List of top Mathematics Questions

The number \(81\) is the coefficient of \( x^k \) in the binomial expansion of \( \left(x^2 + \frac{3}{x}\right)^4 \), \( x \neq 0 \). Then the value of \( k \) equals

If the equation of the sphere through the circle \( x^2 + y^2 + z^2 = 9; \; 2x + 3y + 4z = 5 \) and through the point \( (1,2,3) \) is \( 3(x^2 + y^2 + z^2) - 2x - 3y - 4z = C \), then the value of \( C \) is

In a chess tournament, assume that your probability of winning a game is 0.3 against level 1 players, 0.4 against level 2 players and 0.5 against level 3 players. It is further assumed that among the players 50% are at level 1, 25% are at level 2 and the remaining are at level 3. Suppose that you win the game. Then the probability that you had played with level 1 player is

The coefficient of \( x^3 \) in the expansion of \( (1 + x + 2x^2)(1 - 2x)^5 \) is

The constant term in the expansion of \( \left(x^2 - \frac{2}{x}\right)^6 \) is

A sum of Rs. 280 is to be used to award four prizes. If each prize after the first prize is Rs. 20 less than its preceding prize, then the value of the fourth prize is

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of red ball, the number of blue balls must be

A pair of fair dice are rolled together. The probability of getting a total of 8 is

The area of the region bounded by the curves \( y = |x - 2| \), \( x = 1 \), \( x = 3 \) and \( y = 0 \) is:

If the mean of the first \(n\) odd numbers is \( \frac{n^2}{81} \), then \(n\) equals

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is

The area enclosed between the curves \( y = 2x^2 + 1 \) and \( y = x^2 + 5 \) is:

The equation of the tangent to the curve given by \( x^2 + 2x - 3y + 3 = 0 \) at the point \( (1,2) \) is

The solution of the differential equation \( 5y\,dx = 2x\,dy \) passing through the point \( (1,1) \) is:

The maximum value of \( y = \left(\frac{1}{x}\right)^x \), \( x > 0 \) is

The value of the integral \( \int_{0}^{\pi} \frac{\cos x}{1+\sin^2 x} \, dx \) is

If \( x = 2\cos t - \cos 2t \) and \( y = 2\sin t - \sin 2t \), then \( \frac{dy}{dx} \) at \( t = \frac{\pi}{2} \) is

The value of \( \tan\left[ \sin^{-1}\left(\frac{-1}{\sqrt{2}}\right) \right] \) is

Let \( z_1 = 1 + i\sqrt{3} \) and \( z_2 = 1 + i \), then \( \arg\left( \frac{z_1}{z_2} \right) \) is

The complex number \( \sqrt{2}\left[ \sin \frac{\pi}{8} + i \cos \frac{\pi}{8} \right]^6 \) represents

If \( z^2 + z + 1 = 0 \), where \( z \) is a complex number, then the value of \[ \left( z + \frac{1}{z} \right)^2 + \left( z^2 + \frac{1}{z^2} \right)^2 + \left( z^3 + \frac{1}{z^3} \right)^2 + \cdots + \left( z^6 + \frac{1}{z^6} \right)^2 \] is

If \( \sin^{-1} x + \cos^{-1} 2x = \frac{\pi}{6} \), then the value of \( x \) is

If \( (x,y,z) \) is the solution of the equations \[ x - y - 2z = 3, 2x + y + 4z = 5, 4x - y - 2z = 11, \] then the value of \( y \) equals

If \[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \] is the inverse of the matrix \[ \begin{pmatrix} 1 & 5 \\ 7 & -3 \end{pmatrix}, \] then \( d \) equals