List of top Mathematics Questions

If $x^y = \log x$ , then $\frac{dy}{dx} $ at the point where the curve cuts the $x-axis$ is

The derivative of $\cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) $ with respect to $\cot^{-1} \left(\frac{1-3x^{2}}{3x-x^{3}}\right)$ is

The vectors $\vec{a} = x \hat{i} + (x +1) \hat{j} + ( x +2 ) \hat{k} $ $\vec{b} = (x + 3) \hat{i} + (x +4) \hat{j} + ( x + 5 ) \hat{k} $ , and $\vec{c} = (x + 6) \hat{i} + (x + 7 ) \hat{j} + ( x + 8) \hat{k} $ are co-planar for

If $A, B, C, D$ are four points and $\vec{AB} = \vec{DC}$ , then $\vec{AC} + \vec{BD} = $

If $a= 5, b = 13 , c = 12$ in $\Delta ABC$, then $\tan \frac{B}{4}$ is

If $y = \tan^{-1} ( \sec x - \tan x) $, then $ \frac{dy}{dx} = $

If $\sqrt{1-x^{2} } + \sqrt{1- y^{2}} =x -y $, then $\frac{dy}{dx} = $

The value of $[ \vec{a} - \vec{b} \,\,\,\,\,\, \vec{b} - \vec{c} \,\,\,\,\,\, \vec{c} - \vec{a} ]$ where $|\vec{a}| = 1 , |\vec{b} | = 5 , |\vec{c}| = 3 $

The function $f(x) = \begin{cases} x^2 & \quad \text{for } x < 1\\ 2 - x & \quad \text{for } x \geq 1 \end{cases}$ is

If \( A(\theta) = \left[ \begin{matrix} 1 & -\tan \theta \\ \end{matrix} \right] \) and \( AB = 1 \), then \[ (\cos \theta)B \] is equal to

If the probability density function of a random variable \( X \) is \( f(x) = \frac{x}{2} \) for \( 0 \leq x \leq 2 \), then \[ P(X>1.5 \mid X>1) \] is equal to

If \( x = -5 \) is a root of the equation \[ \begin{vmatrix} 2x+1 & 4 & 8 \\ 2 & 2x & 2 \\ 7 & 6 & 2x \end{vmatrix} = 0 \] then the other roots are

If the rank of the matrix \[ \begin{pmatrix} -1 & 2 & 5 \\ 2 & -4 & -4 \\ 1 & -2 & a + 1 \end{pmatrix} \] is 1, then the value of \( a \) is

A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even}or {even, odd} is

If \( P(A) = \frac{1}{2}, P(B) = \frac{5}{12} \) and \( P(B/A) = \frac{1}{15} \), then \[ P(A \cup B) \] is equal to

If \( x \sin \left( \frac{y}{x} \right) \, dy = \sin \left( \frac{y}{x} \right) - x \, dx \) and \( y(1) = \frac{\pi}{2} \), then the value of \( \cos \left( \frac{y}{x} \right) \) is

The function \( f(x) = x^2 e^{-x} \), \( x>0 \). Then the maximum value of \( f(x) \) is

The value of \( \int_0^\infty \frac{dx}{(a^2 + x^2)^7} \) is equal to

The product of all values of \( \cos(\alpha) + i \sin(\alpha) )^{3/5} \) is equal to

The imaginary part of \( \frac{(1+i)^2}{i(2i-1)} \) is

If \( \vec{a} \) and \( \vec{b} \) are two unit vectors, then the vector \[ (\vec{a} + \vec{b}) \times (\vec{a} \times \vec{b}) \] is parallel to the vector

If \( \theta \) is the angle between the lines \( AB \) and \( AC \) where A, B, and C are the three points with coordinates \( (1, 2, -1) \), \( (2, 0, 3) \), \( (3, -1, 2) \) respectively, then \[ \sqrt{62} \cos \theta \] is equal to

If \( H \) is the harmonic mean between \( P \) and \( Q \), then the value of \[ \frac{H}{P} + \frac{H}{Q} \] is

The simultaneous equations \( Kx + 2y = 1 \), \( K(1 - y) - 2x = 2 \) and \( K + 2y = 3 \) have only one solution when

If \( b^2 \geq 4ac \) for the equation \( ax^4 + bx^2 + c = 0 \), then all the roots of the equation will be real if