List of top Mathematics Questions on Matrices asked in WBJEE

Let A=\(\begin{pmatrix}  0&0  &1 \\   1&0  &0 \\   0&0  &0  \end{pmatrix}\), B=\(\begin{pmatrix}  0&1  &0 \\   0&0  &1 \\   0&0  &0  \end{pmatrix}\) and P=\(\begin{pmatrix}  0&1  &0 \\   x&0  &0 \\   0&0  &y  \end{pmatrix}\) be an orthogonal matrix such that B=PAP^-1 holds. Then

If the matrix M_r is given by M_r=\(\begin{pmatrix}r &r-1 \\ r-1&r \end{pmatrix}\) for r=1,2,3....then det(M₁)+det(M₂)+.......+det(M₂₀₀₈)=

Let A be a square matrix of order 3 whose all entries are 1 and let $I_3$ be the identity matrix of order 3. Then the matrix $A - 3I_3$ is

If the matrix $A=\begin{pmatrix}2&0&0\\ 0&2&0\\ 2&0&2\end{pmatrix},$ then $A^{n}=\begin{pmatrix}a&0&0\\ 0&a&0\\ b&0&a\end{pmatrix}, n\,\in\,N$ where

Let $n\ge2$ be an integer, $A=\begin{pmatrix}\cos\left(2\pi/ n\right)&\sin \left(2\pi / n\right)&0\\ -\sin\left(2\pi / n\right)&\cos\left(2\pi / n\right)&0\\ 0&0&1\end{pmatrix}$ and $?$ is the identity matrix of order $3$. Then

Let $P = \begin{pmatrix}cos \frac{\pi}{4}&-sin \frac{\pi}{4}\\ sin \frac{\pi}{4}&cos \frac{\pi}{4}\end{pmatrix}$ and $X = \begin{pmatrix}\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}\end{pmatrix}$. Then $P^{3}X$ is equal to

If $A = \begin{bmatrix}3&x-1\\ 2x+3&x+2\end{bmatrix}$ is a symmetric matrix, then the value of $x$ is

If the matrix $\begin{bmatrix}a&b\\ c&d\end{bmatrix}$ is commutative with the matrix $\begin{bmatrix}1&1\\ 0&1\end{bmatrix}$, then

The number (101)¹⁰⁰ – 1 is divisible by 

Directions: The following question has four choices, out of which one or more are correct. Assume that the nuclear binding energy per nucleon $\left(\frac{B}{A}\right)$ versus mass number (A) is as shown in the figure. Use this plot to choose the correct answer(s) from the choices given below.

The cubic equation whose roots are the AM, GM and HM of the roots of x² - 2px + q² = 0 is

The value(s) of k for which the equations x² - kx - 21 = 0 and x² - 3kx + 35 = 0 will have a common root is/are

The value of $\sec [{\tan }^{-1}\left(\frac{b+a}{b-a}\right)-{\tan }^{-1}\left(\frac{a}{b}\right)]$

If $x+\frac{1}{x}=2\cos \theta ,$ then for any integer $n,x^n+\frac{1}{x^n}=$