List of top Mathematics Questions

If $A = \left[\begin{matrix}2&0&0\\ 2&2&0\\ 2&2&2\end{matrix}\right]$, then adj (adj A) is equal to

If $\left[\begin{matrix}2+x&3&4\\ 1&-1&2\\ x&1&-5\end{matrix}\right]$ is a singular matrix, then $x$ is

If for the non-singular matrix $A, A^{2} = I$, then find $A^{-1}$.

If $I_3$ is the identity matrix of order 3, then $I^{-1}_3$ is

If n is an integer and if $ \begin{vmatrix} x^n& x^{n+2}& x^{n+3} \\[0.3em] y^n &y^{n+2} & y^{n+3} \\[0.3em] z^n & z^{n+2}&z^{n+3} \end{vmatrix}=(x-y\,(y-z)\,(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$ then n equals

If the points $\left(a_{1}, b_{1}\right)$, $\left(a_{2}, b_{2}\right)$ and $\left(a_{1} + a_{2}, b_{1} + b_{2}\right)$ are collinear, then

If the system of equations $2x + 3y+5 = 0$, $x + ky + 5 = 0$, $kx - 12y - 14 = 0$ has non-trivial solution, then the value of $k$ is

If the trivial solution is the only solution of the system of equations $x - ky + z = 0$ $kx + 3y - kz = 0$ $3x +y - z = 0$ then the set of all values of k is :

If the value of a third order determinant is 11, then the value of the square of the determinant formed by the co-factors will be

If (x + 9) = 0 is a factor of $\begin{vmatrix}x&3&7\\ 2&x&2\\ 7&6&x\end{vmatrix} = 0 $ , then the other factor is:

If x is a positive integer, then $\begin{vmatrix} x! & (x+1)! & (x+2)! \\[0.3em] (x+1)! & (x+2)! & (x+3)! \\[0.3em] (x+2)! & (x+3)! &(x+4)! \end{vmatrix}$ is equal to

If $\begin{vmatrix}y+z&x-z&x-y\\ y-z &z+x&y-x\\ z-y &z-x&x+y\end{vmatrix}= kxyz $ then the value of k is :

Let A be a $3 \times 3$ matrix such that $A\begin{bmatrix}1&2&3\\ 0&2&3\\ 0&1&1\end{bmatrix} = \begin{bmatrix}0&0&1\\ 1&0&0\\ 0&1&0\end{bmatrix} $ Then $A^{-1}$ is :

The solution set of the equation $\begin{vmatrix}1&4&20\\ 1&-2&5\\ 1&2x&5x^{2}\end{vmatrix} = 0$ is

The solution set of the inequality $37 - (3x + 5) \ge 9x - 8 (x - 3)$ is

The solution set of the inequality $ { 5^{x + 2} } > \left( \frac{1}{25} \right)^{ {1 /x}}$ is

The solution set of the inequality $\left|9^{x}-3^{x+1}-15\right|< 2.9^{x}-3^{x}$ is

Write the cofactors of each element of the first column of the following matrices. $A=\left[\begin{matrix}4&-1&2\\ 1&-3&2\\ 3&5&2\end{matrix}\right]$

The average weight of $25$ boys was calculated to be $78.4\, kg$. It was later discovered that one weight was misread as $69$ kg instead of $96 \,kg$. The correct average is

The mean and standard deviation of $100$ observations were calculated as $40$ and $5.1$, respectively by a student who took by mistake $50$ instead of $40$ for one observation. Find the correct standard deviation.

The mean deviation from the median of the following set of observations 5, 3, 9, 12, 3, 10, 12, 21, 18, 12, 21 is

The mean marks of 120 students is 20. It was later discovered that two marks were wrongly taken as 50 and 80 instead of 15 and 18. The correct mean of marks is

The mean of $100$ observations is $50$ and their standard deviation is $5$. The sum of all squares of all the observations is

The mean of 12 numbers is 24. If 5 is added in every number, the new mean is

The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three of the observations are $1$, $2$ and $6$, find the other two observations.