List of top Mathematics Questions

Let the functions \(f\) and \(g\) be defined by \(f(x)=3\sin x,\; -\frac{\pi}{2}\le x\le \frac{\pi}{2}\) and \(g(x)=6-3x^2,\; x\in\mathbb{R}\). Then \(f^{-1}(g(x))=\)

The value of \(\displaystyle \int_{0}^{1} \frac{t}{(t+1)^3}\,dt\) is equal to:

The value of \(\displaystyle \int_{0}^{2\pi} \frac{\sin 2x}{x(2\pi - x)}\,dx\) is equal to:

If \(n\) is an odd natural number and \[ I_n=\int_0^1 e^x(x-1)^n\,dx \] then \( I_n+nI_{n-1} \) is equal to:

If the solution of the differential equation \(\frac{dy}{dx} = \frac{\alpha x^2 + 4x - 4}{2y - 4}\), when \(y(1) = 3\), is \(y^2 - 4y = x^3 + 2x^2 - 4x + c\), then the value of \(\alpha\) is equal to

The integrating factor of the differential equation \(\frac{dy}{dx} + \frac{2y}{20 - x} = 10\) is

If the constraints of a Linear Programming Problem are : \(x + y \leq 6, 2x + y \leq 8, x \geq 0, y \geq 0\), then a corner point of the feasible region is

The area of the region bounded by \(y = \sqrt{x}, y = -x\), and \(x = 4\) (in square units) is

The value of \(\int_0^3 |3x^2 - 3| dx\) is equal to

The value of \(\int 16x^3 \log_e x dx\) is equal to

A ladder AB, of length 13m, has one end A on a levelled horizontal ground and the other end B resting against a vertical wall. If the end A begins to slip away from the wall with constant speed 0.25 m/s, and the end B slips down the wall, then the speed of the end B, when B has reached a height of 5m above the ground, is

Let \(f(x) = -x^3 + 9x^2 - \alpha x - 13\), where \(x \in \mathbb{R}\) and \(\alpha\) is a constant. If the function \(f\) is increasing only in the interval (1,5), then the value of \(\alpha\) is equal to

\(\int \frac{\sec x \sqrt{\sec x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx = \)

If \(s = \sqrt{t + 1}, x = \log s\) and \(y = 6x + 3\), then \(\frac{dy}{dt} =\)

If \(y = \sqrt{x} + 2\cos(\sqrt{x})\), then the value of \(\frac{dy}{dx}\) at \(x = \frac{\pi^2}{4}\) is equal to

If \(f(x) = x - 7, g(x) = 11 - x\), and \(h(x) = f(x)g(x)\), then the maximum value of \(h\) is

If \(y = \sin\left(\tan^{-1}\left(\frac{1}{\sqrt{x^2 - 1}}\right)\right), x > 1\), then \(\frac{dy}{dx} =\)

A committee of 4 people is selected from the members of a school council which consists of 5 students, 4 teachers and 3 administrators. The probability that the committee has no teachers is

The direction ratios of a straight line \(L_1\) are 2,-1,2 and that of another straight line \(L_2\) are 3,6,-2. Then the angle between \(L_1\) and \(L_2\) is

The following set of data is given: 72, 72, 74, 80, 82, 82, 86, 88, 92, 92. The mean deviation from the median is

The events A and B are such that \(P(A)=0.7, P(B')=0.8\) and \(P(A \cup B) = 0.8\). Then \(P(A' \cup B')\) is equal to

The 10 letters of the word STATISTICS are arranged randomly. The probability that the 10-letter arrangement starts with CAT is

If the position vectors of the points P and Q are, respectively, \(5\vec{a} - 6\vec{b}\) and \(\vec{a} + 2\vec{b}\), then the point R with position vector \(2\vec{a}\) divides the line segment joining P and Q internally in the ratio

If the equation of the straight line passing through the point \((a,1,3)\) and parallel to the vector \(\frac{2}{3}\hat{i} + \frac{3}{2}\hat{j} + \hat{k}\) is \(\frac{3x+6}{b} = \frac{2y-2}{3} = \frac{z-3}{1}\), then the value of \(a+b\) is equal to