PYQ Vault
EbooksTutor

Coefficient of a given power of x in (a x^p + b/x^q)^n

This type of question, asked 7 times: 27 Jun 2022, 31 Jan 2023, 6 Apr 2023, 8 Apr 2023, 13 Apr 2023, 9 Apr 2024, 5 Apr 2026 S2. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    27 Jun 2022

    85
    If the coefficient of x10x^{10} in the binomial expansion of (x514+5x13)60\left( \frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}} \right)^{60} is 5kl5^{k}l, where l,k∈Nl,k \in N and ll is coprime to 5 , then kk is equal to

  2. Question 2

    31 Jan 2023

    176
    The coefficient of x−6x^{- 6}, in the expansion of (4x5+52x2)9\left( \frac{4x}{5}+\frac{5}{2x^{2}} \right)^{9}, is

  3. Question 3

    6 Apr 2023

    87
    The coefficient of x18x^{18} in the expansion of (x4−1x3)15\left( x^{4}-\frac{1}{x^{3}} \right)^{15} is

  4. Question 4

    8 Apr 2023

    155
    The absolute difference of the coefficients of x10x^{10} and x7x^{7} in the expansion of (2x2+12x)11\left( 2x^{2}+\frac{1}{2x} \right)^{11} is equal to

    Tap an option to check your answer.

  5. Question 5

    13 Apr 2023

    152
    The coefficient of x5x^{5} in the expansion of (2x3−13x2)5\left( 2x^{3}-\frac{1}{3x^{2}} \right)^{5} is

    Tap an option to check your answer.

  6. Question 6

    9 Apr 2024

    162
    The sum of the coefficient of x2/3x^{2/3} and x−2/5x^{- 2/5} in the binomial expansion of (x2/3+12x−2/5)9\left( x^{2/3}+\frac{1}{2}x^{- 2/5} \right)^{9} is :

    Tap an option to check your answer.

  7. Question 7

    5 Apr 2026 S2

    57
    The coefficient of x2x^{2} in the expansion of (2x2+1x)10,x≠0\left( 2x^{2}+\frac{1}{x} \right)^{10},x \neq 0, is :

    Tap an option to check your answer.