1. Roll No. :
Date :
Time -
MM - 70
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14.
Find the number of terms in the expansion of (a + 2b – 3c)n.
Find the middle term(s) in the expansion of : (1 + x)2n
The coefficients of 2nd, 3rd and 4th terms in the expansion of (1 + x)2n are in A.P., prove that 2n2
– 9n + 7 = 0
If Tr is rth term in the expansion of (1 + x)n in the ascending powers of x, prove that r (r + 1) Tr+2
= (n – r + 1) (n – r)x2 Tr.
If the 3rd, 4th, 5th and 6th terms in the expansion of (x + y)n be a, b, c and d respectively, prove
that
If a, b, c be the three consecutive coefficients in the expansion of (1 + x)n, prove that n =
Using binomial theorem, prove that 6n – 5n always leaves remainder 1 when divided by 25.
If a1, a2, a3 and a4 are the coefficient of any four consecutive terms in the expansion of (1 + x)n,
prove that
Find the sum (33 – 23) + (53 – 43) + (73 – 63) + ... 10 terms.
If a, b, c be the first, third and nth term respectively of an A.P. Prove that the sum to n terms is
If a, b, c are in G.P and . Prove that x, y, z are in A.P.
If a1, a2, a3, ... an are in A.P., where ai > 0 for all i, show that
=
The ratio of the A.M. and G.M. of two positive numbers a and b is m : n, show that:
If p, q, r are in G.P. and the equations px2 + 2qx + r = 0 and dx2 + 2ex + f = 0 have a common
root then show that are in A.P.
2. 6
15.
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17.
Find the sum of, + .......................... up to n terms.
If S1, S2, S3, ......, Sm are the sums of n terms of m A.P.'s whose first terms are 1, 2, 3, ......, m
and common differences are 1, 3, 5, ......, 2m – 1 respectively, show that S1 + S2 + S3 + ...... + Sm =
mn (mn + 1)
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the
numbers are A ± .
