Applied Mathematics

Algebra

Easy

applied

If $A=\begin{bmatrix}0 & 1\\0 & 0\end{bmatrix}$ , then $A^{1999}$ is equal to

$\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$

$\begin{bmatrix}0 & 1\\0 & 0\end{bmatrix}$

$\begin{bmatrix}0 & 0\\0 & 0\end{bmatrix}$

$\begin{bmatrix}1 & 0\\0 & 0\end{bmatrix}$

✅ Correct Option: 3

Direct multiplication gives $A^2=O$ , the null matrix.

Hence every higher power is null, and $A^{1999}=A^{2}\cdot A^{1997}=O$ .

2023: 23 May Shift 3

The solution set of the inequation $\frac{7+5x}{4} \geq \frac{x}{3} - 10$ , $x \in \mathbb{R}$ is :

2023: 11 Aug Shift 1

If $P = \begin{bmatrix} -2 & 2 & 0 \\ 3 & 1 & 4 \end{bmatrix}$ and $Q = \begin{bmatrix} 2 & 0 & -2 \\ 7 & 1 & 6 \end{bmatrix}$ , If $5Q - 3P + 2R = 0$ , then the matrix R is

2023: 22 May Shift 3

The digit in the unit's place of $13^{37}$ is :

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. The solution of $3x + 7 > 12$ is	I. $[-1, \infty)$
B. The solution of $\frac{3x+5}{2} \geq 1$ is	II. $\left[\frac{17}{8}, \infty\right)$
C. The solution of $2x + 5 < 7x + 9$ is	III. $\left(\frac{5}{3}, \infty\right)$
D. The solution of $6x - 5 \geq -2x + 12$ is	IV. $\left(-\frac{4}{5}, \infty\right)$

Choose the correct answer from the options given below:

2023: 7 June Shift 1

The sum of the minor and the cofactor of the element 6 in the determinant $\begin{vmatrix} 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$ is :

2023: 11 Aug Shift 1

If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = 4x$ , then $x =$

If A=[0100]A=\begin{bmatrix}0 & 1\\0 & 0\end{bmatrix}A=[00​10​], then A1999A^{1999}A1999 is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A=\begin{bmatrix}0 & 1\\0 & 0\end{bmatrix}$ , then $A^{1999}$ is equal to