CAT Question Bank  Binomial Theorem

CAT questions binomial theorem
Number of Questions  20
Topic  Binomial theorem
Answer key available?  Yes
Source  Curated Content

Q1) The sum of the coefficients in the expression (1 + x – 3x^2)^2163 is?

Q2) Find the coefficient of ‘x’ in the expansion of (1  2x^3 + x^5) [1 + (1/x)]^8

Q3) Find numerically the greatest term in the expansion of (2 + 3x)^9 when x = 3/2

Q4) If the third term in the expansion of (x + x^logx)^5 is 10,00,000. Find the value of ‘x’. (Note  log in base 10)

Q5) For (x^2 + 3y)^4, Find the coefficient where the sum of exponents of x and y in the expansion is 5

Q6) Find the coefficient of x^7 in the expansion of (1+ 3x  2x^3)^10

Q7) In the binomial expansion of (a  b)^n, n ≥ 5, the sum of the 5th and 6th terms is zero. Then find the value of a/b.

Q8) If the coefficient of 4th and 13th terms in the expansion of [x^2 + (1/x)]^n be equal, then find the term which is independent of x

Q9) Find the coefficient of the term independent of y in the expansion of [(y + 1)/( y^2/3 – y^1/3 + 1)  (y – 1) / (y – y^1/2)]^10

Q10) A man has 2n + 1 friends. The number of ways in which he can invite atleast n + 1 friends for a dinner is 4096. Find the number of friends of the man.

Q11) What is the highest power of 12 in (5^36)  1

Q12) What is d coefficient of x^204 in (x  1)(x^2  2)(x^3  3) ... (x^20  20)

Q13) The sum of the rational terms in (√2 + 3√3 + 6√6)^10 is
a. 12632
b. 12600
c. 126
d. None of these

Q14) Find coefficient of x^8 in (1 − 2x + 3x^2 − 4x^3 + 5x^4 − 6x^5 + 7x^6)^6

Q15) Number of terms in the expansion of (1 + x + x^2)^100 is

Q16) The number of irrational terms in the binomial expansion of (3^(1/5) + 7^(1/3))^100 is

Q17) In the expansion of (3^(x/4) + 3^(5x/4))^n, the sum of the binomial coefficients is 64 and the term with greatest binomial coefficient exceeds the third by (n1), then find x.

Q18) Find the coefficient of x^4 in (1+ 2x + 3x^2 + ... )^1/2

Q19)
a) Find the coefficient of x^11 in (1 + x + x^2 + x^3 + ... + x^20)^15
b) Find the coefficient of x^11 in (x + x^2 + x^3 + ... + x^20)^15
c) Find the coefficient of x^11 in (x^3 + x^4 + ... + x^20)^15