List of top Mathematics Questions

If $x^{2}+\alpha y^{2}+2 \beta y=a^{2} \quad$ represents a pair of perpendicular lines, then $\beta$ equals to

Which of the following is not a correct statement ?

For all complex numbers z of the form 1 + i$\alpha$, $\alpha$ $\epsilon$ R, if z = x + iy, then :

Let $z\ne-i$ be any complex number such that $\frac{z-i}{z+i}$ is a purely imaginary number. Then $z+\frac{1}{z}$ is :

Let $A$ and $B$ be two events such that $P\left(\overline{A\cup B}\right)=\frac{1}{6}, P\left(\overline{A \cap B}\right)=\frac{1}{4}$ and $P\left(\bar{A}\right)=\frac{1}{4}$ where $\overline{A}$ stands for the complement of the event $A$. Then , the events $A$ and $B$ are

A number $x$ is chosen at random from the set $\{1, 2, 3, 4, ....., 100\}$. Define the event: $A =$ the chosen number $x$ satisfies $\frac{\left(x-10\right)\left(x-50\right)}{\left(x-30\right)}\ge0$ Then $P(A)$ is :

The domain of the function $f(x) = \sqrt {\cos x}$ is

Let $a ,b,c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c = 0$ and $5bx + 2by+ d = 0$ lies in the fourth quadrant and is equidistant from the two axes, then

In a class of $60$ students, $25$ students play cricket and $20$ students play tennis, and $10$ students play both the games. Then, the number of students who play neither is

A bag contains $n + 1$ coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $\frac{7}{12}$, then the value of $n$ is.

$AB$ and $CD$ are $2$ line segments ; where $A(2,3,0),B (6, 9, 0), C(-6, -9, 0). P $ and $Q$ are midpoint of $AB$ and $CD$, respectively and $L$ is the midpoint of $PQ$. Find the distance of $L$ from the plane $3x + 4z + 25 = 0$

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is :

If $\sqrt{y}=cos^{-1}x,$ then it satisfies the differential equation $\left(1-x^{2}\right)-x \frac{dy}{dx}=c,$ where $c$ is equal to

The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane $2 x - y + z+ 3 = 0$ is the line.

A fair six-faced die is rolled $12$ times. The probability that each face turns up twice is equal to

The integral $\int x \,cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \,dx\, \left(x > 0\right)$ is equal to :

Let $X_{n}=\left\{z=x+i y:|z|^{2} \leq \frac{1}{n}\right\}$ for all integers $n \geq 1$. Then, $\overset{\infty}{\underset{n=1}{\cap}}$ is

If $ A=\left[ \begin{matrix} 2 & -1 \\ 1 & 2 \\ \end{matrix} \right], $ then $ {{A}^{2}}+2A-3I= $

The mean and variance of a random variable $X$ having a binomial distribution are $4$ and $2$ respectively, find the value of $ P(X=1) $ .

Convert $ \frac {(i+1)}{(\cos \,(\frac{\pi}{4}) -i\,\sin (\frac {\pi} {4})} $ in polar form?

A manufacturer has $ 500\text{ }L $ of a $ 10\% $ solution of acid, find the range of 40% acid to be added to it , such that the acid content in the resultant mixture will be more than $ 15\% $ but less than $ 20\% $ .

Discuss the continuity of the function $ f(x)=\sin 2x-1 $ at the point $ x=0, $ and $ x=\pi $ .

Find the value of $ \sin \,(2\,{{\tan }^{-1}}x),\,|x|\le 1 $

Solve $ {{\sin }^{-1}}\,2x+{{\cos }^{-1}}\,2x+2\,{{\tan }^{-1}}\,x=\pi $

Find $ \frac{dy}{dx}, $ if $ y={{\sin }^{2}}x+{{\cos }^{4}}x $