List of top Mathematics Questions

The sequence $\log \,a$, $\log \frac{a^{2}}{b}, \,\log \frac{a^{3}}{b^{2}}, ...........$ is

$^{15}C_{3} +\,^{15}C_{5} + .. ...+\,^{15}C_{15} $ will be equal to

The value of $ \sum\limits_{n=0}^{\infty }{\frac{{{n}^{2}}+4}{n\,!}} $ is equal to

The equation of the plane perpendicular to the $z$-axis and passing through $ (2,-3,5) $ is

If $ {{4}^{x}}={{16}^{y}}={{64}^{z}}, $ then

If $A$ is a square matrix of order $3$ and a is a real number, then determinant $ |\alpha \,\,\,A| $ is equal to

The value of the integral $ \int{\frac{1}{{{e}^{2x}}+{{e}^{-2x}}}}\,\,dx $ is equal to

The number of straight lines which can be drawn through the point $ (-2,\,\,\,2) $ so that its distance from $ (-3,\,\,1) $ will be equal $6$ units is

The ratio in which ZX-plane divides the line segment AB joining the points $ A(4,2,3) $ and $ B(-2,4,5) $ is equal to

The contrapositive statement of the proposition $ p\to \sim q $ is

A force $2$ units acts along the line $ x-4=y-5. $ The moment of the force about the point $ (1,\,\,1) $ along $Z-axis$ is equal to

The value of $k$ for which the equation $ {{x}^{2}}-4xy-{{y}^{2}}+6x+2y+k=0 $ represents a pair of straight lines is

If $ f(x)\,=kx\,-\,\cos \,x $ is monotonically increasing for all $ x\in R, $ then

The three distinct points $ A(at_{1}^{2},\,2a{{t}_{1}}),\,\,B(at_{2}^{2},\,\,2a{{t}_{2}}) $ and $ C(0,\,a) $ (where $a$ is a real number) are collinear, if

The equation of the line parallel to x-axis and tangent to the curve $ y=\frac{1}{{{x}^{2}}+2x+5} $ is

The value of $ \cos \frac{\pi }{7}.\,\cos \frac{2\pi }{7}.\,\cos \frac{4\pi }{7} $ is equal to

$\begin{vmatrix} {Sin \alpha}&{ \cos\alpha} &Sin ({\alpha+ \delta })\\ {Sin \beta}&{ Cos \beta}& Sin ({\beta+\delta}) \\ {Sin \gamma}&{ Cos \gamma}&Sin ({\gamma+\delta})\\ \end{vmatrix} $ is equal to

$G = \left\{\begin{bmatrix} x&x \\[0.3em] x & x \end{bmatrix} , x \text{ is a nonzero real number} \right\}$ is a group with respect to matrix multiplication. In this group, the inverse of $\begin{bmatrix} \frac{1}{3} &\frac{1}{3} \\[0.3em] \frac{1}{3} & \frac{1}{3} \end{bmatrix}$ is

Suppose $ P(2,\,y,\,z) $ lies on the line through $ A(3,-1,4) $ and $ B(-4,2,1) $ . Then, the value of z is equal to

In $n$ is an odd positive integer and $(1+x +x^2 +x^3)^n =\displaystyle\sum_{r=0}^{3n} a_rx^r$ then $a_0 -a_1+a_2-a_3 +\dots -a_{3n}$ is equal to

Angles of elevation of the top of a tower from three points (collinear) $A, B$ and $ C$ on a road leading to the foot of the tower are $30^\circ$, $45^\circ$ and $60^\circ$ respectively. The ratio of $AB$ to $BC$ is

The derivative of $tan ^{-1}[\frac{Sin x}{1+ Cos x}]$ with respect to $tan^{-1}[\frac{Cos x}{1+Sin x}]$ is

The value of $\left| \frac{1+ i \sqrt{3}}{\left( 1 + \frac{1}{i+1}\right)^2} \right|$ is

The sum of the first n terms $ \frac {1^2}{1} +\frac {1^2+2^2}{1+2}+ \frac {1^2 +2^2+3^2}{1+2+3}+$ $\dots$ is

If $\alpha , \beta ,\gamma$ are the roots of $x^3-2x+1=0$, then the value of $(\sum \frac {1} {\alpha +\beta -\gamma}$) is