Let M= A= ( ll a & b c & d ): a, b, c, d 3, 2, 1,0 . Define f: M … - Vidyadip

MCQ

Let $M=\left\{A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right): a, b, c, d \in\{\pm 3, \pm 2, \pm 1,0\}\right\} .$ Define $f: M \rightarrow z$, as $f(A)=\operatorname{det}(A)$ for all $A \in M$, where $Z$ is set of all integers. Then the number of $A \in M$ such that $f(A)=15$ is equal to $.....$

✓
$16$
B
$32$
C
$48$
D
$71$

✓

Answer

Correct option: A.

$16$

a
$|\mathrm{A}|=\mathrm{ad}-\mathrm{bc}=15$

where $a, b, c, d \in\{\pm 3, \pm 2, \pm 1,0\}$

Case $\mathrm{I} \mathrm{ad}=9 \,\& \,\mathrm{bc}=-6$

For ad possible pairs are $(3,3),(-3,-3)$

For bc possible pairs are $(3,-2),(-3,2),(-2,3),\left(2_{6}-3\right)$

So total matrix $=2 \times 4=8$

Case $II$ ad $=6 \,\&\, \mathrm{bc}=-9$

Similarly total matrix $=2 \times 4=8$

$\Rightarrow$ Total such matrices are $=16$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If A and B are two events such that $\text{P(A)}\neq0$ and $\text{P(B)}\neq1,$ then $\text{P}(\overline{\text{A}}|\overline{\text{B}})=$

$1-\text{P}(\text{A}|\text{B})$
$1-\text{P}(\overline{\text{A}}|\text{B})$
$\frac{1-\text{P}(\text{A}\cup\text{B})}{\text{P}(\overline{\text{B}})}$
$=\frac{\text{P}(\overline{\text{A}})}{\text{P}(\overline{\text{B}})}$

In order that the function $f(x) = {(x + 1)^{\cot \,x}}$ is continuous at $x = 0 , f(0)$ must be defined as

The function $f(x)=[x]$, where $[x]$ denotes the greatest integer less than or equal to $x$, is continuous at

$\int_1^{\sqrt 3 } {\frac{1}{{1 + {x^2}}}dx} $ is equal to

The straight line $2 x-3 y=1$ divides the circular region $x^2+y^2 \leq 6$ into two parts. If

$S=\left\{\left(2, \frac{3}{4}\right),\left(\frac{5}{2}, \frac{3}{4}\right),\left(\frac{1}{4},-\frac{1}{4}\right),\left(\frac{1}{8}, \frac{1}{4}\right)\right\},$ then the number of point(s) in $S$ lying inside the smaller part is

The solution of the differential equation $x\sec y\frac{{dy}}{{dx}} = 1$ is

Choose the correct answer from the given four options.

If two events are independent, then:

They must be mutually exclusive.
The sum of their probabilities must be equal to 1.
(a) and (b) both are correct.
None of the above is correct.

Let R be a relation on the set N given by R = {(a, b): a = b - 2, b > 6}. Then,

(2, 4) ∈ R
(3, 8) ∈ R
(6, 8) ∈ R
(8, 7) ∈ R

For real numbers x and y, define xRy if $\text{x}-\text{y}+\sqrt{2}$ is an irrational number. Then the relation R is:

Reflexive.
Symmetric.
Transitive.
None of these.

The solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{y}}{\text{x}}+\frac{\phi(\frac{\text{y}}{\text{x}})}{\phi'(\frac{\text{y}}{\text{x}})}$ is:

$\phi(\frac{\text{y}}{\text{x}})=\text{Kx}$
$\text{x}\phi(\frac{\text{y}}{\text{x}})=\text{K}$
$\phi(\frac{\text{y}}{\text{x}})=\text{Ky}$
$\text{y}\phi(\frac{\text{y}}{\text{x}})=\text{K}$