Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2015MathematicsDeterminants

The remainder when the determinant | array lll 2014²⁰¹⁴ & 2015²⁰¹⁵ & 2016²⁰¹⁶ 2017²⁰¹⁷ & 2018²⁰¹⁸ & 2019²⁰¹⁹ 2020²⁰²⁰ & 2021²⁰²¹ & 2022²⁰²² array | is divided by 5 is.

Options

  1. A1
  2. B2
  3. C4
  4. 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

Practice Determinants on Quantrex Academy →

More from Determinants

Let A = [a_ ij ] be a square matrix of order 3 3 , where the elements are defined as a_ ij = cases i - 2j & if i = j 0 & if i > j 1 & if i < j cases then the value of |A^t| is 2026Let A be a square matrix of order 3 3 . If |A| = -4 , then the value of | A⁻¹ -2 | is: 2026Given P = bmatrix 2 & & 1 1 & 2 & 2 1 & 3 & 3 bmatrix is the adjoint of a 3 3 matrix A and |A| = 3 , then the value of is: 2026Which of the following is correct? 2026If A and B are invertible square matrices of order n, then which of the following is not correct? 2026The system of equations x + 2y = 3 and 2x + 3y = 3 has 2026A value of lying between 0 and 2 and satisfying | array ccc 1+ ^2 & ^2 & 4 4 ^2 & 1+ ^2 & 4 4 ^2 & ^2 & 1+4 4 array |=0 2025If the inverse of [ array ccc -x & 14 x & 7 x 0 & 1 & 0 x & -4 x & -2 x array ] is [ array ccc 2 & 0 & 7 0 & 1 & 0 1 & -2 & 1 array ] , then | array ccc x & x+1 & x+2 x+1 & x+2 & x 2025 Full Determinants list All KVPY PYQs