M.C.Q (1 Marks)

Question 11 Mark

If any matrix has order $m \times n$, then number of elements :

Answer

Question 21 Mark

Find value of $x$ in equation $\left[\begin{array}{c}x+y+z \\ x+z \\ y+z\end{array}\right]=\left[\begin{array}{l}9 \\ 5 \\ 7\end{array}\right]$

Answer

$x+y+z=9$
$y+z=7$
Subtracting equation $(ii)$ from $(i)$
$x=9-7$
$x=2$

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Question 31 Mark

If $A=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ two matrix, then find AB ?

Answer

(A)
$AB =\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]=\left[\begin{array}{cc}4-3 & 6-6 \\ -2+2 & -3+4\end{array}\right]$ $=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$

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Question 41 Mark

If $\left[\begin{array}{cc}3 c+6 & a-d \\ a+d & 2-3 b\end{array}\right]=\left[\begin{array}{cc}12 & 2 \\ -8 & -4\end{array}\right]$ then find $a b-c d$ :

Answer

(A)
$3 c+6=12 \Rightarrow c=2$....(1)
$a-d=2$....(2)
$a+d=-8$....(3)
$
2-3 b=-4 ......(4)
$
On adding equation (2) and (3), $2 a=6 \Rightarrow a=-3$
Put the value is equation (2)
$-3-d=2 \Rightarrow d=-5
$
From equation (4)
$3 b=6$
$\Rightarrow \quad b=2$
then $a b-c d=(-3)(2)-(2)(-5)=-6+10=4$

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Question 51 Mark

All possible number of matrix of order $2 \times 3$ which has every entry is 1or 2.

Answer

(C)
number of elements of $2 \times 3$ order of matrix $=2$ $\times 3=6$ All possible number of matrix having element 1 or $2=2^6=64$

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Question 61 Mark

Two matrix $P =\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right]$ and $Q ^{ T }=\left[\begin{array}{rrr}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right]$, Find $P-Q$ :

Answer

(A)
$
\begin{aligned}
P-Q^T & =\left[\begin{array}{cc}
3 & 4 \\
-1 & 2 \\
0 & 1
\end{array}\right]-\left[\begin{array}{cc}
-1 & 1 \\
2 & 2 \\
1 & 3
\end{array}\right] \\
& =\left[\begin{array}{cc}
3+1 & 4-1 \\
-1-2 & 2-2 \\
0-1 & 1-3
\end{array}\right]=\left[\begin{array}{cc}
4 & 3 \\
-3 & 0 \\
-1 & -2
\end{array}\right]
\end{aligned}
$

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Question 71 Mark

Matrix $A =\left[a_{i j}\right]_{3 \times 3}$ defined such that :$
a_{i j}=\left\{\begin{array}{cc}
2 i+3 j, & i < j \\
5, & i=j \\
3 i-2 j, & i>j
\end{array}\right.$
Number of elements in matrix $A,$ having greater from $5 ?$

Answer

Here $a_{11}=5, a_{12}=8, a_{13}=11$
$a_{21}=4, a_{22}=5, a_{23}=13$
$a_{31}=7, a_{32}=5, a_{33}=5$
$3$ elements having greater from $5.$

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Question 81 Mark

If matrix $A$ and $B$ has order respectively $m \times n$ and $n \times p$ then order of AB is :

Answer

(D) $m \times p$

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Question 91 Mark

Matrix $X=\left[\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right],\left(X^2-X\right)$

Answer

$X^2=X X\left[\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right]\left[\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right]=\left[\begin{array}{lll}2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2\end{array}\right]$
$X^2-X=\left[\begin{array}{lll}2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2\end{array}\right]-\left[\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right]$
$=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]$
$=2\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
$=2 I$

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Question 101 Mark

If $A=\left[\begin{array}{cc}\sin ^2 \theta & \sec ^2 \theta \\ \operatorname{cosec}^2 \theta & \frac{1}{2}\end{array}\right]$ and $B=\left[\begin{array}{cc}\cos ^2 \theta & -\tan ^2 \theta \\ -\cot ^2 \theta & \frac{1}{2}\end{array}\right]$ the value of $A + B$ will be :

Answer

(D) $\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$

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Question 111 Mark

For any square matrix $A, A+A^{\prime}$ will be :

Answer

(B) Symmetric matrix

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Question 121 Mark

If matrix $B =\left[b_{i j}\right]_{2 \times 4}$, then number of elements is B will be :

Answer

(D)
In matrix B, has 2 rows and 4 columns.
$\therefore \quad$ number of elements $=2 \times 4=8$ Correct option is (D).

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Question 131 Mark

If a matrix has symmetric and skew symmetric, then this matrix will be :

Answer

(A)
because only zero matrix has such matrix which has symmetric and also skew symmetric.

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Question 141 Mark

If $A=\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1\end{array}\right]$, then $A$ will be :

Answer

(A)
because a square matrix know as diagonal matrix if except diagonal all other elements are zero.

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Question 151 Mark

If $A =\left[\begin{array}{ll}1 & a \\ 0 & 1\end{array}\right]$ then $A ^4$ equals to :

Answer

(D)
$
\begin{aligned}
A^2 & =A \cdot A=\left[\begin{array}{ll}
1 & a \\
0 & 1
\end{array}\right]\left[\begin{array}{ll}
1 & a \\
0 & 1
\end{array}\right] \\
A^2 & =\left[\begin{array}{cc}
1 & 2 a \\
0 & 1
\end{array}\right] \\
A^4=A^2 A^2 & =\left[\begin{array}{cc}
1 & 2 a \\
0 & 1
\end{array}\right]\left[\begin{array}{cc}
1 & 2 a \\
0 & 1
\end{array}\right]=\left[\begin{array}{cc}
1+0 & 2 a+2 a \\
0+0 & 0+1
\end{array}\right] \\
& =\left[\begin{array}{cc}
1 & 4 a \\
0 & 1
\end{array}\right]
\end{aligned}
$
Hence correct option is (D).

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Question 161 Mark

If $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1\end{array}\right]$, then $A^2=$ ?

Answer

(A)
$
\begin{aligned}
A^2=A \cdot A & =\left[\begin{array}{lll}
1 & 0 & 1 \\
0 & 0 & 0 \\
1 & 0 & 1
\end{array}\right]\left[\begin{array}{lll}
1 & 0 & 1 \\
0 & 0 & 0 \\
1 & 0 & 1
\end{array}\right] \\
& =\left[\begin{array}{lll}
2 & 0 & 2 \\
0 & 0 & 0 \\
2 & 0 & 2
\end{array}\right] \\
& =2\left[\begin{array}{lll}
1 & 0 & 1 \\
0 & 0 & 0 \\
1 & 0 & 1
\end{array}\right]=2 A
\end{aligned}
$
Hence correct option is (A).

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Question 171 Mark

If $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$, then $A$ is :

Answer

(B)
because every element of diagonal is 1 and except
1 all elements are zero

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MATHS M.C.Q (1 Marks)

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