List of top Mathematics Questions

Option : No Option Orientation : Vertical If the angle between the tangents drawn to the circle $x^2 + y^2 -12 x - 16y = 0$ at the points w here the line $5y = 5x + k$ cut the circle is $60^{\circ}$ , then the value of $k$ is
If $A = \begin{bmatrix}k/2&0&0\\ 0&1/3&0\\ 0&0&m/4\end{bmatrix} $ and $A^{-1} = \begin{bmatrix}1/2&0&0\\ 0&1/3&0\\ 0&0&1/4\end{bmatrix}$ then $ k + l + m = $
For the matrix $A = \begin{pmatrix}3&-3&4\\ 2&-3&4\\ 0&-1&1\end{pmatrix}, A^{-1} = $
A random variable X has the following probability distribution The variance of this random variable is
$ \displaystyle \lim_{x \to 0} \frac{a^{\tan \, x} - a^{\sin \, x}}{\tan \, x - \sin \, x}$ is equal to $(a > 0)$
$\lim_{x \to \infty} \frac{3x^3 + 2x^2 - 7x + 9 }{4x^3 + 9x - 2 }$ is equal to
In a triangle ABC if $\cos \, A + \cos \, B + \cos \, C = \frac{3}{2}$ , then the triangle is
The value of the integral $\int^{\pi}_0 \frac{x \tan \, x}{\sec \, x + \tan \, x} dx $ is equal to
The value of $\sin^{4} \frac{\pi}{8} + \sin^{4} \frac{3 \pi}{8} + \sin^{4} \frac{5\pi}{8} + \sin^{4} \frac{7\pi}{8} $ is
If two circles of radii $r_1$ and $r_2$ touch externally then length of a common tangent is
If $I = \int^\limits{\pi/4}_{0} (\sqrt{\tan \, x } + \sqrt{\cot \, x} ) dx $ then value of I is
From the top of a lighthouse, the angles of depression of two stations on the oposite sides of it at a distance d apart are $\alpha$ and $\beta$. The height of the lighthouse is
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3 - 3x^2 + 3x + 7 = 0$, and w is cube root of unity, then the value of $\frac{\alpha-1}{\beta-1} + \frac{\beta-1}{\gamma-1} + \frac{\gamma-1}{\alpha-1}$ is equal to
The perimeter of the locus represented by arg $\left( \frac{z + i}{z-i}\right) = \frac{\pi}{4}$ is equal to
The number of solutions of the equation $\sin \, 2x + 2 \, \sin \, x - \cos \, x - 1 = 0$ in the range $0 \leq x \leq 2 \pi$ is
If $\cos^{-1} \frac{3}{5} + \cos^{-1} \frac{12}{13} = \cos^{-1} k$, then the value of $k$ is
If $\cos \, 3x \, \cos \, 2x \, \cos \, x = \frac{1}{4} $ and $0 < x < \frac{\pi}{4}$, then the value of $x$ is
If $(1 + \tan \, 1^{\circ})(1 + \tan \, 2^{\circ}) ...... (1 + \tan \, 45^{\circ}) = 2^n$, then n is
The interval in which the function $f\left(x\right) = \frac{4x^{2}+1}{x}$ is decreasing is :
If the parabola $y^2 = 4ax$ passes through the point $(1, -2)$, then the tangent at this point is

There are two integers 34041 and 32506, when divided by a three-digit integer $n$, leave the same remainder. What is the value of $n$?

What is the remainder when $1!+2!+3!+\cdots+100!$ is divided by $7$? 

If $(67^{67}+67)$ is divided by $68$, the remainder is: 

Find the value of $1(1!)+2(2!)+3(3!)+\cdots+20(20!)$. 

Find the remainder when  \[6^{\underbrace{66\cdots6}_{100 \text{ times}}}\] is divided by 10.