Download App

STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
The remainder when the determinant $\left|\begin{array}{lll} 2014^{2014} & 2015^{2015} & 2016^{2016} \\ 2017^{2017} & 2018^{2018} & 2019^{2019} \\ 2020^{2020} & 2021^{2021} & 2022^{2022} \end{array}\right|$  is divided by $5$ is
  • A
    $1$
  • B
    $2$
  • C
    $3$
  • ✓
    $4$
✓

Answer

Correct option: D.
$4$
d
(d)

Let

$D=\left|\begin{array}{lll}2014^{2014} & 2015^{2015} & 2016^{2016} \\ 2017^{2017} & 2018^{2018} & 2019^{2019} \\ 2020^{2020} & 2021^{2021} & 2022^{2022}\end{array}\right|$

$D=\left|\begin{array}{ccc}(2015-1)^{2014} & (2015)^{2015} & (2015+1)^{2016} \\ (2015+2)^{2017} & (2020-2)^{2018} & (2020-1)^{2019} \\ (2020)^{2020} & (2020+1)^{2021} & (2020+2)^{2022}\end{array}\right|$

Remainder when divided by $5$ , is

$D=\left|\begin{array}{ccc}1 & 0 & 1 \\2^{2017} & 2^{2018} & -1 \\0 & 1 & 2^{2022}\end{array}\right|$

$=1\left(2^{4040}+1\right)+2^{2017}$

$=(5-1)^{2020}+1+2(5-1)^{1008}$

$=1+1+2=4$

 

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 STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A, A^2 + B^2$ is equal to:
→
$A $ $10\,cm$  long rod $ AB$  moves with its ends on two mutually perpendicular straight lines  $OX$ and $OY$ . If the end $ A$ be moving at the rate of $2\,cm/\sec $, then when the distance of  $A$ from $ O $ is $8\,cm$, the rate at which the end $B$ is moving, is
→
Integrating factor of the differential equation, $(1-\text{x}^2)\frac{\text{dy}}{\text{dx}}-\text{xy}=1$ is:
→
If $[x]$ denotes the greatest integer less than or equal to $x,$ then the value of the integral $\int_0^2 {{x^2}[x]\,dx} $ equals
→
What is the value of $\int_{0}^{\frac{ \pi}{2}}\frac{\sqrt{\tan\text{x}}}{\sqrt{\tan}\text{x}+\sqrt{\cot}\text{x}}\text{dx}?$
→
The value of  $x $ for which the angle between the vectors $a = - \,3i + xj + k$ and $b = xi + 2xj + k$ is acute and the angle between  $ b$  and $x-$ axis lies between $\pi /2$ and $\pi $ satisfy
→
The feasible solution for a $LPP$ is shown in Figure Let $z=3 x-4 y$ be the objective function. Maximum of $Z$ occurs at $......$
→
If the area bounded by $y = a{x^2}$ and $x = a{y^2}$, $a > 0$, is $1$, then $a = $
→
A flash light has $8$ batteries out of which $3$ are dead. $IF$ two batteries are selected without replacement and tested, then the probability that both are dead is,
→
If a matrix has mm rows and nn columns then its order is:
→