List of top Mathematics Questions

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If $99$ more identical balls are addded to the total number of balls used in forming the equilaterial triangle, then all these balls can be arranged in a square whose each side contains exactly $2$ balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is :
The value of $\cot\left(\sum\limits^{19}_{n=1} \cot^{-1} \left(1+ \sum\limits^{n}_{p=1} 2p\right)\right) $ is :
A supporting element on a curved opening is called as
A regular hexagonal pyramid is sliced by a plane such that it passes through the centre of its axis. How many additional edges shall be created.
The equation of the plane containing the $\frac{x}{2} = \frac{y}{3} =\frac{z}{4} $ and perpendicular to the plane containing the straight lines $\frac{x}{3} = \frac{y}{4} = \frac{z}{2} $ and $\frac{x}{4} = \frac{y}{2} = \frac{z}{3} $ is :
The sum of the values of x satisfying \(\tan(\frac{\pi}{4}+x)+\tan(\frac{\pi}{4}-x)=2\) in the interval \([0,2\pi]\) is:
If a, b, c are odd positive integers, then number of integral solutions of a + b + c = 13, is
The sum of odd integers from 1 to 2001 is:
The function given by: xmyn = (x + y)m+n is:
A circle of maximum possible size is cut from a square sheet. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be area of the final square?
A class has n students, we have to form a team of the students including at least two students and also excluding at least two students. The number of ways of forming the team is
The differential equation of all non vertical lines in a plane is:
Evaluate the integral. \(\displaystyle\int^{3}_{2}x^4dx\)
The average age of 20 students in a class is 15 years. If the teacher’s age is including, the average increases by 1. What is the teacher’s age?
Let the following system of equations kx + y + z =1x + ky + z = kx + y + kz=k2Has no solution. Find
Area bounded by\( y=x^3 , y=8\) and \(x=0\) is
You have a 9 x 9 x 9 cm box. How many cubes of side 5 cm will you be able to fit inside it?
A determinant is chosen at random from the set of order 2 with elements 0 or 1 only. The probability that the determinant chosen non zero is
If \(\int \frac{dx}{x^3 (1+x^6)^{\frac{2}{3}}} = f(x) (1+ x^{6})^{\frac{1}{3}} + C\) where C is a constant of integration, then \(f(x)\) is equal to :
Let $\vec{a} = \hat{i} + \hat{j} + \sqrt{2} \hat{k} , \vec{b} = b_1 \hat{i} + b_2 \hat{j} + \sqrt{2} \hat{k}$ and $\vec{c} = 5 \hat{i} + \hat{j} + \sqrt{2} \hat{k}$ be three vectors such that the projection vector of $\vec{b}$ on $\vec{a}$ , If $\vec{a} + \vec{b}$ is perpendicular to $\vec{c}$, then $| \vec{b}|$ is equal to :
Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is :
The third term of a G.P. is 9. The product of its first five terms is
A circle touching the x-axis at $(3, 0)$ and making an intercept of length $8$ on the y-axis passes through the point :
If cos x = |sin x| then, the general solution is
A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S = {1, 2, 3, 4, 5, 6, 7} and reports that it is even. The probability that it is actually even is