If the sum of the coefficients in the expansion of (a2x2 – 6ax + 11)10, where a is constant is 1024, then the value of a is 1) 5 2) 1 3) 2 4) 3 5) 4 Solution: (4) 3... View Article
Let (1 + x)n = 1 + a1x + a2x2 + …+ anxn. If a1, a2 and a3 are in AP, then the value of n is 1) 4 2) 5 3) 6 4) 7 5) 8 Solution: (4) 7... View Article
For r = 0, 1, …, 10 let Ar, Br and Cr denote, respectively the coefficient of xr in the expansion of (1 + x)10, (1 + x)20 and (1 + x)30. Then ∑r=110 Ar (B10 Br – C10 Ar) = 1) B10 - C10 2) A10 (B102 - C10A10) 3) 0 4) C10 - B10 Solution: (4) C10 - B10... View Article
The expression nC0 + 2nC1 + 3nC2 + (n + 1)nCn is equal to 1) (n + 1)2n 2) 2n(n + 2) 3) (n + 2)2n-1 4) (n + 2)2n+1 Solution: (3) (n + 2)2n-1... View Article
If C0, C1, … Cn denote the binomial coefficients in the expansion of (1 + x)n. Then, the value of C1 – 2C2 + 3C3 – 4C4 + ….(up to n terms) is 1) 2n 2) 2-n 3) 0 4) 1 Solution: (3) 0... View Article
15C3 + 15C5 + …+ 15C15 is equal to 1) 214 2) 214 - 15 3) 214 + 15 4) 214 - 1 Solution: (2) 214 - 15... View Article
If nC4, nC5, and nC6 are in AP, then n is 1) 7 or 14 2) 7 3) 14 4) 14 or 21 Solution: (1) 7 or 14... View Article
If the binomial coefficients of (3r)th and (r + 2)th terms in the binomial expansion of (1 + x)2n are equal, then 1) n = r 2) n = r + 1 3) n = 2r 4) n = 2r - 1 Solution: (3) n = 2r... View Article
[1 + (C1 / C0)] [1 + (C2 / C1)] [1 + (C3 / C2)] + …… [1 + (Cn / Cn-1)] = 1) [n + 1] / n! 2) [n + 1]n / (n - 1)! 3) [n + 1]n / (n)! 4) [n - 1]n / (n!) Solution: (3) [n + 1]n / (n)!... View Article
The sum ∑i=0m (10, i) (20, m – i) for i ∈ [0, m], (where (p, q) = 0, if p > q) is maximum when ‘ m ‘ is 1) 5 2) 10 3) 15 4) 20 Solution: (3) 15... View Article
(C1 / C0) + 2 (C2 / C1) + 3 (C3 / C2) + …….. + n (Cn / Cn-1) = 1) [n (n - 1)] / 2 2) [n (n + 1)] / 2 3) [(n + 1) (n + 2)] / 2 4) None of these Solution: (2) [n (n + 1)] / 2... View Article
If n is an integer with 0 ≤ n ≤ 11, then the minimum value of n!(11 – 1) ! is attained, when a value of n equals 1) 11 2) 5 3) 7 4) 9 Solution: (2) 5... View Article
mCr+1 + ∑k=mn kCr = 1) nCr+1 2) n+1Cr+1 3) nCr 4) None of these Solution: (2) n+1Cr+1... View Article
If S = given expression, then S = 1) [2n+1 - 1] / (n + 1) 2) [3n+1 - 1] / (n + 1) 3) [3n - 1] / n 4) [2n - 1] / n Solution: (2) [3n+1 - 1] / (n + 1)... View Article
The value of (nC1)2 + (nC2)2 + (nC3)2 +… + (nCn)2 is 1) (2nCn)2 2) 2nCn 3) 2nCn + 1 4) 2nCn - 1 Solution: (4) 2nCn - 1... View Article
The term independent of x in the expansion of [x3 – (2 / x2)]15 is 1) T7 2) T8 3) T9 4) T10 Solution: (4) T10... View Article
The middle term in the expansion of [x – (1 / x)]18 is 1) 18C9 2) -18C9 3) 18C10 4) -18C10 Solution: (2) -18C9 The middle term of the expansion [x - (1 / x)]18 is T10. T9+1 = 18C9 x9... View Article
The sum of coefficients in the expansion of [(1 / x) + 2x]n is 6561. The coefficient of term independent of x is 1) 16 8C4 2) 8C4 3) 8C5 4) None of these Solution: (1) 16 8C4... View Article
The term independent of x in the expansion of [(2√x / 5) – (1 / 2x √x)]11 is 1) 5th term 2) 6th term 3) 11th term 4) No term Solution: (4) No term... View Article
The largest coefficient in the expansion of (1 + x)24 is 1) 24C24 2) 24C13 3) 24C12 4) 24C11 Solution: (3) 24C12 The binomial coefficient of the middle term is the greatest binomial... View Article
