CUET UG Mathematics — Calculus previous year questions with solutions.
The approximate volume of a cube of side a meters on increasing the side by 4% is:
The area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum is:
$\int \left(\frac{1+x+x^2}{1+x^2}\right) e^{\tan^{-1} x} dx =$
If $\sqrt{1-x^2} + \sqrt{1-y^2} = a(x-y)$, then $\frac{dy}{dx} =$
The maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 27$ is:
The area enclosed between the curves $y = x^2$ and $x = y^2$ is
The function $f(x) = \frac{x-1}{x(x^2-1)}, x \neq 1, f(1) = 1$, is discontinuous at
Match **List - I** with **List - II**. | | List - I | | List - II | |---|---|---|---| | (A) | $x = 2at^2, y = at^4$ | (I) | Inverse trignometric function | | (B) | $f(x) = (2x + 3)^3$ | (II) | Implicit function | | (C) | $xy + y^2 = \tan(x + y)$ | (III) | Parametric function | | (D) | $y = \tan^{-1}\left(\frac{3x - x^3}{1 - 3x^2}\right), -\frac{1}{\sqrt{3}} < x < \frac{1}{\sqrt{3}}$ | (IV) | Composite function | Choose the **correct** answer from the options given below :
The integral $\int e^x \left(\frac{x-1}{2x^2}\right) dx$ is equal to:
The condition on a and b, such that for $y = \frac{a}{x} - \frac{b}{x^2}$, $\frac{dy}{dx} = 0$ at $x=1$ is :
The value of the integral $\int_{2}^{4} \frac{x}{x^2+1} dx$ is :
The sum of order and degree of the differential equation $\frac{\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2y}{dx^2}} = p$ is :
$\int_0^{\pi/2} \sqrt{1 - \sin 2x} \, dx$ is equal to :
The rate of change of the area of a circular disc with respect to its circumference when radius is 3 is :
The value of $\int_{0}^{3} |2x - 6| dx$ is :
The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of : (A) first order and first degree (B) second order and first degree (C) second order and second degree (D) second order Choose the correct answer from the options given below :
The area of the shaded portion  is :
The area enclosed between $y^2 = 4x$, $x = 1$, $x = 4$ in first quadrant is :
The slope of the tangent to the curve $x = at^2$, $y = 2at$ at 't' is :
If m and n are respectively the order and degree of the differential equation : $\left(\frac{d^2 y}{dx^2}\right)^5 + 6 \frac{\left(\frac{d^2 y}{dx^2}\right)^3}{\frac{d^3 y}{dx^3}} + \frac{d^3 y}{dx^3} = x^2 + 5$, then :
The area enclosed between the curve $y = x^2 + 2$ and x-axis between $x = 0$ and $x = 3$ is :
The interval in which the function $f(x) = 2x^3 - 3x^2 - 36x + 7$ is strictly decreasing is :
$\int \frac{\sqrt{\tan x}}{\sin x \cos x} dx$ equals :
The derivative of $\sec(\tan \sqrt{x})$ with respect to x is :