JEE Main202313 Apr 2023Evening ShiftMathematicsBinomial TheoremActual

The coefficient of x 5 in the expansion of 2 x 3 - 1 3 x 2 5 is

Options

A80 9
B9
C8
D26 3

Correct answer

A. 80 9

Step-by-step solution

General term of the binomial expansion of 2 x 3 - 1 3 x 2 5 is T r + 1 = 5 C r ( 2 x 3 ) 5 - r   - 1 3 x 2 r ⇒ T r + 1 = C r 5 2 5 - r - 1 3 r x 15 - 5 r For coefficient of x 5 , we must have 15 - 5 r = 5 ⇒ r = 2 So, required coefficient is = C 2 5 ( 2 ) 3 1 9 = 10 × 8 × 1 9 = 80 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 JEE Main PYQs