Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

In the expansion of (2^ 1 5 +7^ 1 7 )¹⁰⁵ , which of the following holds good?

Options

  1. ANumber of rational terms are 4.
  2. BNumber of irrational terms are 102.
  3. CExactly one middle term is irrational.
  4. DBoth middle terms are irrational.

Correct answer

D. Both middle terms are irrational.

Step-by-step solution

aligned T_ r+1 & = ¹⁰⁵ C_r (2^ 1 5 )^ 105-r 7^ r 7 & = ¹⁰⁵ C_r 2^ 105-r 5 7^ r 7 aligned Clearly r should be a multiple of 7 and 5 , r=0,35,70,105 Number of rational terms =4 Number of irrational terms =102 Middle term =T₅₃ and T₅₄ are both irrational.

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 Most Important Selected Qs for JEE Advanced PYQs