List of top Mathematics Questions

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

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

The least value of $2x^2 + y^2 + 2xy + 2x - 3y + 8$ for real numbers $x$ and y 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 variance of first $20$ natural numbers is

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 ?

The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is

If the four points with position vectors $-2\hat{i}+\hat{j}+k, \hat{i} +\hat{j}+\hat{k}, \hat{j}-\hat{k}, $ and $\lambda\hat{j}+\hat{k}$ are coplanar, then $\lambda=$

For all real values of \(a_0, a_1, a_2, a_3\) satisfying \(a_{0}+\frac{a_{1}}{2}+\frac{a_{2}}{3}+\frac{a_{3}}{4}=0\), the equation \(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}=0\) has a real root in the interval

The area of the region bounded by the curve $y = x^3$, its tangent at $(1, 1)$ and $x-axis$ is

A fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

If $\sin^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\frac{x^{4}}{8}+...\right)-\frac{\pi}{6}$ where $\left|x\right| < 2$ then the value of $x$ is

If $f \left(x\right)=\begin{vmatrix}1&x&x+1\\ 2x&x\left(x-1\right)&\left(x-1\right)x\\ 3x\left(x-1\right)&x\left(x-1\right)\left(x-2\right)&\left(x-1\right)\end{vmatrix}$ Then $f (100)$ is equal to

The value of \(\lambda\), such that the following system of equations \(2x - y - 2z = 2\); \(x - 2y + z = -4\); \(x + y + \lambda z = 4\) has no solution, is

Area of the region bounded by $y = |x|$ and $y = -|x| + 2$ is

The trigonometric equation $\sin^{-1}x = 2 \sin^{-1}2a$ has a real solution if

If $f:[0, \pi / 2) \rightarrow R$ is defined as $f(\theta)=\begin{vmatrix}1 & \tan \theta & 1 \\ -\tan \theta & 1 & \tan \theta \\ -1 & -\tan \theta & 1\end{vmatrix}$. Then, the range of $f$ is