List of top Mathematics Questions

For any 2 $\times$ 2 matrix A, if A (adj. A) = $\begin{bmatrix}10&0\\ 0&10\end{bmatrix}$ en | A | is equal to :

If $a^{-1} + b^{-1} + c^{-1} = 0$ such that $\begin{vmatrix}1+a&1&1\\ 1&1+b&1\\ 1&1&1+c\end{vmatrix} = \lambda$ then the value of $\lambda$ is :

If $A = \begin{bmatrix}-2&6\\ -5&7\end{bmatrix} $ , then adj A:

If $A^2 - A + I = 0$ , then the inverse of A is

If $A = \begin{bmatrix}3&-3&4\\ 2&-3&4\\ 0&-1&1\end{bmatrix} $ , then $A^{-1}$ equal to:

If A and B are square matrices of order 3, such that $| A | = - 1, | B | = 3$ then the determinant of 3 AB is equal to

If $a$, $b$, $c$ are the roots of the equation $x^{3}-3x^{2}+3x+7=0$, then the value of $\left|\begin{matrix}2bc-a^{2}&c^{2}&b^{2}\\ c^{2}&2ac-b^{2}&a^{2}\\ b^{2}&a^{2}&2ab-c^{2}\end{matrix}\right|$ is

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. $A=\left[\begin{matrix}4&-1&2\\ 1&-3&2\\ 3&5&2\end{matrix}\right]$