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Revision Quiz | Binomial Theorem

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Question 1

The sum of the series

Question 2

The number of different terms in the expansion of

Question 3

What is the co-efficient of x² in the expansion of (1+4x+x²)¹^⁄² is equal to?

Question 4

The number of natural numbers n in the interval [1005, 2010] for which the polynomial: 1 + x + x³ + x³ + ... + x^n-1 divides the polynomial 1 + x² + x⁴ + x^t + ... + x²⁰¹⁰ is

Question 5

Find the coefficient of

Question 6

Find number of terms in

Question 7

In how many ways 10 identical oranges can be given to 3 children from 3 baskets having 7,6,4 oranges respectively?

Question 8

For x∈R, x≠-1 if

then a₁₇ is equal to:

Question 9

The number of ways of selecting n things out of 3n things, of which n are of one kind and alike, and n are of a second kind and alike and the rest are unlike, is.

Question 10

Find the sum of the series
1+(0.2)+(0.2)²+(0.2)³+(0.2)⁴+(0.2)⁵+....

Question 11

Find the sum of the coefficients of (1+x

Question 12

If the coefficient of x³ and x⁴ in the expansion of (1 + ax + bx²) (1 – 2x)¹⁸ in powers of x are both zero, then (a, b) is equal to

Question 13

In the binomial expansion of (a – b)ⁿ, n ≥ 5, the sum of 5^th and 6^th terms is zero, then a/b equals

Question 14

Directions: Assertion–Reason type questions. Each of these questions contains two statements: statement–1 (Assertion) and Statement–2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Statement–1:

ⁿC_r = (n + 2) 2^n–1
Statement–2:

ⁿC_r x^r = (1 + x)ⁿ + nx (1 + x)^n–1

Question 15

The coefficient of

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Dec 7JEE & BITSAT