List of top Mathematics Questions

The smallest integer function $f x ) = [x]$ is

The value of the determinant $ \left| \begin{matrix} 15! & 16! & 17! \\ 16! & 17! & 18! \\ 17! & 18! & 19! \\ \end{matrix} \right| $ is equal to

A triangle has its three sides equal to p, q and r. If the coordinates of its vertices are $A\left(x_{1}, y_{1}\right)$, $B\left(x_{2}, y_{2}\right)$ and $C\left(x_{3}, y_{3}\right)$, then $\left|\begin{matrix}x_{1}&y_{1}&2\\ x_{2}&y_{2}&2\\ x_{3}&y_{3}&2\end{matrix}\right|^{2}$ is equal to

Adj. (AB) - (Adj. B)(Adj. A) =

Compute $\left(AB\right)^{-1}$, if $A = \left[\begin{matrix}1&1&2\\ 0&2&-3\\ 3&-2&4\end{matrix}\right]$ and $B^{-1}=\left[\begin{matrix}1&2&0\\ 0&3&-1\\ 1&0&2\end{matrix}\right]$

Consider the system of linear equations $a_{1}x + b_{1}y +c_{1}z + d_{1} = 0,$ $ a_{2}x + b_{2}y +c_{2}z + d_{2} = 0,$ $a_{3}x + b_{3}y +c_{3}z + d_{3} = 0$, Let us denote by $\Delta\left(a,b,c\right)$ the determinant $\begin{vmatrix}a_{1}&b_{1}&c_{1}\\ a_{2}&b_{2}&c_{2}\\ a_{3}&b_{3}&c_{3}\end{vmatrix},$ if $\Delta\left(a,b,c\right)$ # $0$, then the value of x in the unique solution of the above equations is

Determinant of a skew symmetric matrix of even order is

Determinant of a skew symmetric matrix of odd order is

Evaluate the determinant $\Delta=\left|\begin{matrix}log_{3} \,512&log_{4} \,3\\ log_{3} \,8 &log_{4} \,9\end{matrix}\right|$

Evaluate the following determinants, $\left|\begin{matrix}a+ib&c+id\\ -c+id&a-id\end{matrix}\right|\quad$

Find the minor of $a_{22}$ of the matrix $\left[\begin{matrix}1&6&1\\ 5&3&0\\ 2&2&9\end{matrix}\right]\cdot$

Find $x$, if $\left[\begin{matrix}1&2&x\\ 1&1&1\\ 2&1&-1\end{matrix}\right] $ is singular.

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