KVPY2015MathematicsDeterminants
The remainder when the determinant | array lll 2014²⁰¹⁴ & 2015²⁰¹⁵ & 2016²⁰¹⁶ 2017²⁰¹⁷ & 2018²⁰¹⁸ & 2019²⁰¹⁹ 2020²⁰²⁰ & 2021²⁰²¹ & 2022²⁰²² array | is divided by 5 is.
Options
- A1
- B2
- C4
- D4
Correct answer
D. 4
Step-by-step solution
| array ccc (2015-1)²⁰¹⁴ & (2015)²⁰¹⁵ & (2015+1)²⁰¹⁶ (2017)²⁰¹⁷ & (2018)²⁰¹⁸ & (2019)²⁰¹⁹ (2020)²⁰²⁰ & (2021)²⁰²¹ & (2022)²⁰²² array | Raminder = | array ccc 1 & 0 & 1 2²⁰¹⁷ & 2²⁰¹⁸ & -1 0 & 1 & 2²⁰²² array |= (4⁴⁰⁴⁰+1 )+ (2²⁰¹⁷ )1+(5-1)⁴⁰⁰⁰+2(4)¹⁰⁰⁸=1+1+2(1)=4