List of top Mathematics Questions

The value of $ {{\cos }^{2}}\left( \frac{\pi }{4}+\theta \right)-{{\sin }^{2}}\left( \frac{\pi }{4}-\theta \right) $ is
If the foot of the perpendicular from $ (0,0,0) $ to a plane is $ (1,2,2), $ then the equation of the plane is
$ABC$ is a triangle $G$ is the centroid $ D$ is the mid- point of $BC$. If $A - (2, 3) $ and $G = (7, 5)$, then the point $D$ is
Let $ {{z}_{1}} $ and $ {{z}_{2}} $ be the roots of the equation $ {{z}^{2}}+pz+q=0 $ where p, q are real. The points represented by $ {{z}_{1}},{{z}_{2}} $ and the origin form an equilateral triangle, if
Given $ tan\text{ }A $ and $ tan\text{ B} $ are the roots of $ {{x}^{2}}-ax+b=0 $ . The value of $ {{\sin }^{2}}(A+B) $ is
The probability of choosing a number divisible by $6$ or $8$ from among $1$ to $90$ is
On the set $N$ of all natural numbers define the relation $R$ by $a R b$ if and only if the $G.C.D.$ of $a$ and $b$ is $2$, then $R$ is
When three dice are thrown the probability of getting a $4$ or $5$ so on each of the dice simultaneously is
The condition that the roots of the equation $ {{x}^{3}}+3p{{x}^{2}}+3qx+r=0 $ are in the Arithmetic Progression is:
If a line makes angles $ \frac{\pi }{3} $ and $ \frac{\pi }{4} $ with the $x$ and $y$-axis respectively, then the angle made by the line and $Z$-axis is
If the circles $x^2 + y^2 - 2x - 2y - 7 = 0$ and $x^2 + y^2 + 4x + 2y + k = 0$ cut orthogenally, then the length of the common chord of the circles is
If $A =\begin{bmatrix} {1}&{-1} &{1}\\ {2}&{1}& {-3} \\ {1}&{1}&{1}\\ \end{bmatrix} ,10B \begin{bmatrix} {4}&{2} &{2}\\ {-5}&{0}& {\alpha} \\ {1}&{-2}&{3}\\ \end{bmatrix} $ and $B$ is the inverse of $A$, then the value of $\alpha$ is
The $ x- $ axis, $ y- $ axis and a line passing through the point A (6, 0) form a triangle $ABC$. If $ \angle A=30{}^\circ , $ then the area of the triangle, in sunits is
The number of common tangents to the circles $x^2+y^2=4 $ and $ x^2+y^2-6x-8y-24=0 $ is
The conjugate of the complex number $ \frac {(1+i)^2}{1-i}$ is
The area enclosed by the pair of lines $xy = 0$ , the line $x - 4 = 0$ and $y + 5 = 0$ is
The equation of the plane passing through the points $ (a,0,0),(0,b,0) $ and $ (0,0,c) $ is
The angle between the asymptotes of the hyperbola $x^2 - 3y^2 = 12$ is
The amplitude of $\sin \frac{\pi}{5} + i\left( 1 - \cos \frac{\pi}{5}\right) $
The maximum value of $ f(x) = \frac{\log x}{x} , 0 < x < \infty$ is
If the medians $AD$ and $BE$ of the triangle with vertices $A(0, b), B(0, 0), C(a, 0)$ are mutually perpendicular, then
If $a$ and $ b$ are positive integers such that $a^2 - b^2$ is a prime number, then $a^2 - b^2$ is
The ninth term of the expansion $\left(3x-\frac {1}{2x}\right)^8$ is
A vector perpendicular to the plane containing the points $A (1, -1, 2), B (2, 0, -1), C (0,2,1)$ is
The solution of $Tan^{-1}x+ 2cot^{-1}x=\frac {2\pi}{3}$ is