List of top Mathematics Questions

A batsman has a certain average of runs for 11 innings. In the 12\(^{\text{th}}\) inning. He makes a score of 90 runs, thereby increasing his average by 5. His new average is:

Which of the following numbers is a perfect square?

A sum of money at simple interest doubles itself in 8 years. What is the rate of interest per annum?

A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them after six months with an amount equal to that B. In what proportion should the profit at the end of one year be distributed among A, B and C?

If A : B = 2 : 3 and B : C = 4 : 5, find the ratio A : C.

Find the difference between the place value and the face value of the digit 7 in the number 4782.

Three numbers are in the ratio of 3 : 4 : 5, and their least common multiple (LCM) is 2400. Their highest common factor (HCF) is

The integral \[ \int \frac{x^2}{1+x^6}\,dx \] is equal to:

If the direction ratios of two lines are given by $ l + m + n = 0 $ and $ mn - 2ln + lm = 0 $, then the angle between the lines is:

Identify the correct set of molecules with zero dipole moment:

If the median of the following distribution is 32.5, then find the values of x and y.

In the adjoining figure, the slant height of the conical part is :

If the area of triangle \(ABC\) is \(b^2 - (c - a)^2\), then \(\tan B =\)

In a \(\triangle ABC\), \(a = 1, b = \sqrt{3}\) and \(\angle C = \frac{\pi}{6}\). Then the measure of the third side \(c =\)

The value of \[ \lim_{n \to \infty} \left\{ \frac{1}{n+m} + \frac{1}{n+2m} + \frac{1}{n+3m} + \dots + \frac{1}{n+nm} \right\} \] is:

If \(I = \int \frac{\sin x + \sin^3 x}{\cos 2x} dx = P \cos x + Q \log \left| \frac{\sqrt{2} \cos x - 1}{\sqrt{2} \cos x + 1} \right|\) (where \(c\) is a constant of integration), then values of \(P\) and \(Q\) are respectively

The dimensions of a window are 156 cm \(\times\) 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Three tennis balls are just packed in a cylindrical jar. If radius of each ball is \(r\), volume of air inside the jar is

Find the value of \(k\) if the function \(f(x) = \dfrac{k\sin x}{x}\) is continuous at \(x = 0\) and \(f(0)=3\).

If $P = \begin{pmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{pmatrix}$ is the adjoint of a $3 \times 3$ matrix A and $det(A) = 4$, then $\alpha =$

Let f and g be two differentiable functions satisfying $g'(5) = \frac{3}{4}$, $g(5) = 6$ and $g = f^{-1}$. Then $f'(6) =$

If $\begin{vmatrix} \alpha & \beta & \gamma \\ a & b & c \\ l & m & n \end{vmatrix} = (-1)^K \begin{vmatrix} m & n & l \\ b & c & a \\ \beta & \gamma & \alpha \end{vmatrix}$, then the least value of K is

The coefficient of $x^{3}$ in the expansion of $(1 - \frac{3}{4}x)^{\frac{1}{2}}$ is

\( T_m \) denotes the number of triangles that can be formed with the vertices of a regular polygon of \( m \) sides. If \( T_{m+1} - T_m = 15 \), then \( m = \)

If \( -1 + i \) is a root of the equation \( x^4 + 4x^3 + 5x^2 + 2x - 2 = 0 \), then the real roots of this equation are