1. Third term of (x + y)⁴ is:
(A) 4x²y²
(B) 4x³y
(C) 6x²y²
(D) 6x³y
2. The number of terms in the expansion (a + b)¹³ are:
(A) 12
(B) 13
(C) 14
(D) 15
3. The value of nCr is:
(A) n! / (r!(n–r)!)
(B) n / (r(n–r))
(C) n! / r!(n–r)
(D) n! / (n–r)!
4. The second last term in the expansion of (a + b)⁷ is:
(A) 7a⁶b
(B) 7ab⁶
(C) 7b⁷
(D) 15
5. ⁶C₄ will have the value:
(A) 10
(B) 15
(C) 20
(D) 25
6. ³C₀ will have the value:
(A) 0
(B) 1
(C) 2
(D) 3
7. In the expansion of (a + b)ⁿ the general term is:
(A) nCr a^(n–r) b^r
(B) n–rCr a^r b^(n–r)
(C) n–r+1Cr–1 a^(n) b^(r–1)
(D) n–r–1Cr–1 a^(n) b^r
8. In the expansion of (a + b)ⁿ the term n–rCr a^(n–r) b^r will be:
(A) nth term
(B) rth term
(C) (r+1)th term
(D) None of these
9. In the expansion of (a + b)ⁿ the rth term is:
(A) nCr a^(n–r) b^r
(B) nC(n–r) a^r b^(n–r)
(C) nC(n–r+1) a^(n) b^(r–1)
(D) nC(n–r–1) a^(n) b^(r–1)
10. In the expansion of (1 + x)ⁿ the coefficient of 3rd term is:
(A) nC₀
(B) nC₁
(C) nC₂
(D) nC₃
11. In the expansion of (a + b)ⁿ the sum of the exponents of a and b in any term is:
(A) n
(B) n–1
(C) n+1
(D) None of these
12. The middle term in the expansion of (a + b)⁶ is:
(A) 15a⁴b²
(B) 20a³b³
(C) 15a²b⁴
(D) 6ab⁵
13. The value of nCn is equal to:
(A) 0
(B) 1
(C) n
(D) –n
14. The expansion of (1 + x)⁻¹ is:
(A) 1 – x + x² – x³ + …
(B) 1 + x – x² + x³ – …
(C) 1 + x + x²/2! + x³/3! + …
(D) 1 – x + x²/2! – x³/3! + …
15. The expansion of (1 – x)⁻¹ is:
(A) 1 + x + x² + x³ + …
(B) 1 + x – x² + x³ – …
(C) 1 + x + x²/2! – x³/3! + …
(D) 1 – x + x² – x³ + …
16. Binomial series for (1 + x)ⁿ is valid only when:
(A) x < 1
(B) x < –1
(C) |x| < 1
(D) None of these
17. The value of ²ⁿCₙ is:
(A) (2n)! / (n! n!)
(B) (2n)! / (n! n!)
(C) (2n)! / n!
(D) (2n)! / [n(n–1)!]
18. The middle term of (4x – y)⁴ is:
(A) 6 (4x)²y²
(B) 6
(C) 8
(D) 4xy