List of top Mathematics Questions

If \[ \int \frac{2x^2+3}{(x^2-1)(x^2-4)} \, dx = \log \left[ \left( \frac{x-2}{x+2} \right)^a \cdot \left( \frac{x+1}{x-1} \right)^b \right] + c \] where \( c \) is the constant of integration, then the value of \[ a+b = \, ? \] 

If \(z = x + iy\) is a complex number, then the equation \(\left| \frac{z+i}{z-i} \right| = \sqrt{3}\) represents the
\(\cot^{-1} (2 \cos(2 \text{cosec}^{-1}(\sqrt{2}))) = \dots\)

Evaluate: \[ \lim_{x \to \infty} \left( \frac{x+8}{x+1} \right)^{x+5} = \, ? \] 

The area of a parallelogram whose diagonals are the vectors \(2\bar{a} - \bar{b}\) and \(4\bar{a} - 5\bar{b}\), where \(\bar{a}\) and \(\bar{b}\) are unit vectors forming an angle of \(45^\circ\) is
21 friends were invited for a party. Two round tables can accommodate 12 and 9 friends each, The number of ways of the seating arrangements of friends is .....
\(\int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} dx =\)
Evaluate the integral with square root in denominator. \[ \int \frac{\sin 2x \cos 2x}{\sqrt{9-\cos^4 2x}}\,dx \]
\(\int_0^2 \frac{3x+1}{x^2+4} dx\)
Evaluate the definite integral. $$ \int_{\frac{\pi}{3}}^{\frac{2\pi}{3}} \frac{x}{1+\sin x} \, dx = $$
If $$ y = \sin^{-1} \left( \frac{2x}{1+x^2} \right) + \sec^{-1} \left( \frac{1+x^2}{1-x^2} \right) $$ then the value of $$ \frac{dy}{dx} $$ at $$ x = \sqrt{3} $$ is
The area bounded by the curve \(x = 2 - y - y^2\) and the Y-axis is
The value of \(\sin^2 5^\circ + \sin^2 10^\circ + \dots + \sin^2 85^\circ + \sin^2 90^\circ =\)
If the vectors \(m\hat{i} + m\hat{j} + n\hat{k}, \hat{i} + \hat{k}, n\hat{i} + n\hat{j} + p\hat{k}\) lie in a plane then...
The population increases from \(40000\) to \(80000\) in \(20\) years, then the population in another \(40\) years will be

The p.d.f. of a continuous random variable \(X\) is \(f(x)\).
\[ f(x)= \begin{cases} \dfrac{x^2}{18}, & -3 \le x \le 3 \\ 0, & \text{otherwise} \end{cases} \] Then find \(P(|X|<2)\).

Which of the following statements has the truth value \(T\)?
A. Cube roots of unity are in Geometric Progression and their sum is \(1\) 
B. \[ 4 + 7 > 10 \iff 2 + 8 < 10 \] 
C. \[ \exists x \in \mathbb{N} \text{ such that } x^2 - 3x + 2 = 0 \text{ and } \exists n \in \mathbb{N} \text{ such that } n \text{ is an odd number} \] 
D. \[ 3+i \text{ is a complex number } \; \text{or} \; \sqrt{2}+\sqrt{3}=\sqrt{5} \]

If the function \(f(x)\) is continuous in \([0, \pi]\) then \(a - b =\)
If the pair of straight lines \(xy - x + y - 1 = 0\) and the line \(x + ky - 3 = 0\) are concurrent, then the value of \(k\) is equal to
If \(y + \frac{d}{dx}(xy) = x(\sin x + \log x)\) then
The angle between the lines \(3x = 2y = -z\) and \(-x = 6y = -4z\) is
For a real number \(x\), \([x]\) denotes the greatest integer less than or equal to \(x\). Then the value of \(\left[ \frac{1}{2} \right] + \left[ \frac{1}{2} + \frac{1}{100} \right] + \left[ \frac{1}{2} + \frac{2}{100} \right] + \dots + \left[ \frac{1}{2} + \frac{99}{100} \right] =\)
If the sum of the squares of the distances of a point \(P(x, y, z)\) from the three co-ordinate axes is \(324\), then the distance of point \(P\) from the origin is ....
The degree of the differential equation \(\frac{d^2y}{dx^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log \left( \frac{d^2y}{dx^2} \right)\) is
A coin is tossed until one head appears or a tail appears \(4\) times in succession. The probability distribution of the number of tosses is