List of top Mathematics Questions

The optimal solution of the L.P.P. \( Z = 8x + 3y \) subject to the constraints \( x + y \leq 3 \), \( 4x + y \leq 6 \), \( x \geq 0 \), \( y \geq 0 \) is
The distance of the point \( (2, -1, 0) \) from the plane \( 2x + y + 2z + 8 = 0 \) is
If \( n(X) = 700 \), \( n(A) = 200 \), \( n(B) = 300 \), \( n(A \cap B) = 100 \), where \( X \) is the universal set and \( A \) and \( B \) are subsets of \( X \), then \( n(A' \cap B') = \)
For the probability distribution of \( X \) given below, the variance of \( X \) is
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
In a single throw of three dice, the probability of getting a sum of at least 5 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
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