NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The remainder obtained when 7 100 is divided by 13 is

Options

Correct answer

C. 9

Step-by-step solution

7 100 = 7 2 50 = 49 50 = 52 - 3 50 = C 0 50 52 50 - C 1 50 52 49 ⋅ 3 + . . . - C 49 50 52 3 49 + C 50 50 3 50 = 13 K + 3 50 = 13 K + 3 3 16 ⋅ 3 2 = 13 K + 26 + 1 16 ⋅ 9 = 13 K + 9 C 0 16 ⋅ 26 16 + C 1 16 ⋅ 26 15 + . . . + C 15 16 ⋅ 26 + C 16 16 = 13 K + 9 13 K 1 + 1 = 13 K + 9 K 1 + 9

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 NTA Abhyas JEE Main PYQs