List of top Mathematics Questions

The coefficient of $x^{50}$ in the expansion of $\frac{\left(3-5x\right)}{\left(1-x\right)^{2}}$ equals

The co-efficient of $x^{-12}$ in the expansion of$\left(x+\frac{y}{x^3}\right)^{20}$is

The co-efficient of $x^3$ in the expansion of $(1-x+x^2)^5$ is

The circle $ x^2 + y^2 - 25 = 0$ and $3(x^2 + y^2) - 30x - 40)' + 175 = 0$ touch each other at

The cartesian equation of the line $l$ when it passes through the point $(x_1, y_1, z_1)$ and parallel to the vector $\vec{b}=a\hat{i}+b\hat{j}+c\hat{k}$, is

The bag $'A'$ contains $5$ white and $3$ black balls while the bag $'B'$ contains $4$ white and $7$ black balls. One of the bags is chosen at random and a ball is drawn from it. What is the probability that the ball is white?

The area under the curve $y = | \cos \, x - \sin \, x |, 0 \le x \le \frac{\pi}{2},$ and above x-axis is :

The arithmetic mean of first n odd natural numbers is

The area of the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1 $ is :

The area of the region bounded by the curves y =| x - 2 |, x = 1, x = 3 and the x-axis is

The area of the parallelogram formed by the lines $ax+by+c_1=0, \: ax+by+c_2=0, \: px+qy+r_1=0, \: px+qy+r_2=0$

The area bounded by the line $y - x$ , x-axis and lines $x = -1$ to $x = 2$, is

The area bounded by the parabola $y^2 = 4x$ and the line $2x - 3y + 4 = 0$, in square unit, is

The area in the first quadrant bounded by $y = 4x^2$ , x = 0, y =1 and y = 4 is

The area bounded by the curve $y = x^2$, the normal at (1, 1) and the x-axis is :

The area bounded by the curves y = lnx, y = ln |x|,y = | ln x | and y = | ln |x| | is

The area above the x-axis enclosed by the curves $x^2-y^2 = 0$ and $x^2 + y - 2 = 0$ is

The area bounded by the curve $x = 3y^{2} - 9$ and the line $x = 0$, $y = 0$ and $y = 1$ is

The angle of intersection of the two curves $xy = a^2$ and $x^2 + y^2 = 2a^2$ is

The angle between the pair of tangents drawn from the point (1, 2) to the ellipse $3x^2 + 2y^2 = 5 $ is

The angle between two lines $\frac{x+1}{2} = \frac{y+3}{2} = \frac{z-4}{-1} $ and $\frac{x-4}{1} = \frac{y+4}{2} = \frac{z+1}{2} $ is :

The $A.M., H.M. $ and $G.M.$ between two numbers are $\frac {144} {15}$ 15 and 12,. but not necessarily in this order. Then $H.M., G.M. $ and $A.M.$ respectively are

The 10th common term between the series $3 + 7 + 11 + ......$ and $ 1 + 6 + 11 + ......$ is

The 10th term of the sequence $\sqrt3,\sqrt{12}, \sqrt{27}......... $ is

The $7^{th}$ term in the expansion of $\left(x^{2}+\frac{1}{x^{2}}+2\right)^{n} $ is