CUET UG Mathematics — Calculus previous year questions with solutions.
The area of the region bounded by the curve $x = y^2$ and the line $x = 4$ is equal to :
$\int_{\frac{1}{3}}^{1} \frac{(x - x^3)^{\frac{1}{3}}}{x^4} dx =$
The area bounded by $x = \sqrt{9 - y^2}$, $x - y + 3 = 0$ and x-axis is :
Match List I with List II | List - I | List - II | |---|---| | A. $\int \frac{dx}{x^2 - a^2} =$ | I. $\log_e\left\lvert x + \sqrt{x^2 + a^2}\right\rvert + C$ | | B. $\int \frac{dx}{a^2 - x^2} =$ | II. $\frac{1}{2a}\log_e\left\lvert\frac{x-a}{x+a}\right\rvert + C$ | | C. $\int \frac{dx}{\sqrt{x^2 - a^2}} =$ | III. $\frac{1}{2a}\log_e\left\lvert\frac{a+x}{a-x}\right\rvert + C$ | | D. $\int \frac{dx}{\sqrt{x^2 + a^2}} =$ | IV. $\log_e\left\lvert x + \sqrt{x^2 - a^2}\right\rvert + C$ | Choose the correct answer from the options given below:
$\int \sqrt{x^2 - 4x + 5} \, dx =$
The line $ax + by = 7$ is a tangent to the curve $y = \frac{x-7}{(x-2)(x-3)}$ at the point where it cuts the x-axis A. The y-intercept of the line is $-0.7$ B. $b = -7$ C. $a = 1$ D. the line passes through the point $(-13, -1)$ E. $b = -20$ Choose the correct answer from the options given below:
The interval in which the function given by $f(x) = x^2 e^{-x}$ is strictly increasing is:
The interval in which $f(x) = \frac{x}{2} + \frac{2}{x}$ is a decreasing function of $x$ is :
The smaller of the areas enclosed by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$ is
Match List I with List II | List - I | List - II | |---|---| | A. $\int_{-\pi/2}^{\pi/2} \sin^7 x \, dx$ | I. $\frac{\pi}{2}$ | | B. $\int_{-\pi/2}^{\pi/2} \sin^2 x \, dx$ | II. $\frac{\pi}{4}$ | | C. $\int_0^{\pi/2} \frac{1}{1 + \tan x} \, dx$ | III. 0 | | D. $\int_0^{\pi} \lvert \cos x \rvert \, dx$ | IV. 2 |
General solution of the differential equation $\frac{dy}{dx} + \frac{\sqrt{1 - y^2}}{\sqrt{1 - x^2}} = 0$ is A. $\tan^{-1} x + \tan^{-1} y = C$ B. $\sin^{-1} x - \cos^{-1} y = C$ C. $x\sqrt{1 - y^2} - y\sqrt{1 - x^2} = C$ D. $\sin^{-1} x + \sin^{-1} y = C$ E. $\cos^{-1} x + \cos^{-1} y = C$ (where C is arbitrary constant) Choose the correct answer from the options given below
If $x = \int_0^y \frac{dt}{\sqrt{1+9t^2}}$ and $\frac{d^2y}{dx^2} = \lambda y$, then, $\lambda$ is equal to
If $x^y = e^{x-y}$, then $\frac{dy}{dx} =$
Based on above information answer the following question : The area of the flower bed $(A(x))$ is given by :
If $f(x) = \begin{cases} 1 - 2x, & x \leq 0 \\ 1 + 2x, & x > 0 \end{cases}$, then $\int_{-1}^{1} f(x) \, dx =$
Consider the following statements for the curve $f(x) = x|x|$ and find that which of the following(s) are/is correct : (A) $f(x) = x|x|$ is differentiable at $x = 0$. (B) $f(x) = x|x|$ is continuous at $x = 0$ but not differentiable at $x = 0$. (C) $f(x) = x|x|$ has point of infection at $x = 0$. (D) $f(x) = x|x|$ is symmetrical about y-axis. Choose the correct answer from the options given below :
Distance between Sumit and Amit in terms of $x$ is :
The value of $x$ for which $\frac{dy}{dx} = 0$, is
Solution of the differential equation $(x + xy)dy - y(1 - x^2)dx = 0$ is
The value of $\int_0^1 e^x (x + 1) \, dx$ is equal to
The interval in which the function $f(x) = 2x^3 + 3x^2 - 12x + 1$ is strictly increasing is -
$\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx =$
The differential equation representing family of curves $y = e^{-2x}(a \cos x + b \sin x)$, where a and b are arbitrary constant, is :
The function $f(x) = 6(2x^4 - x^2)$ is strictly increasing in