For natural numbers and m and n , if (1 – y)m (1 + y)n = 1 + a1y + a2y2 + … and a1 = a2 = 10, then (m , n) is 1) (35 , 20) 2) (45 , 35) 3) (35 , 45) 4) (20 , 45) Solution: (3) (35 , 45)... View Article
If n = 5, then (nC0)2 + (nC1)2 + (nC2)2 + …+ (nC5)2 1) 250 2) 254 3) 245 4) 252 5) 258 Solution: (4) 252... View Article
The sum of the last eight coefficients in the expansion of (1 + x)15 is 1) 216 2) 215 3) 214 4) None of these Solution: (3) 214... View Article
The sum of series 20C0 – 20C1 x + 20C2 x2 – 20C3 + …+ 20C20 x20 is 1) – 20C10 2) (1/2) 20C10 3) 0 4) 20C10 Solution: (2) (1/2) 20C10... View Article
If C0, C1, C2.., Cn denote the binomial coefficients in the expansion of (1 + x)n, then C0 + (C1 / 2) + (C2 / 3) + ….. Cn / (n + 1) = 1) [2n+1 - 1] / (n + 1) 2) [2n - 1] / (n + 1) 3) [2n-1 - 1] / (n - 1) 4) [2n+1 - 1] / (n + 2) Solution: (1) [2n+1 - 1] / (n + 1)... View Article
If (1 + x – 3x2)10 = 1 + a1x + a2x2 + a20x20, then a2 + a4 + a6 + ..+ a20 is equal to 1) [310 + 1] / 2 2) [39 + 1] / 2 3) [310 - 1] / 2 4) [39 - 1] / 2 Solution: (3) [310 - 1] / 2... View Article
If (1 + x)n = C0 + C1x + C2x2 + … + Cnxn. Then, C0C1 + C1C2 + …+ Cn –1 Cn is equal to 1) [2n! / (n - 1)! (n + 1)!] 2) [(2n - 1)! / (n - 1)! (n + 1)!] 3) [2n! / (n + 2)! (n + 1)!] 4) None of these Solution: (1) [2n! / (n - 1)!... View Article
The value of (1 / 81n) – (10 / 81n) 2nC1 + (102 / 81n) 2nC2 – (103 / 81n) 2nC3 + ….. + (102n / 81n) is 1) 2 2) 0 3) 1/2 4) 1 Solution: (4) 1... View Article
Coefficient of t24 in (1 + t2)12 (1 + t12) (1 + t24) is 1) 12C6 + 3 2) 12C6 + 1 3) 12C6 4) 12C6 + 2 Solution: (4) 12C6 + 2... View Article
The value of sum of the series 3 . nC0 – 8 nC1 + 13 nC2 – 18nC3 + … up to (n + 1) terms is 1) 0 2) 3n 3) 5n 4) None of these Solution: (1) 0... View Article
(C0 / 1) + (C2 / 3) + (C4 / 5) + (C6 / 7) + ….. = 1) 2n+1 / (n + 1) 2) (2n+1 - 1) / (n + 1) 3) 2n / (n + 1) 4) None of these Solution: (3) 2n / (n + 1)... View Article
8C0 / 6 – 8C1 + 8C2 . 6 – 8C3 . 62 +…+ 8C8 . 67 is equal to 1) 0 2) 67 3) 68 4) 58 / 6 Solution: (4) 58 / 6... View Article
The value of 15C8 + 15C9 – 15C6 – 15C7 is 1) – 1 2) 0 3) 1 4) None of these Solution: (2) 0... View Article
15C0 . 5C5 + 15C1 . 5C4 + 15C2 . 5C3 + 15C3 . 5C2 + 15C4 . 5C1 is equal to 1) 220 - 25 2) 20! / 5! 15! 3) (20!/5! 15!) - 1 4) [20! / (5! 15!)] - [15! / (5! 10!)] 5) 15! / 5! 10! Solution: (4) [20! / (5! 15!)] - [15!... View Article
n – 2Cr + 2n -2Cr -1 + n -2Cr – 2 is equal to 1) n+1Cr 2) nCr 3) n+1Cr+1 4) n -1Cr Solution: (2) nCr... View Article
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