Test Details

Matrices And Determinants

Dec 03, 6:30 PM

720 minutes

Dec 05, 7:00 PM

20.0 marks

MCQ

13 questions

Rahul Gayke

Teacher

Class Details

Mathematics

Biology

XI Science

Mathematics

Biology

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Question Text

Question 1 :
If $A$ is a $3\times 3$ matrix and $\text{det} (3A)=k(\text{det} A)$, then $k=$

Question 2 :
If $A$ is a square matrix such that $\displaystyle { A }^{ 2 }=A$, then $\displaystyle \left| A \right| $ equals

Question 3 :
If $\begin{vmatrix}a & -b & -c\\-a & b & -c \\ -a & -b & -c\end{vmatrix}+\lambda abc=0$, then $\lambda$ is equal to

Question 4 :
The value of the determinant $\begin{vmatrix} 5 & 1 \\ 3 & 2 \end{vmatrix}$

Question 5 :
If the value of the determinant $\begin{vmatrix}m & 2\\ -5 & 7\end{vmatrix}$ is $31$, find $m$.

Question 7 :
If $a\neq6,b,c$ satisfy $\begin{vmatrix} a&2b&2c \\ 3&b&c \\ 4&a&b \end{vmatrix}=0,$ then $abc =$

Question 8 :
<div>Find the value of the following determinant: </div>$\begin{vmatrix}1.2 & 0.03\\ 0.57 & -0.23\end{vmatrix}$

Question 9 :
If $\begin{vmatrix}3x & 7\\ -2 & 4\end{vmatrix} = \begin{vmatrix} 8 &7 \\ 6 & 4\end{vmatrix}$, then find the value of $x$

Question 10 :
The value of determinant $\begin{vmatrix}\cos \alpha&-\sin \alpha &1\\\sin \alpha&\cos \alpha &1\\\cos(\alpha+\beta)&-\sin (\alpha+\beta)&1\end{vmatrix}$

Question 11 :
The value of the determinant $\begin{vmatrix} \cos^2 \dfrac{\theta}{2}&\sin^2\dfrac{\theta}{2}\\ \sin^2\dfrac{\theta}{2} &\cos^2\dfrac{\theta}{2} \end{vmatrix}$ for all values of $\theta $, is

Question 12 :
If $m = \begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}$ and $n = \begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$, then what is the value of the determinant of $m \cos \theta - n \sin \theta$?

Question 13 :
If the value of the determinant $\begin{vmatrix} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \end{vmatrix}$ is positive, then

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