Question

The number of terms in (1 + x)101 (1 + x2 – x)100 is

Solution

Correct option is

202

E = (1 + x)1 [(1 + x) (1 + x2 – x)]100­

   = (1 + x) (1 +x3)100

   = (1 + x) [101 terms in (1 + x3)100]

   = 101 + 101 = 202 terms in E.

SIMILAR QUESTIONS

Q1

If the sum of the coefficients in the expression of (1 + 2x)n is 6561. The greatest term in the expression at x = 1/2 is

Q2

The number of terms in the expression of (a + b + c)n, where n Ïµ N, is

Q3

The number of terms which are free from fractional powers in the expansion of (a1/5 + b2/3)45a ≠ b is

Q4

If n is an odd natural, then  equals

Q5
Q6

The coefficient of xm in (1 + x)r + (1 + x)r+1 + (1 + x)r+2 +….+ (1 + x)nr≤ m ≤ n is

Q7

 respect to x, is

Q8

 is a polynomial of degree 5, then n

Q9

If in the expression of (1 + x)m (1 – x)n. the coefficient of x and x2 are 3 and – 6 respectively, then m is

Q10

In the binomial expansion of (a – b)n, n ≤ 5, the sum of the 5th and 5thterms is zero. Then  equals