Sequence and Series-Quiz-16

Sequence and Series Quiz-16

Dear Readers,

The unit Sequence and Series holds sheer significance in the JEE Advanced and other engineering exams. It has a weightage of 8%. With focused practice good marks can be fetched from this section. These questions are important in achieving your success in JEE and Other Engineering Exams..

Q1. 
  If the geometric and harmonic means of two numbers are 16 12 4/5, then the ratio of one number to the other is

•  1:4
•  2:3
•  1:2
•  2:1

Solution

Q2.  Sum of certain consecutive odd positive integers is 57²-13²
  Number of integers are

•  40
•  37
•  44
•  51

Solution

Q3.  Consider three distinct real numbers a,b,c in a G.P. with a²+b²+c²=t² and a+b+c=αt. Sum of the common ratio and its reciprocal is denoted by S
  Complete set of a² is

•   (1/3,3)
•   [1/3,3]
•   (1/3,3)-{1}
•   (-∞,1/3)∪(3,∞)

Solution

Q4.  In a G.P., the sum of the first and last term is 66, the product of the second and the last but one is 128 and the sum of the terms is 126
  If an increasing G.P. is considered, then the number of terms in G.P. is

•  9
•  8
•  12
•  6

Solution

Q5.  Four different integers form an increasing A.P. One of these numbers is equal to the sum of the squares of the other three numbers. Then
  The product of all numbers is

•  -2
•  1
•  0
•  2

Solution

Q6.  Consider the sequence in the form of groups (1), (2, 2), (3, 3, 3), (4, 4, 4, 4), (5, 5, 5, 5), …
  The 2000th term of the sequence is not divisible by

•  3
•  9
•  7
•  None of These

Solution

Q7.  There are two sets A and B each of which consists of three numbers in A.P. whose sum is 15 and where D and d are the common differences such that D-d=1. If p/q=7/8, where p and q are the product of the numbers, respectively, and d>0 in the two sets
  Sum of the product of the numbers in set A taken two at a time is

•  51
•  71
•  74
•  86

Solution

Q8.  Let A_1,A_2,A_3,…,A_m be the arithmetic means between -2 and 1027 and G_1,G_2,G_3,…,G_n be the geometric means between 1 and 1024. The product of geometric means is 2⁴⁵and sum of arithmetic means is 1025×171
 

•  512
•  2046
•  1022
•  None of these

Solution

Q9.  Two consecutive numbers from 1,2,3,…,n are removed. The arithmetic mean of the remaining numbers is 105/4
  The value of n lies in

•   [45, 55]
•   [52, 60]
•   [41, 49]
•  None of These

Solution

Q10.  Two arithmetic progressions have the same numbers. The ratio of the last term of the first progression to first term of the second progression is equal to the ratio of the last term of the second progression to the first term of the first progression and is equal to 4, the ratio of the sum of the n terms of the first progression to the sum of the n terms of the second progression is equal to 2
  The ratio of their common difference is

•  12
•  24
•  26
•  9

Solution