Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202122 Jul 2021Morning ShiftMathematicsBinomial TheoremActual

The number of elements in the set n ∈ 1 , 2 , 3 , … , 100 ∣ ( 11 ) n > ( 10 ) n + ( 9 ) n is ___________.

Correct answer

0

Step-by-step solution

We have to check 11 n > 10 n + 9 n ⇒ 11 n - 9 n > 10 n ⇒ ( 10 + 1 ) n - ( 10 - 1 ) n > 10 n Using a + b n - a - b n = 2 C 1 n · a n - 1 · b + C 3 n · a n - 3 · b 3 + C 5 n · a n - 5 · b 5 + . . . ⇒ 2 C 1 n · 10 n - 1 + C 3 n · 10 n - 3 + C 5 n · 10 n - 5 + ⋯ ⋯ > 10 n ⇒ 2 n · 10 n - 1 + 2 C 3 n · 10 n - 3 + C 5 n · 10 n - 5 + ⋯ ⋯ > 10 n … 1 For n = 5 , the L . H . S . is 2 · 5 &#

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 JEE Main PYQs