List of top Mathematics Questions

The sum of the infinite series $ 1 + (1 + a) x + (1 + a + a^2) x^2 + (1 + a + a^2 + a^3) x^3+ ............$ where $0 < a, x < 1$ is

The sum of the infinite series $\frac{1}{2}\left(\frac{1}{3}+\frac{1}{4}\right)-\frac{1}{4}\left(\frac{1}{3^{2}}+\frac{1}{4^{2}}\right)+\frac{1}{6}\left(\frac{1}{3^{3}}+\frac{1}{4^{3}}\right)-...$ is equal to

The sum of the divisors of $2^4\cdot 3^3 \cdot 5^3$ is

The sum of squares of deviations for 10 observations taken from mean 50 is 250. The co-efficient of variation is

The sum of an infinite number of terms of a G.P. is 20, and the sum of their squares is 100, then the first term of the G.P. is

The standard variance of 35, 40, 42, 36, 27 :

The standard deviation for the following data is.

The solution of the equation $\frac{dy}{dx}=\sqrt\frac{1-y^2}{1-x^2}$ is

The solution of $x \, dy - y \, dx + x^2 \, e^x \, dx = 0$ is :

The solution of differential equation $\frac{dy}{dx}-3y=sin\,2x$ is

The solution of the differential equation xdy + ydx = 0 is:

The solution of the differential equation $xdy + ydx = xydx$ when $y(1) = 1$ is

The slope of the line touching both the parabolas $ y^2 = 4x$ and $x^2 = - 32y$ is

The sixth term in the expansion of $\left[2^{\log _{2} \sqrt{9^{x-1}+7}}+\frac{1}{2^{\frac{1}{5} \log _{2}\left(3^{x-1}+1\right)}}\right]$ is 84. Then the number of values of $x$ is

The sine of the angle between the vectors $\overrightarrow{i}-2\overrightarrow{j}+3\overrightarrow{k}$ and $2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ is

The shortest distance between the lines $\frac{x-5}{4}=\frac{y-7}{-5}=\frac{z+3}{-5}$ and $\frac{x-8}{7}=\frac{y-7}{1}=\frac{z-5}{-3}$

The shortest distance between the lines $\vec{r}=\left(8+3\lambda\right)\hat{i}-\left(9+16\lambda\right)\hat{j}+\left(10+7\lambda\right)\hat{k}$ and $\vec{r}=15\hat{i}+29\hat{j}+5\hat{k}+\mu\left(3\hat{i}-8\hat{j}-5\hat{k}\right)$ is

The set of intelligent students in a class is

The set of real values of x for which $\log_{0.2} \frac{x +2}{x} \leq 1$ is

The second, third and fourth terms in the binomial expansion $(x+a)^n$ are $240$, $720$ and $1080$, respectively. Find $x$, $a$ and $n$ respectively.

The S.D. of the first n natural numbers is

The relation between a, b, a' and b' such that the two lines ax + by = c and a'x + b'y = c' are perpendicular is

The ratio in which the line $3x + 4y + 2 = 0$ divides the distance between the lines $3x + 4y + 5 = 0$ and $3x + 4y - 5 = 0$ is

The proposition $p \Rightarrow \sim (p \wedge \sim q)$ is

The projection of the line segment joining the points (-1, 0, 3) and (2, 5, 1) on the line whose direction ratios are (6, 2, 3) is