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JEE Questions for Maths Sequences And Series Quiz 1 - MCQExams.com
JEE
Maths
Sequences And Series
Quiz 1
The mean of the series a,a + nd, a + 2nd is
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a + (n -d
0%
a + nd
0%
a + (n + 1)d
0%
None of these
If A.M and G.M of x and y are in the ratio p : q the x : y is
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0%
0%
2)
0%
0%
0%
The third term of a geometric progression is 4. The product of the first five terms is
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0%
43
0%
45
0%
44
0%
none of these
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0%
0%
2)
0%
0%
none of these
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A.P.
0%
G.P.
0%
H.P.
0%
none of these
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2n - n -1
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1- 2-n
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n + 2-n – 1
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2n + 1.
The arithmetic mean of first n odd natural number is
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n2
0%
2n
0%
n
0%
3n
If sum of n terms of an AP is 2n + 3n
2
, then rth term is
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2r + 3r2
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3r2 - 4r + 1
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6r - 1
0%
4r + 1
If the sum to 2n terms of an AP 2,5,8,11,...is equal to the sum of n terms of an AP 57,59,61,63,...,then n is equal to
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0%
10
0%
11
0%
12
0%
13
If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an AP is
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0%
1700
0%
1650
0%
3300
0%
3400
0%
3500
If a, b, c are in arithmetic progression, then the value of (a + 2b - c)(2b + c - a)(a + 2b + c) is
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16abc
0%
4abc
0%
8abc
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3abc
The sets S
1
,S
2
, S
3
,... are given by
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0%
320
0%
322
0%
324
0%
326
If p th term of an arithmetic progression is q and the qth term is p, then 10th term is
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p - q + 10
0%
p +q + 11
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p + q - 9
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p + q - 10
if a
2
, b
2
, c
2
are in AP, then which of the following is also an AP?
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sin A, sin B , sin C
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tan A, tan B, tan C
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cot A , cot B , cot C
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None of these
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a, b, c are in AP
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c,a,b are in AP
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a2, b2,C2 are in AP
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a,b,c are in GP
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c2, a2, b2 are in AP
If the arithmetic mean of a and b is
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0%
-1
0%
0
0%
1
0%
None of these
Let T
r
be the rth term of an AP whose first term is a and common difference is d. If for some positive integers m, n ,m # n, T
m
= 1/n and T
n
= 1/m, then a - d equals
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0%
0
0%
1
0%
1/(mn)
0%
Let a
1
, a
2
, a
3
,... be terms of an AP. If
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0%
7/2
0%
2/7
0%
11/41
0%
41/11
Three numbers are in AP such that their sum is 18 and sum of their squares is 158. The greatest number among them is
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0%
10
0%
11
0%
12
0%
None of these
The number log2
7
is
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an integer
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a rational number
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an irrational number
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a prime number
The sum of the integers from 1 to 100 which are divisible by 3 and 5, is
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0%
2317
0%
2632
0%
315
0%
2489
If a,b and c are in AP, then which one of the following is not true?
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0%
a+ k, b+k and c+k in AP
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ka, kb and kc are in AP
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a2, b2 and C2 are in AP
If χ, y and z in AP, then
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AP
0%
Gp
0%
HP
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AP and Hp
If ln(a + c), ln (a – c), ln (a – 2b + c) are in A.P., then
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a, b, c are in A.P.
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a2, b2, c2 are in A.P.
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a, b, c are in G.P.
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a, b, c are in H.P.
Consider an infinite geometric series with first term a and common ratio r. If the sum is 4 and the second term is 3/4, then
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a = 2, r = 3/8
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a = 4/7, r = 3/7
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a = 3/2, r = 1/2
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a = 3, r = 1/4
If a, b and c are positive numbers in a GP, then the roots of the quadratic equation (log
e
a) χ
2
— (2 log
e
b) χ + (log
e
c)= 0 are
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0%
0%
2)
0%
1 and loga c
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- 1 and logc a
The sum of first three terms of a GP is 7/9 and their product is -8/ 27. Find the common ratio of the series
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r = - 2/3 or - 3/2
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r = - 2/3 or 3/2
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r = 2/3 or - 3/2
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r = 2/ 3 or 3/2
The sum of first 8 terms of the geometric series 2 + 6 + 18 + 54 +... is
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0%
6506
0%
5650
0%
6650
0%
6560
For what values of x, the numbers - 1, χ, - 3/4 are in GP?
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3/2
0%
√3/4
0%
√3/2
0%
3/√2
Which term of the series √2, 2/3, 2√2/9,... is 16/2187?
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10th term
0%
8th term
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9th term
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11th term
The sum of 0.2 + 0.22 + 0.222 + ...to n terms is equal to
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0%
0%
2)
0%
0%
Suppose a, b and c are in AP and a
2
, b
2
and c
2
are in GP. If a < b < c and a + b + c = 3/2, hen the value of a is
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0%
1/2√2
0%
1/2√3
0%
1/2 - 1/√3
0%
1/2 - 1/√2
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0%
0%
ea - e
0%
0%
If the sequence {a
n
} is in GP, such that a
4
/a
6
= 1/ 4 and a
2
+ a
5
= 216, then a
1
is equal to
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0%
12 or 108/7
0%
10
0%
7 or 54/7
0%
None of these
Let S
k
be the sum of an infinite GP series whose first term k is k and common ratio is k/(k +(k> 0). Then, the value of
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loge 4
0%
loge 2 - 1
0%
1 - loge 2
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1 - loge 4
The value of χ which satisfies 8
1+cos χ +cos
2
χ +...
= 64 in [ -π, π] is
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± π/2 , ± π/3
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± π/3
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± π/2 , ± π/6
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± π/6 , ± π/3
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0%
2
0%
3
0%
5
0%
6
If the (p+ q)th term of a geometric series is m and the (p - q )th term is n, then the pth term is
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(mn)1/2
0%
mn
0%
m + n
0%
m - n
The 5th term of the series
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1/3
0%
1
0%
2/5
0%
If S is the sum, P is the product and R is the sum of the reciprocals of n terms of a GP, then P
2
is equal to
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(S/R)n
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S/R
0%
(R/S)n
0%
R/S
If a
1
, a
2
,...a
50
are in GP, then
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0
0%
1
0%
a1/a2
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a25/a24
0%
2a1/3a2
Fifth term of a GP is 2, then the product of its 9 term is
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0%
256
0%
512
0%
1024
0%
None of these
The sum of infinity of the progression 9 - 3 + 1 - 1/3 + ... is
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0%
9
0%
9/2
0%
27/4
0%
15/2
If {a
n
} is a sequence with a
0
= p and a
n
- a
n-1
= ra
n-1
for n ≥ 1, then the terms of the sequence are in
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an arithmetic progression
0%
a geometric progression
0%
a harmonic progression
0%
an arithmetico - geometric progression
If 0 < ∅ < π/2,
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χyz = χz + y
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χyz = χy + z
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χyz = yz + χ
0%
χyz = χ + yz
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0%
2
0%
4
0%
6
0%
8
The product ((32)
1/6
(32)
1/36
... to ∞ is
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0%
16
0%
32
0%
64
0%
0
0%
62
If S is the sum of an infinite GP and a is the first term, then the Common ratio r is given by
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0%
0%
2)
0%
0%
If f(χ) = χ + 1/2. Then, the number of real values of χ for which the three unequal terms f(χ), f(2χ) and f(4χ) are in HP is
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0%
1
0%
0
0%
3
0%
2
If H is the harmonic mean between P and q, then the value of
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0%
2
0%
2)
0%
1/2
0%
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