CUET UG Mathematics — Calculus previous year questions with solutions.
If $y = \log_e(\sec e^{x^2})$ then $\frac{dy}{dx} =$
If $y = 3^x + e^x + x^x + x^3$, then the value of $\frac{dy}{dx}$ at $x = 3$ is
The solution of the differential equation $log_e\left(\frac{dy}{dx}\right) = 3x + 4y$ is given by
The area of the region $\{(x, y): x^2 + y^2 \leq 1 \leq x + y\}$ is
If $f(x) = 2x^3 - 15x^2 + 36x + 1$, $x \in [1, 5]$, then the absolute minimum value of $f(x)$ is:
The area (in sq. units) of the bigger portion of region enclosed by the curves $4x^2 + 9y^2 = 36$ and $2x + 3y = 6$ is
Area of the bounded region between the curve $y = |x - 2|$ and the line $y = 2$ is:
The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $C(x) = 0.007x^3 + 26x^2 + 15x + 400$. The marginal cost when 10 items are produced is:
If $y = 5e^{2x} + 4e^{3x}$, then $\frac{d^2y}{dx^2}$ equals:
Which of the following functions $f(x)$ are differentiable at $x = 0$? (A) $|x|$ (B) $|x - 1|$ (C) $|\sin x|$ (D) $|\cos x|$ (E) $x^2$ Choose the correct answer from the options given below:
The general solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = ax + by$ is
The area (in sq. units) of the region bounded by the line $y = x + 2$, $x = 0$, $x = 1$ and $y = 0$ is
The interval(s), where the function $f(x) = \begin{cases} \frac{1-e^x}{e^{2x}-1} & : x \neq 0 \\ \frac{-1}{2} & : x = 0 \end{cases}$ is increasing, is/ are:
$\int_1^{\sqrt{3}} \frac{1}{1+x^2} dx$ is equal to:
Area of the region bounded by the curve $y = \sin x$ and x-axis between $x = \frac{\pi}{2}$ and $x = \frac{3\pi}{2}$ is
If $y = 3e^{2x} + 2e^{3x}$, then $\frac{d^2y}{dx^2} + 6y$ is equal to
The particular solution of the differential equation $\frac{dy}{dx} = e^{x^2/2} + xy$, when $x = 0$, $y = 1$, is
For $y \neq 0$, the particular solution of the differential equation $2ye^{x/y}dx + (y - 2xe^{x/y})dy = 0$ at the point (1, 1) is
The area (in sq. units) of the region bounded by the curve $x^2 = 250y$, $y = 0$ and $x = 50$ is
The radius of spherical balloon is decreasing at the rate of 0.1cm/sec, the rate at which its volume is decreasing, when its radius is 0.5cm is
The function $f(x) = \frac{x}{3} + \frac{3}{x}$ is increasing in the interval:
Match List-I with List-II Consider the function f(x) = 2x³ - 21x² + 36x + 80, x∈[0, 6]. Then | List-I | List-II | |---|---| | (A) one of its critical points is at x = | (I) -28 | | (B) Its absolute maximum value is | (II) -42 | | (C) Its absolute minimum value is | (III) 97 | | (D) Its second derivative at x = 0 is | (IV) 6 | Choose the correct answer from the options given below:
The general solution of the differential equation $\frac{dy}{dx} = xy + x + y + 1$ is
The interval, on which the function $f(x) = x^2e^{-x}$ is increasing, is equal to