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

Match the following ( array ll Column-I & Column - II array l (A) If (x+ 1 x +x^2+ 1 x^2 )^9=a₀ x⁻¹⁸+a₁ x⁻¹⁷+ .+a₃₆ x¹⁸, then (a₀+a₂+ .+a₃₆ ) is equal to array & (p) 2²⁴ (B) If (1+x+x^2+x^3 )³³=a₀+a₁ x+a₂ x^2+ . .+a_ 3 g x³³, then (a₀ . & (q) (18 2¹⁹+1 ) (C) ²⁰ C ₂+2 ₂+ ²⁰ C ₁₂+3 + ₃ ²⁰ C ₄+ +19 ²⁰ C ₂₀ is equal to & (r) (2^8+2¹⁷ ) (D) ²⁰ C ₁+2 ²⁰ C ₂+3 ²⁰ C ₃+4 ²⁰ C ₄+ . .+10 ²⁰ C ₁₀ is equal to & (5) 20 (2¹⁸+ ¹⁹ C

Options

  1. A( A ) ( s ) ;( B ) ( r ) ;( C ) ( t ) ;( D ) ( p )
  2. B( A ) ( p ) ;( B ) ( r ) ;( C ) ( s ) ;( D ) ( t )
  3. C( A ) ( r ) ;( B ) ( p ) ;( C ) ( q,t ) ;( D ) ( s )
  4. D( A ) ( q ) ;( B ) ( s ) ;( C ) ( p ) ;( D ) ( r )

Correct answer

C. ( A ) ( r ) ;( B ) ( p ) ;( C ) ( q,t ) ;( D ) ( s )

Step-by-step solution

(A) (x+ 1 x +x^2+ 1 x^2 )^9=a₀ x⁻¹⁸+a₁ x⁻¹⁷+ . .+a₃₆ x¹⁸ Put X =1 and -1 , and odd We get. (a₀+a₂+ . .+a₃₆ )= (2^8+2¹⁷ ) (B) (1+x+x^2+x^3 )¹³=a₀+a₁ x+a₂ x^2+ . .+a₃₉ x³⁹ Put fourth roots of unity, 1, , ^2, ^3 and add together We get. (a₀+a₄+a₈+a₁₂+ . .+a₆₆ )= 2²⁶ 4 =2²⁴ (C) ²⁰ C ₂+2 . ³⁰ C ₃+3 ²⁰ C ₄+ . .+19 . ²⁰ C ₂₀ Let (1+ x )²⁰= ²⁰ C ₀+ ²⁰ C ₁ x + ²⁰ C ₂ x ^2+ + ²⁰ C ₂₀ x ²⁰ divide by x , and differentiae both sides, ( ²⁰ C ₂+2 ²⁰ C ₃+19 ²⁰ C ₂₀ )= (18 2¹⁹ )+1 (D) aligned & ²⁰ C ₁+2 . ¹⁰ C ₂+3 ²⁰ C ₃+4 . ²⁰ C ₄

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