Sequences & Series Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If the A.M. between a and b is m times their H.M. thena : b =
(a)
(b)
(c)
(d) None of these
2. The sum of each of two sets of three terms in A.P. is 15. The common
difference of the first set is greater than that of the second by 1 and the
ratio of the products of the terms in the first set and that of the second
set is 7 : 8. The ratio of the smallest terms in two sets of terms is
(a)
(b)
(c)
(d) None of these
Page 2


PART-I (Single Correct MCQs)
1. If the A.M. between a and b is m times their H.M. thena : b =
(a)
(b)
(c)
(d) None of these
2. The sum of each of two sets of three terms in A.P. is 15. The common
difference of the first set is greater than that of the second by 1 and the
ratio of the products of the terms in the first set and that of the second
set is 7 : 8. The ratio of the smallest terms in two sets of terms is
(a)
(b)
(c)
(d) None of these
3. Sum of the series
up to n terms is equal to
(a)
(b)
(c)
(d)
4. The sum to n terms of the series
2 + 5 +14 + 41 + ........ is
(a)
(b)
(c)
(d) None of these
5. If x = 1 + a + a
2
 + ....................to infinity and
y = 1 + b + b
2
 + ...................to infinity, where a, b are proper fractions,
then  1 + ab + a
2
b
2
 + .....to infinity is equal :
(a)
(b)
(c)
Page 3


PART-I (Single Correct MCQs)
1. If the A.M. between a and b is m times their H.M. thena : b =
(a)
(b)
(c)
(d) None of these
2. The sum of each of two sets of three terms in A.P. is 15. The common
difference of the first set is greater than that of the second by 1 and the
ratio of the products of the terms in the first set and that of the second
set is 7 : 8. The ratio of the smallest terms in two sets of terms is
(a)
(b)
(c)
(d) None of these
3. Sum of the series
up to n terms is equal to
(a)
(b)
(c)
(d)
4. The sum to n terms of the series
2 + 5 +14 + 41 + ........ is
(a)
(b)
(c)
(d) None of these
5. If x = 1 + a + a
2
 + ....................to infinity and
y = 1 + b + b
2
 + ...................to infinity, where a, b are proper fractions,
then  1 + ab + a
2
b
2
 + .....to infinity is equal :
(a)
(b)
(c)
(d)
6. The sum of the series  is
(a) 1
(b) 0
(c)
(d) 4
7. If S
1
, S
2
, S
3
, ...., S
n
 are the sum of infinite geometric series whose first
terms are 1, 2, 3, ..., n and  whose comon ratios are 
respectively, then the value of
 is equal to
(a)
(b)
(c)
(d) None of these
8. If a
1
, a
2
, a
3
,...., a
n
, .... are in A.P. such that a
4
 – a
7
 + a
10
 = m, then the
sum of first 13 terms of this A.P., is :
(a) 10 m
(b) 12 m
(c) 13 m
(d) 15 m
9. If a, b, c are in G.P. and x, y are the arithmetic  means between a, b, and
b, c respectively, then  is equal to
(a) 0
(b) 1
Page 4


PART-I (Single Correct MCQs)
1. If the A.M. between a and b is m times their H.M. thena : b =
(a)
(b)
(c)
(d) None of these
2. The sum of each of two sets of three terms in A.P. is 15. The common
difference of the first set is greater than that of the second by 1 and the
ratio of the products of the terms in the first set and that of the second
set is 7 : 8. The ratio of the smallest terms in two sets of terms is
(a)
(b)
(c)
(d) None of these
3. Sum of the series
up to n terms is equal to
(a)
(b)
(c)
(d)
4. The sum to n terms of the series
2 + 5 +14 + 41 + ........ is
(a)
(b)
(c)
(d) None of these
5. If x = 1 + a + a
2
 + ....................to infinity and
y = 1 + b + b
2
 + ...................to infinity, where a, b are proper fractions,
then  1 + ab + a
2
b
2
 + .....to infinity is equal :
(a)
(b)
(c)
(d)
6. The sum of the series  is
(a) 1
(b) 0
(c)
(d) 4
7. If S
1
, S
2
, S
3
, ...., S
n
 are the sum of infinite geometric series whose first
terms are 1, 2, 3, ..., n and  whose comon ratios are 
respectively, then the value of
 is equal to
(a)
(b)
(c)
(d) None of these
8. If a
1
, a
2
, a
3
,...., a
n
, .... are in A.P. such that a
4
 – a
7
 + a
10
 = m, then the
sum of first 13 terms of this A.P., is :
(a) 10 m
(b) 12 m
(c) 13 m
(d) 15 m
9. If a, b, c are in G.P. and x, y are the arithmetic  means between a, b, and
b, c respectively, then  is equal to
(a) 0
(b) 1
(c) 2
(d)
10. If x > 1, y > 1, z > 1 are in G.P. then  are in
:
(a) A.P.
(b) H.P.
(c) G..P.
(d) None of these
11. If p, q, r are in A.P., a is G.M. between p and q and b is G.M. between q
and r, then a
2
, q
2
, b
2
 are in
(a) G.P.
(b) A.P.
(c) H.P
(d) None of these
12. If S, P and R are the sum, product and sum of the reciprocals of n terms
of an increasing G.P respectively and S
n
 = R
n
.P
k
, then k is equal to
(a) 1
(b) 2
(c) 3
(d) None of these
13. If a, b, c, d are in G.P. then
(a) a + b, b + c, c + d are in G.P.
(b) (b – c)
2
 + (c – a)
2 
+ (d – b)
2 
= (a – d)
2
(c) (a
2 
+ b
2 
+ c
2
)  (b
2 
+ c
2
 + d
2
) = (ab + bc + cd)
2
(d) All are correct
14. The sum of n terms of two arithmetic series are in the ratio 2n + 3 : 6n +
5, then the ratio of their 13th terms is
(a) 53 : 155
(b) 27 : 87
(c) 29 : 83
(d) 31 : 89
15. Let a, b, c, be in A.P. with a common difference d. Then 
Page 5


