List of top Mathematics Questions

The sum of the numbers $436.32$, $227.2$ and $0.301$ in appropriate significant figures is

The sum of two positive integers is at most 5. The difference between two times of second number and first number is at most 4. If the first number is x and second number y, then for maximizing the product of these two numbers, the mathematical formulation is

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