
If $y = \sqrt{ax + b}$ then $y\frac{d^2y}{dx^2} + (\frac{dy}{dx})^2 =$
Derivative of $x^x$ with respect to $x\log x$ is
For the function $f(x) = -2x^3 + 3x^2 + 36x - 10$, which of the following is/are true? (A) $f$ is increasing in $(-\infty, -2)$ (B) $f$ is increasing in $(-2, 3)$ (C) $f$ is decreasing in $(-\infty, -2)$ (D) $f$ is decreasing in $(3, \infty)$ Choose the correct answer from the options given below:
The area of the region bounded by the curves $y = x^2 + 2$, $y = x$, $x = 0$ and $x = 2$ is
If $f(a-x) = f(x)$, then $\int_0^a xf(x)dx$ is equal to
$\int \sin x \sin 2x \sin 3x dx$ is equal to
The function $f(x) = x^2e^{-2x}$ increases on