List of top Mathematics Questions

If the normal at $(ap^2, 2ap)$ on the parabola $y^2 = 4ax,$ meets the parabola again at $(aq^2, 2aq)$, then

If $e$ and $e^{'}$ are the eccentricities of hyperbolas $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ and its conjugate hyperbola, then the value of $\frac{1}{e^{2}}+\frac{1}{e^{'2}}$ is

For the hyperbola $\frac{x^{2}}{\cos ^{2} \alpha}-\frac{y^{2}}{\sin ^{2} \alpha}=1$, which of the following remains constant when $\alpha$ varies

The length of the straight line $x - 3y = 1$ intercepted by the hyperbola $x^2 - 4y^2 = 1$ is

The probability that the same number appear on throwing three dice simultaneously, is

Let A be an orthogonal non-singular matrix of order $n$, then the determinant of matrix $AI _{ n }$ ie, $\left| A - I _{ n }\right|$ is equal to

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, odd} or {even, odd, even} is

A coin is tossed n times. The probability of getting head at least once is greater than 0.8, then the least value of n is

For a party $8$ guests are invited by a husband and his wife. They sit in a row for dinner. The probability that the husband and his wife sit together is

If (x +y )sin u = $x^2y^2$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = $

Let $ f(x)=\left\{ \begin{matrix} \frac{\tan x-\cot x}{x-\frac{\pi }{4}}, & x\ne \frac{\pi }{4} \\ a, & x=\frac{\pi }{4} \\ \end{matrix} \right. $ the value of a so that $ f(x) $ is continuous at $ x=\frac{\pi }{4} $

If $\sin^{-1} x + \sin^{-1} y = \frac{\pi}{2}$ , then $\cos^{-1} x + \cos^{-1} y$ is equal to

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

If $ P\left(A\right)=\frac{1}{12}, P\left(B\right)=\frac{5}{12},$ and $P\left(B|A\right) =\frac{1}{15}$ then $p\left(A\cup B\right)$ is equal to

If the rank of the matrix $\begin{bmatrix}-1 &2&5\\ 2&-4&a-4\\ 1&-2&a+1\end{bmatrix}$ is 1, then the value of $a$ is

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

The differential equation of the system of all circles of radius $r$ in the $xy$ plane is

Let $A = \{1,2,3,....., n\}$ and $B = \{a,b,c\}$, then the number of functions from $A$ to $B$ that are onto is

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

The sum of the series $ \frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+... $ upto $ n $ term is

Area of the region satisfying $x \leq 2, y \leq|x|, x-$ axis and $x \geq 0$ is:

If $(\cos \theta+i \sin \theta)(\cos 2 \theta+i \sin 2 \theta) \ldots . .(\cos n \theta+i \sin n \theta)=1$, then the value of $\theta$ is, $m \in N$

If a=\(\log _{2} 3, b=\log _{2} 5, c=\log _{7} 2,\) then \(\log _{140} 63\) in terms of a, b, c is

The solution of the differential equation $\frac{d y}{d x}+\frac{2 y x}{1+x^{2}}=\frac{1}{1+x^{22}}$ is

For all complex numbers $z _{1}, z _{2}$ satisfying $\left| z _{1}\right|=12$ and $\left| z _{2}-(3+4 i )\right|=5$, the minimum value of $\left|z_{1}-z_{2}\right|$ is