List of top Mathematics Questions

The two vertices of a triangle are $(4,2,1)$ and $(5,1,4)$. If the centroid is $(5,2,3)$, then the third vertex is

The triplet $(x, y, z)$ is chosen from the set $\{1,2,3,... n\}$, such that $x \le y < z$. The number of such triplets is

The transformation 'orthogonal projection on X- axis' is given by matrix

The three concurrent edges of a parallelepiped represents the vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ such that $[\overrightarrow{a}\,\overrightarrow{b}\,\overrightarrow{c}]= \lambda$. Then the volume of the parallelopiped whose three concurrent edges are the three concurrent diagonals of three faces of the given parallelopiped is

The term independent of $x$ in the expansion of $(x- \frac {3} {x^2})^{18}$

The symbolic form of "(either p) or (not p )" is

The symbolic form of "p and q" is

The sum of two unit vectors is a unit vector. The magnitude of their difference is

The sum of the infinite series $\sin^{-1}\frac{1}{\sqrt2}+\sin^{-1}\left(\frac{\sqrt2-1}{\sqrt6}\right)+\sin^{-1}\left(\frac{\sqrt3-\sqrt2}{\sqrt{12}}\right)+...+\sin^{-1}\left(\frac{\sqrt n-\sqrt{n-1}}{\sqrt{n(n+1)}}\right)$ is

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