Class 11 maths jee Brilliant Pala Question Paper - Sequence and series

SEQUENCE AND SERIES




QUESTIONS
1. A man arrange to pay off a debt of 3600 by 40 annual instalments which are in A.P. When 30 of the
instalments are paid he dies leaving one third of the debt unpaid. The value of the 8th instalment is
A) Rs.55 B) Rs.50 C) Rs.60 D) Rs. 65

1 1 1
h n are two A.P. Such that x 3  h 2  8 and x 8  h 7  20 , then
2. If x1 , x 2 ......, x n and , , .........,
h1 h 2
x5.h10 equals :
A) 3200 B) 1600 C) 2650 D) 2560
3. In a sequence of 9 terms, the first 5 terms are in A.P whose common difference is 2 and the last 5
terms are in G.P whose common ratio is 1/2. If the middle terms of the A.P and G.P are equal, then the
middle term of the G.P is
A) 1/3 B) 4/3 C) 5/3 D) 7/3
4. If the sum of an infinitely decreasing G.P. is 3 and the sum of the squares of its terms is 9/2. Then the
sum of the cubes of the terms is:
A) 107/13 B) 97/13 C) 107/24 D) 108/13
5. If S is the sum to infinity of a Geometric progression, whose first term is ‘a’, then the sum of the first n
terms is:

n
  a 
n
 a
A) S 1   B) a 1  1   
 S   S 


  S 
n
  a n 
C) a 1  1    D) S 1  1  S  
  a     

6. A ball is dropped from a height of 48 meters and rebounds 2/3 of the distance it falls. If it continues to
fall and rebound in this way the distance the ball travels before coming to rest is ( in meters)




1

, A) 144 B) 120 C) 240 D) 96

9 99 999 9999
7. The sum of the series  2 3        is:
19 19 19 19 4
A) 19/18 B) 18/19 C) 7/18 D) 18/17
  

8. Let a, b, c be in AP. If 0 < a, b, c < 1, x  a
n 0
n
, y   b n and z   c n , then
n 0 n 0

A) 2y = x + z B) 2x = y + z

xz 2xz
C) y  D) y 
xz xz

1 1 1
9. Let , , ......,  x i  0 for i  1, 2, ...., n  be in A.P. such that x1  4 and x 21  20 . If n is the
x1 x 2 xn
n
1
least positive integer for which x n  50 then  x  is equal to :
i 1  i 



1
A) 3 B)
8

13 13
C) D)
4 8
1 2 3 n
10. Given the sequence 1011 , 1011 , 1011 , ......1011 . The smallest value of n  N such that the product of the
first ‘n’ terms of the sequence exceeds one lakh is
A) 10 B) 11 C) 12 D) 9
11. Given a sequence of ten numbers, if the first number is 2 and each other number is the square of the
preceeding number, then the 10th number is
A) between 1010 and 1015
B) between 1025 and 1050
C) between 1050 and 1075
D) more than 10100
12. A sequence is such that the sum of its any number of terms, begining from the first, is four times as
large as the square of the number of terms. If the nth term of such a sequence is 996. Then the value
of n is equal to
(A) 100 (B) 112 (C) 125 (D) 132
13. Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new
numbers are in A.P. Then the common ratio of the G.P. is



2