JEE Main202227 Jul 2022Morning ShiftMathematicsBinomial TheoremActual

The remainder when 2021 2022 + 2022 2021 is divided by 7 is

Options

Correct answer

A. 0

Step-by-step solution

We know 2023 = 7 × 289 So 2021 2022 + 2022 2021 = 2023 - 2 2022 + 2023 - 1 2021 = 7 m 1 + 2 2022 + 7 m 2 + - 1 2021 = 7 m 1 + m 2 + 8 674 - 1 = 7 m 1 + m 2 + ( 7 + 1 ) 674 - 1 = 7 m 1 + m 2 + 7 m 3 + 1 - 1 = 7 m 1 + m 2 + m 3 This is a multiple of 7 Hence, remainder is 0

Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

If 26 ( 2^3 3 12 2 + 2^5 5 12 4 + 2^7 7 12 6 + + 2¹³ 13 12 12 ) = 3¹³ - , then is equal to: 2026 If (1 - x^3)¹⁰ = _ r=0 ¹⁰ a_r x^r (1-x)^ 30-2r , then 9a₉ a₁₀ is equal to __________. 2026 If the coefficients of the middle terms in the binomial expansions of (1 + x)²⁶ and (1 - x)²⁸ , 0 , are equal, then the value of is: 2026 The coefficient of x^2 in the expansion of (2x^2 + 1 x )¹⁰ , x 0 , is : 2026 If the sum of the coefficients of x^7 and x¹⁴ in the expansion of ( 1 x^3 - x^4 )^n , x 0 , is zero, then the value of n is __________. 2026 In the expansion of (9x- 1 3 x )¹⁸ , x>0 , if the term independent of x is (221)k , then k is equal to: 2026 Let the smallest value of k N , for which the coefficient of x^3 in (1+x)^3 + (1+x)^4 + (1+x)^5 + + (1+x)⁹⁹ + (1+kx)¹⁰⁰ , x 0 , is (43n + 101 4 ) (¹⁰⁰C₃ ) for some n N , be p . The 2026 If for 3 r 30 , 30 30-r + 3 30 31-r + 3 30 32-r + 30 33-r = m r , then m equals: 2026 Full Binomial Theorem list All JEE Main PYQs