Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

Let λ denote the number of terms in the expansion of 1 + 5 x + 10 x 2 + 10 x 3 + 5 x 4 + x 5 20 . If unit’s place and ten’s place digits in 3 λ are O and T , then O + T is equal to

Correct answer

3

Step-by-step solution

1 + 5 x + 10 x 2 + 10 x 3 + 5 x 4 + x 5 20 = 1 + x 5 20 = 1 + x 100 Number of terms = 101 = λ 3 101 = 3 ⋅ 3 100 = 3 ⋅ 9 50 = 3 10 - 1 50 = 3 C 50 0 ⋅ 10 50 - C 50 1 ⋅ 10 49 + . … … . . + C 50 48 ⋅ 10 2 - C 50 49 ⋅ 10 + C 50 50 = 3 100 K + 50 × 49 2 × 100 - 50 × 10 + 1 = 3 K × 100 + 3 × 25 × 49 × 100 - 500 × 3 + 3 = Multiple of 100 + 3 ⇒ one’s place is 3 and ten’s place is 0 Hence, O + T = 3

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: 2026If (1 - x^3)¹⁰ = _ r=0 ¹⁰ a_r x^r (1-x)^ 30-2r , then 9a₉ a₁₀ is equal to __________. 2026If 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: 2026The coefficient of x^2 in the expansion of (2x^2 + 1 x )¹⁰ , x 0 , is : 2026If 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 __________. 2026In the expansion of (9x- 1 3 x )¹⁸ , x>0 , if the term independent of x is (221)k , then k is equal to: 2026Let 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 2026If 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