#### 11th Standard Maths Matrices and Determinants English Medium Free Online Test One Mark Questions 2020 - 2021

11th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. If aij =${1\over2}(3i-2j)$ and A=[aij]2x2 is ______

(a)

$\begin{bmatrix} {1\over 2}& 2 \\ -{1\over2} & 1 \end{bmatrix}$

(b)

$\begin{bmatrix} {1\over 2}& -{1\over2} \\ 2& 1 \end{bmatrix}$

(c)

$\begin{bmatrix} 2& 2\\ {1\over 2}& -{1\over2} \end{bmatrix}$

(d)

$\begin{bmatrix} -{1\over 2}& {1\over2} \\ 1& 2 \end{bmatrix}$

2. If A = $\begin{bmatrix}\lambda & 1 \\ -1 & -\lambda \end{bmatrix}$ ,then for what value of $\lambda$, A2 = O?

(a)

0

(b)

$\pm 1$

(c)

-1

(d)

1

3. The value of x, for which the matrix A = $\begin{bmatrix} e^{x-2}& e^{7+x} \\ e^{2+x} & e^{2x+3} \end{bmatrix}$ is singular is

(a)

9

(b)

8

(c)

7

(d)

6

4. If $\triangle$ = $\begin{vmatrix} a&b &c \\ x & y & z \\ p &q &r \end{vmatrix}$then $\begin{vmatrix} ka&kb &kc \\ kx & ky & kz \\k p &kq &kr \end{vmatrix}$ is

(a)

$\triangle$

(b)

k$\triangle$

(c)

3k$\triangle$

(d)

k3$\triangle$

5. If a $\neq$ b, b, c satisfy $\begin{vmatrix} a&2b &2c \\3 & b & c \\ 4 & a & b \end{vmatrix}=0,$ then abc

(a)

a + b + c

(b)

0

(c)

b3

(d)

ab + bc

6. If $\left\lfloor . \right\rfloor$ denotes the greatest integer less than or equal to the real number under consideration and −1$\le$ x < 0, 0 $\le$ y < 1, 1 $\le$ z < 2, then the value of the determinant $\begin{vmatrix} \left\lfloor x \right\rfloor +1& \left\lfloor y \right\rfloor & \left\lfloor z \right\rfloor \\ \left\lfloor x \right\rfloor & \left\lfloor y \right\rfloor +1& \left\lfloor z \right\rfloor \\ \left\lfloor x \right\rfloor & \left\lfloor y \right\rfloor & \left\lfloor z \right\rfloor +1\end{vmatrix}$ is

(a)

$\left\lfloor z \right\rfloor$

(b)

$\left\lfloor y \right\rfloor$

(c)

$\left\lfloor x \right\rfloor$

(d)

$\left\lfloor x \right\rfloor$+1

7. Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?

(a)

A + B is a symmetric matrix

(b)

AB is a symmetric matrix

(c)

AB = (BA)T

(d)

AT B = ABT

8. If $\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}$, then the value of x+y is _________ .

(a)

5

(b)

6

(c)

4

(d)

3

9. On using elementary row operation R1⟶R1-3R2 in the following matrix equation $\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}$________.

(a)

$\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}$

(b)

$\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} -1 & -3 \\ 1 & 1 \end{pmatrix}$

(c)

$\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 1 & -7 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}$

(d)

$\begin{pmatrix} 4 & 2 \\ -5 & -7 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ -3 & -3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}$

10. The value of$\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+sin\theta & 1 \\ 1 & 1 & 1+cos\theta \end{matrix} \right|$ is _____________

(a)

3

(b)

1

(c)

2

(d)

$\frac{1}{2}$