List of top Mathematics Questions

If $\frac{z-1}{z+1}$ is purely imaginary, then

If $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \left(a > b\right)$ and $x^{2} - y^{2} = c^{2}$ cut at right angles, then

If $\left(\frac{3}{2}+i\frac{\sqrt{3}}{2}\right)^{50} \, =3^{25} \left(x+iy\right),$ where $x$ and $y$ are real, then the ordered pair $(x,y)$ is

If $ f(x) = log_x $ { $ ln(x) $ },then $ f'(e) $ is equal to

If $ \begin{vmatrix}\left(x+a\right)&b&c\\ a&\left(x+b\right)&c\\ a&b&\left(x+c\right)\end{vmatrix} $ = 0 , then $ x $ =

If the sum of first $ n $ natural numbers is $ 1/5 $ times the sum of their squares, then $ n $ is equal to

If $ log_{10}2, log_{10}(2^x-1) $ and $ log_{10}(2^x+3) $ are in $AP$, then $x$ =

The inverse of a symmetric matrix is

If the $ (3r)^{th} \,and\, (r+2)^{th} $ terms in the binomial expansion of $ (1 + x)^{2n} $ are equal, then

The value of the integral $ \int ^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \bigg ( x^2 + \log \frac{\pi - x }{ \pi + x } \bigg ) \, \cos \, x \, dx $

If $a_1, a_2, a_3,... $ are in harmonic progression with $a_1 = 5$ and $ a_{20} = 25.$ Then, the least positive integer $n$ for which $a_n < 0,$ is

If $ lim_{ x \to \infty} \bigg( \frac{x^2 + x + 1}{x + 1} - ax - b \bigg) $ = 4, then

If $X$ and $Y$ are two events such that $P (X | Y )=\frac{1}{2}, P(X | Y)=\frac{1}{3.} \, and \, P(X \cap Y)\frac{1}{6}$ Then, which of the following is/are correct?

Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2x-y=1.$ The points of contacts of the tangents on the hyperbola are

Four fair dice $D_1, D_2, D_3$ and $D_4$ each having six faces numbered $1, 2, 3, 4, 5$ and $6$ are rolled simultaneously. The probability that D$_4$ shows a number appearing on one of $D_1, D_2$ and $D_3$, is

The point $P$ is the intersection of the straight line joining the points $Q(2, 3, 5)$ and $R (1, - 1, 4)$ with the plane $5x - 4y - z = 1$. If $S$ is the foot of the perpendicular drawn from the point $T (2,1, 4)$ to $QR$, then the length of the line segment $PS$ is

The equation of a plane passing through the line of intersection of the planes $x + 2y + 3z = 2$ and $x - y + z = 3$ and at a distance $\frac{2}{\sqrt 3}$ from the point $(3,1, -1)$ is

If $\overrightarrow{a} $ and $ \overrightarrow{b}$ are vectors such that $| \overrightarrow{a}+\overrightarrow{b} |=\sqrt{29}$ and $\overrightarrow{a}\times(2\widehat{i}+3\widehat{j}+4\widehat{k})=(2\widehat{i}+3\widehat{j}+4\widehat{k})\times\overrightarrow{b},$ then a possible value of $ (\overrightarrow{a}+\overrightarrow{b})(-7\widehat{i}+2\widehat{j}+3\widehat{k} is $

A ship is fitted with three engines $ E_1, E_2$ and $E_3 $ The engines function independently of each other with respective probabilities $\frac {1}{2}, \frac {1}{4}$ and $\frac{1}{4}$. For the ship to be operational at least two of its engines must function. Let $X$ denotes the event that the ship is operational and let $ X_1 , X _2 $ and $ X_ 3 $ denote, respectively the events that the engines $ E_1 , E_2$ and $E_3 $ are functioning. Which of the following is/are true?

The fixed point $P$ on the curve $ y = x^2 - 4x + 5 $ such that the tangent at $ P $ is perpendicular to the line $ x + 2y = 7 $ is given by

The value of $^{10}C_1+^{10}C_2+^{10}C_3+....+^{10}C_9 $ is

The domain and range of \( f(x) = \sin^{-1}(x) \) are:

If \( S = \sum_{n=0}^{\infty} \frac{(\log x)^{2n}}{(2n)!} \), then \( S \) is equal to