Mathematics
TIME: 2.5 hr. MM:
General Instructions:
* All Questions are compulsory.
* Marks are given alongwith the questions individually.
* Use of calculator is not permitted.
Q.1 In an A.P., the first term is 2 and the sum of the first five terms is one-forth of the next five
terms. Show that 20th term is -112.
Q.2 If -1 -1 +
+
n n
n n
a b
a b
is the A.M between a and b, then find the value of n.
Q.3 Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an
A.P. and the ratio of 7th and (m -1)th numbers is 5:9. Find the value of m.
Q.4 The difference between any two consecutive interior angles of a polygon is 50. If the smallest
angle is 1200, find the number of the sides of the polygon.
Q.5 Evaluate S
=
11
k 1
(2 + 3k)
Q.6 Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and
128 , 32, 8, 2,
2
1
.
Q.7 If A and G be A.M. and G.M., respectively between two positive numbers. Prove that the
numbers are A± (A+G)(A-G).
Q.8 Find the sum to n terms of the series: 5 + 11 + 19 +29 + 41 …
Q.9 Find the sum to n terms of the series 52 + 62 + 72 +…+202
Q.10 Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3
( S2 – S1)
Q.13 Find the sum upto n terms .6 +. 66 +. 666+…
Q 14 If S1, S2, S3 are the sum of first n natural numbers, their squares and their cubes, respectively,
show that 9 S2
2 = S3 (1 + 8S1).
Q.15 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on
second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish
the work. Find the number of days in which the work was completed.
Q.16 The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of mth and nth
term is (2m – 1) : ( 2n -1)
Q.17. Find the sum to n terms
...
3 4
1
2 3
1
1 2
1 +
´
+
´
+
´
Q.18 The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first
term is 11, then find the number of terms.
Q.19 If a and b are the roots of x2 – 3x + p = 0 and c, d are roots of x2 – 12x + q = 0, where a, b, c, d
form a G.P. Prove that (q + p) : (q – p) = 17 : 15.
Q.20 A person writes a letter to four of his friends. He asks each one of them to copy the letter and
mail to four different persons with instructions that they move the chain similarly. Assuming
that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent
on the postage
when 8th set of letter is mailed.
Q.21 If the first and n th term of a G.P are a and b respectively and if P is the product on n terms,
prove that p2 = (ab)n
Q.22 Insert 6 numbers between 3 and 24 such that the resulting sequence is an A.P.Labels: India Question Papers