PART-I (Single Correct MCQs)
1. If the A.M. between a and b is m times their H.M. thena : b =
(a)
(b)
(c)
(d) None of these
2. The sum of each of two sets of three terms in A.P. is 15. The common
difference of the first set is greater than that of the second by 1 and the
ratio of the products of the terms in the first set and that of the second
set is 7 : 8. The ratio of the smallest terms in two sets of terms is
(a)
(b)
(c)
(d) None of these
3. Sum of the series
up to n terms is equal to
(a)
(b)
(c)
(d)
4. The sum to n terms of the series
2 + 5 +14 + 41 + ........ is
(a)
(b)
(c)
(d) None of these
5. If x = 1 + a + a
2
 + ....................to infinity and
y = 1 + b + b
2
 + ...................to infinity, where a, b are proper fractions,
then  1 + ab + a
2
b
2
 + .....to infinity is equal :
(a)
(b)
(c)
(d)
6. The sum of the series  is
(a) 1
(b) 0
(c)
(d) 4
7. If S
1
, S
2
, S
3
, ...., S
n
 are the sum of infinite geometric series whose first
terms are 1, 2, 3, ..., n and  whose comon ratios are 
respectively, then the value of
 is equal to
(a)
(b)
(c)
(d) None of these
8. If a
1
, a
2
, a
3
,...., a
n
, .... are in A.P. such that a
4
 – a
7
 + a
10
 = m, then the
sum of first 13 terms of this A.P., is :
(a) 10 m
(b) 12 m
(c) 13 m
(d) 15 m
9. If a, b, c are in G.P. and x, y are the arithmetic  means between a, b, and
b, c respectively, then  is equal to
(a) 0
(b) 1
(c) 2
(d)
10. If x > 1, y > 1, z > 1 are in G.P. then  are in
:
(a) A.P.
(b) H.P.
(c) G..P.
(d) None of these
11. If p, q, r are in A.P., a is G.M. between p and q and b is G.M. between q
and r, then a
2
, q
2
, b
2
 are in
(a) G.P.
(b) A.P.
(c) H.P
(d) None of these
12. If S, P and R are the sum, product and sum of the reciprocals of n terms
of an increasing G.P respectively and S
n
 = R
n
.P
k
, then k is equal to
(a) 1
(b) 2
(c) 3
(d) None of these
13. If a, b, c, d are in G.P. then
(a) a + b, b + c, c + d are in G.P.
(b) (b – c)
2
 + (c – a)
2 
+ (d – b)
2 
= (a – d)
2
(c) (a
2 
+ b
2 
+ c
2
)  (b
2 
+ c
2
 + d
2
) = (ab + bc + cd)
2
(d) All are correct
14. The sum of n terms of two arithmetic series are in the ratio 2n + 3 : 6n +
5, then the ratio of their 13th terms is
(a) 53 : 155
(b) 27 : 87
(c) 29 : 83
(d) 31 : 89
15. Let a, b, c, be in A.P. with a common difference d. Then 
 are in :
(a) G.P. with common ratio e
d
(b) G.P with common ratio e
1/d
(c) G.P. with common ratio
(d) A.P.
16. If p
th
, q
th
 and r
th
 terms of an A.P. are equal to corresponding terms of a
G.P. and these terms are respectively x, y, z, then
x
y–z
. y
z–x
. z
x–y
 equals
(a) 0
(b) 1
(c) 2
(d) None of these
17. For the series 
(a)
(b)
(c)
(d) None of these
18. If a
1
, a
2, ........
a
n+1
 are in A.P. then  is
(a)
(b)