List of top Mathematics Questions

Simplify \( \sqrt{2} + \sqrt{2} + 2 \cos 4\theta = \)
Evaluate the integral \( \int e^x \left( \frac{1 - x}{1 + x^2} \right)^2 dx = \)
If \( \sin(y + z - x) \), \( \sin(z + x - y) \), and \( \sin(x + y - z) \) are in A.P., then
The approximate value of the function \( f(x) = x^3 + 5x^2 - 7x + 10 \) at \( x = 1 \) is
If the sum of the slopes of the pair of lines given by \( 4x^2 + 2hxy - 7y^2 = 0 \) is equal to the product of the slopes, then \( h \) is
If \( f(x) = 2x^2 + bx + c \), \( f(0) = 3 \) and \( f(2) = 1 \), then \( (f \circ f)(1) = \)
If \( CP \) and \( CD \) is a pair of semi-conjugate diameters of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \), then \( CP^2 + CD^2 = \)
A line makes angles \( \alpha \), \( \beta \), \( \gamma \) with the co-ordinate axes, then \( \cos 2\alpha + \cos 2\beta + \cos 2\gamma \) is equal to
The solution of the differential equation \( \log \left( \frac{dy}{dx} \right) = 9x - 6y + 6 \) is (given that \( y = 1 \) when \( x = 0 \))
If \( y = \tan^{-1} \left( \frac{x - \sqrt{1 - x^2}}{x + \sqrt{1 - x^2}} \right) \), then \( \frac{dy}{dx} \) is
The number of solutions of the equation \( \tan x + \sec x = 2 \cos x \) lying in the interval \( [0, 2\pi] \) is
Radium decomposes at a rate proportional to the amount present. If half the original amount disappears in 1600 years, then the percentage loss in 100 years is
The derivative of \( f(\tan x) \) w.r.t. \( g(\sec x) \) at \( x = \frac{\pi}{4} \), where \( f'(1) = 2 \) and \( g'( \sqrt{2} ) = 4 \), is
In a single throw of three dice, the probability of getting a sum of at least 5 is
If \( y = e^{\sin(\cosec^{-1}x)} \), then \( \dfrac{dy}{dx} \) is
If \( f(x) = e^{x}g(x) \), \( g(0) = 4 \), and \( g'(0) = 2 \), then \( f'(0) = \)
If \( f(x) = \frac{3x+4}{5x-7} \), \( x \neq \frac{7}{5} \), and \( g(x) = \frac{7x+4}{5x-3} \), \( x \neq \frac{3}{5} \), then \[ (g \circ f)(3) = \]
The cumulative distribution function of a continuous random variable \( X \) is given by \( F(X = x) = \dfrac{\sqrt{x}}{2} \). Then \( P(X>1) \) is

If \(f(x) = \dfrac{2x + 3}{3x - 2}\), \( x \neq \dfrac{2}{3} \), then \( f \circ f \) is{

With usual notations in \( \triangle ABC \), if \( C = 90^\circ \), then \( \tan^{-1}\left(\dfrac{a}{b+c}\right) + \tan^{-1}\left(\dfrac{b}{c+a}\right) \) is
If \( u = \tan^{-1}\!\left(\dfrac{1+x^2-1}{x}\right) \) and \( v = \tan^{-1}\!\left(\dfrac{2x(1-x^2)}{1-2x^2}\right) \), then \( \dfrac{du}{dv} \) at \( x = 0 \) is
If the elements of matrix \( A \) are the reciprocals of the elements of the matrix \( \begin{pmatrix} 1 & \omega & \omega^2 \\ \omega & \omega^2 & 1 \\ \omega^2 & 1 & \omega \end{pmatrix} \), where \( \omega \) is a complex cube root of unity, then
Evaluate \( \int \frac{x^2}{(x+1)^2(x+2)^2} \, dx \)
Evaluate \( \sin^{-1}\left(\frac{1}{2}\right) + \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) + \cot^{-1}\left(-\frac{1}{\sqrt{3}}\right) \)
If \( P(A) = \frac{2}{5}, \, P(B) = \frac{1}{4}, \, P(A \cup B) = \frac{1}{2}, \) then \( P(A' \cup B') = \)