Quiz for Binomial Theorem

Q1: What is the number of terms in the expansion of (x + a)^n?

A. n B. n+1 C. 2n D. 2n+1

Q2: Which term is the greatest in the expansion of (1 + x)^n when x = 1?

A. Middle term B. Last term C. First term D. Cannot be determined

Q3: In the expansion of (1 + x)^6, the coefficient of x^3 is:

A. 15 B. 20 C. 10 D. 30

Q4: The term independent of x in the expansion of (x^2 + 1/x)^6 is:

A. x^0 B. x C. x^2 D. x^3

Q5: In (2 + x)^5, the term containing x^3 is:

A. 10x^3 B. 40x^3 C. 80x^3 D. 160x^3

Q6: What is the middle term in the expansion of (1 + x)^10?

A. 5th term B. 6th term C. 7th term D. None

Q7: The general term in the binomial expansion of (a + b)^n is:

A. nCr * a^r * b^(n-r) B. nCr * a^(n-r) * b^r C. nPr * a^r * b^(n-r) D. None

Q8: In (1 + 2x)^4, the coefficient of x^3 is:

A. 16 B. 32 C. 48 D. 64

Q9: In the expansion of (1 - x)^n, the coefficients of even powers are:

A. Positive B. Negative C. Zero D. Alternating

Q10: Sum of coefficients in (x + 1)^n is:

A. n B. 2^n C. n+1 D. n^2

Q11: The term independent of x in (x + 1/x)^n exists only when:

A. n is odd B. n is even C. Always exists D. Never exists

Q12: The coefficient of x^5 in (1 + x)^10 is:

A. 100 B. 252 C. 120 D. 210

Q13: The number of terms in (a + b + c)^3 is:

A. 6 B. 8 C. 10 D. 9

Q14: Which of the following is not true for Binomial Theorem?

A. Valid for positive integers only B. Valid for negative indices C. Infinite terms for fractional powers D. Only 2 terms allowed in expansion

Q15: The coefficient of x^n in (1 + x)^2n is:

A. ^2nCn B. ^nCn C. 2n D. n

Q16: The ratio of coefficients of x^2 and x^3 in (1 + x)^5 is:

A. 2:3 B. 5:10 C. 10:10 D. 10:15

Q17: What is the value of (1 + x)^0?

A. 0 B. x C. 1 D. Undefined

Q18: Which of the following expansions will have alternating signs?

A. (1 - x)^n B. (1 + x)^n C. (x - 1)^n D. (1 + x)^n + (1 - x)^n

Q19: In (a + b)^6, the coefficient of a^2b^4 is:

A. 15 B. 20 C. 6 D. 10

Q20: Which one is a binomial expression?

A. x^2 + 1 B. x + y + z C. x^2 - y^2 + 1 D. x^3

Q21: The binomial expansion is based on:

A. Combinations B. Permutations C. Integration D. Matrices