List of top Mathematics Questions

Amplitude of the complex number $i\, \sin \bigg( \frac{\pi}{19} \bigg)$ is
The shortest distance between the lines $\frac{ x - 3}{3} = \frac{y-8}{-1}= \frac{z - 3}{1} $ and $\frac{ x + 3}{-3} = \frac{y +7}{2}= \frac{z - 6}{4} $ is
The area in square units bounded by the normal at $(1, 2)$ to the parabola $y^2 = 4x, x$-axis and the curve is given by
If $A = \begin{bmatrix}1&0\\ 1&1\end{bmatrix}$ and $A^8 = aA +bI,$ then $(a , b) = $
If $\int\limits \frac{\cos \, 8x + 1}{ \tan \, 2x - \cot \, 2x} dx = a \, \cos \, 8x + c , $ then $a$ =
The differential equation of the family of parabolas $y^2 = 4ax$, where $a$ is parameter, is
The value of $c$ in Lagrange's theorem for the function $f(x) = \log (\sin \, x)$ in the interval $\left[ \frac{\pi}{6} , \frac{5 \pi}{6} \right]$ is
The maximum area in square units of an isosceles triangle inscribed in an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with its vertex at one end of the major axis is
The medians $AD$ and $BE$ of a triangle with vertices $A(0, b), B(0, 0) $ & $C(a, 0)$ are perpendicular to each other, if
$\int\limits \frac{x^3 -1}{x^3 + x} dx = $
If $A = \begin{bmatrix}a&0&0\\ 0&a&0\\ 0&0&a\end{bmatrix}$, then det(adj A) is
The number of bijective functions from the set $A$ to itself, if $A$ contains $108$ elements is -
A straight line meets the coordinates axes at $A$ and $B$, so that the centroid of the triangle $OAB\, is \, (1, 2)$. Then the equation of the line $AB$ is
Given $5$ line segments of lengths $2, 3, 4, 5, 6 $ units. Then, the no. of triangles that can be formed by joining these segments is
Let $X$ be a random variable with its expectation $ E(X)=3 $ and its variance $ V(X)=2 $ . If $V$ is another random variable defined by $ Y=10X, $ then the ordered pair $ (E(Y),\,V(Y)) $ is equal to
The number of the solutions of the equation $ {{5}^{2x-1}}+{{5}^{x+1}}=250, $ is/are
The integrating factor of the differential equation $\frac{d y}{d x}+\left(3 x^{2} \tan ^{-1} y-x^{3}\right)\left(1+y^{2}\right)=0$is
Let $x_{n}=\left(1-\frac{1}{3}\right)^{2}\left(1-\frac{1}{6}\right)^{2}\left(1-\frac{1}{10}\right)^{2} ........ \left(1-\frac{1}{\frac{n\left(n+1\right)}{2}}\right)^2, n \ge 2.$ Then the value of $\displaystyle \lim_{n \to \infty} x_n$ is
Given that $x$ is a real number satisfying $\frac{5x^{2}-26x+5}{3x^{2}-10x+3} < 0 ,$ then
The least value of $2x^2 + y^2 + 2xy + 2x - 3y + 8$ for real numbers $x$ and y is
The variance of first $20$ natural numbers is
$\left\{x\,\in\,R : \left| \cos\,x\right|\ge \sin\,x\right\} \cap\left[0, \frac{3\pi}{2}\right]= $
If $\omega$ is an imaginary cube root of unity, then the value of the determinant $\begin{vmatrix}1+\omega&\omega^{2}&-\omega\\ 1+\omega^{2}&\omega&-\omega^{2}\\ \omega+\omega^2&\omega&-\omega^{2}\end{vmatrix}$
The value of $2 \cot ^{-1} \frac{1}{2}-\cot ^{-1} \frac{4}{3}$ is
In a certain town, $60\%$ of the families own a car, $30\%$own a house and $20\%$ own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both ?