The remainder when the determinant2014 -2014- 2015-2015- 2016-20162017-2017- 2018-2018- 2019-20191 12020 -2020- 20212021- 2022 -2022lend matrix -right -is divided by 5 is-

The correct option is D 4 | (2015 1)^2014 amp;(2015)^2015 amp;(2015+1)^2016 (2017)^2017 amp;(2018)^2018 amp;(2019)^2019 (2020)^2020 amp;(2021)^202 ...

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Byju's Answer

Standard XII

Mathematics

Finding Inverse Using Elementary Transformations

The remainder...

Question

The remainder when the determinant

$∣ ∣ ∣ ∣ ∣ \begin{matrix} 2014^{2014} & 2015^{2015} & 2016^{2016} 2017^{2017} & 2018^{2018} & 2019^{2019} 2020^{2020} & 2021^{2021} & 2022^{2022} \end{matrix} ∣ ∣ ∣ ∣ ∣$

is divided by 5 is.

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Solution

The correct option is D
4

$∣ ∣ ∣ ∣ ∣ \begin{matrix} (2015 - 1)^{2014} & (2015)^{2015} & (2015 + 1)^{2016} (2017)^{2017} & (2018)^{2018} & (2019)^{2019} (2020)^{2020} & (2021)^{2021} & (2022)^{2022} \end{matrix} ∣ ∣ ∣ ∣ ∣ Remainder = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & 1 2^{2017} & 2^{2018} & - 1 0 & 1 & 2^{2022} \end{matrix} ∣ ∣ ∣ ∣ ∣ = (4^{4040} + 1) + (2^{2017}) 1 + (5 - 1)^{4040} + 2 (4)^{1008} = 1 + 1 + 2 (1) = 4$

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Similar questions

The remainder when the determinant

∣ ∣ ∣ ∣ ∣ \begin{matrix} 2014^{2014} & 2015^{2015} & 2016^{2016} 2017^{2017} & 2018^{2018} & 2019^{2019} 2020^{2020} & 2021^{2021} & 2022^{2022} \end{matrix} ∣ ∣ ∣ ∣ ∣

is divided by

5

is.

Q. The remainder when the determinant

∣ ∣ ∣ ∣ ∣ \begin{matrix} 2014^{2014} & 2015^{2015} & 2016^{2016} 2017^{2017} & 2018^{2018} & 2019^{2019} 2020^{2020} & 2021^{2021} & 2022^{2022} \end{matrix} ∣ ∣ ∣ ∣ ∣

is divided by

5

Q. If

\frac{2017}{x + 2017} + \frac{2018}{y + 2018} + \frac{2019}{x + 2019} = - 2015

, then

\frac{x}{x + 2017} + \frac{y}{y + 2018} + \frac{z}{z + 2019}

equals

(2014^2-2020)(2014^2+4028-3)(2015)/2011(2013)(2016)(2017)

Q. The population of rabbits over a duration in a zoo is tabulated as follows:
Year Population of Rabbit
(in thousand)

2015	3
2016	5
2017	6
2018	7
2019	8
2020	9

Choose the line graph that correctly depicts the data set.

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The remainder when the determinant ∣∣ ∣ ∣∣201420142015201520162016201720172018201820192019202020202021202120222022∣∣ ∣ ∣∣ is divided by 5 is.

The correct option is D 4 ∣∣ ∣ ∣∣(2015−1)2014(2015)2015(2015+1)2016(2017)2017(2018)2018(2019)2019(2020)2020(2021)2021(2022)2022∣∣ ∣ ∣∣Remainder=∣∣ ∣ ∣∣1012201722018−10122022∣∣ ∣ ∣∣=(44040+1)+(22017)1+(5−1)4040+2(4)1008=1+1+2(1)=4

The remainder when the determinant

$∣ ∣ ∣ ∣ ∣ \begin{matrix} 2014^{2014} & 2015^{2015} & 2016^{2016} 2017^{2017} & 2018^{2018} & 2019^{2019} 2020^{2020} & 2021^{2021} & 2022^{2022} \end{matrix} ∣ ∣ ∣ ∣ ∣$

is divided by 5 is.