If the expansion in powers of x of the function is a0 + a1x + a2x2 + a3x3 + … , then an is
For natural numbers m, n if (1 − y)m (1 + y)n = 1 + a1y + a2y2 + … , and a1 = a2 = 10, then (m, n) is
(20, 45)
(35, 20)
(45, 35)
(45, 35)
The value of ,where [x] denotes the greatest integer not exceeding x is
af(a) − {f(1) + f(2) + … + f([a])}
[a] f(a) − {f(1) + f(2) + … + f([a])}
[a] f([a]) − {f(1) + f(2) + … + f(a)}
[a] f([a]) − {f(1) + f(2) + … + f(a)}
If a1, a2, … , an are in H.P., then the expression a1a2 + a2a3 + … + an−1an is equal to
n(a1 − an)
(n − 1) (a1 − an)
na1an
na1an
The coefficient of the middle term in the binomial expansion in powers of x of (1 +αx)4 and of (1−αx )6 is the same if α equals
-5/3
3/5
-3/10
-3/10
Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + .....
If B – 2A = 100λ, then λis equal to
496
232
248
464