List of top Mathematics Questions

The probability that a leap year will have 53 Fridays or 53 Saturday is

\[\log(\sin 1^\circ) \times \log(\sin 2^\circ) \times \ldots \times \log(\sin 90^\circ) \text{ is}\]

If \( x = t \) and \( y = \frac{1}{t} \), then \(\frac{dy}{dx}\) is equal to:

The plane which bisects the line segment joining the points (-3,-3,4) and (3,7,6) at right angles, passes through which one of the following points ?

The mean and the median of the following ten numbers in increasing order $10, 22, 26, 29, 34, x 42, 67, 70,\, y$ are $42$ and $35$ respectively, then $\frac{y}{x}$ is equal to :

The plane through the intersection of the planes $x + y + z = 1$ and $2x + 3y - z + 4 = 0$ and parallel to y-axis also passes through the point :

Two integers are selected at random from the set {1, 2,...., 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :

The sum $1+ \frac{1^{3} +2^{3}}{1+2} + \frac{1^{3}+2^{3}+3^{3}}{1+2+3} +.... + \frac{1^{3} +2^{3}+3^{3} +....+15^{3}}{1+2+3+...+15} - \frac{1}{2} \left(1+2+3+...+15\right)$

Let $Z$ be the set of integers. If $A \, = \, \{ x \in Z : 2^{ (x+2) (x^2 - 5x + 6)} \}=1$ and $B \, = \, \{ \, x \in Z: -3 <2x -1 <9 \}$, then the number of subsets of the set $A \times B$, is :

Let $A$ and $B$ be two invertible matrices of order $3 \times 3$. If $\text{det} (ABA^T) = 8$ and $\text{det} (AB^{-1}) = 8$, then $\text{det} (BA^{-1} BT) $ is equal to :

The value of the integral $\int \limits^{2}_{-2} \frac{\sin^{2}x}{\left[\frac{x}{\pi}\right] + \frac{1}{2}} dx $ (where [x] denotes the greatest integer less than $^{20}C_r$ or equal to x) is :

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 :

Let $A(4,-4)$ and $B(9,6)$ be points on the parabola, $y^2 + 4x$. Let $C$ be chosen on the arc $AOB$ of the parabola, where $O$ is the origin, such that the area of $\Delta ACB$ is maximum. Then, the area (in s units) of $\Delta ACB$, is :

The value of $\int\limits^{\pi/2}_{-\pi/2} \frac{dx}{\left[x\right]+\left[\sin x\right]+4} $ where [t] denotes the greatest integer less than or equal to t, 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

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?

Evaluate the integral. \(\displaystyle\int^{3}_{2}x^4dx\)

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: