JEE Questions for Maths Sequences And Series Quiz 2

If χ, y, z are in HP, then log(χ + z) + log (χ - 2y + z) is equal to

0%
log(χ-z)
0%
2log(χ-z)
0%
3log(χ-z)
0%
4log(χ-z)

If 4a² + 9b² + 16c² = 2(3ab + 6bc + 4ca), where a, b and c are non - zero numbers, then a, b, c are in

0%
AP
0%
GP
0%
HP
0%
None of these

If two positive numbers are in the ratio of 3 + 2√2 : 3 - 2√2, then the ratio between their AM and GM is

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6 : 1
0%
3 : 2
0%
2 : 1
0%
3 : 1

The minimum value of 2^sinχ + 2^cosχ is

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21 - 1/√2
0%
21 + 1/√2
0%
2√2
0%
2

If log_χ aχ, log_χ bχ and log_χ cχare in AP, where a, b, c and χ belong to (1, ∞), then a, b and c are in

0%
AP
0%
Hp
0%
Gp
0%
None of these

If χ, y and z are in geometric progression, then log_χ 10, log_y 10 and log_z 10 are in

0%
AP
0%
GP
0%
HP
0%
None of these

GM and HM of two numbers are 10 and 8, respectively. The numbers are

0%
5, 20
0%
4, 25
0%
2, 50
0%
1, 100

If a, b, c are in GP and χ, y are arithmetic mean of a, b and b, c respectively, then 1/χ + 1/y is equal to

0%
2/b
0%
3/b
0%
b/3
0%
b/2
0%
1/b

In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the middle term of an AP is equal to the middle term of the GP, then the middle term of the entire sequences is

0%
-(10/31)
0%
10/31
0%
32/31
0%
-(31/32)

If a, b, c are in GP and 4a, 5b, 4c are in AP such that a + b + c = 70, then value of b is

0%
5
0%
10
0%
15
0%
20

If a^1/χ = b^1/y = c^1/z and a, b, c are in geometric progression, then χ, y, z are in

0%
AP
0%
GP
0%
HP
0%
None of these

The difference between two numbers is 48 and the difference between their arithmetic mean and their geometric mean is 18. Then, the greater of two numbers is

0%
96
0%
60
0%
54
0%
49

Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4, then

0%
0%
2)
0%
0%

If a is positive and also A, G are the arithmetic mean and the geometric mean of the roots of χ² - 2aχ + a² = 0 respectively, then

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A = G
0%
A = 2 G
0%
2A = G
0%
A2 = G
0%
A =G2

Three numbers whose sum is 15 are in AP. If they are added by 1, 4 and 19 respectively, then they are in GP. The numbers are

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2, 5, 8
0%
26, 5, -16
0%
2, 5, 8 and 26, 5, -16
0%
None of these

If AM of two numbers is twice of their GM, then the ratio of greatest number to smallest number is

0%
7 - 4√3
0%
7 + 4√3
0%
21
0%
5

If H₁ and H₂ are two harmonic means between two positive numbers a and b (a ≠ b), A and G are the arithmetic and geometric means between a and b, then
Maths-Sequences and Series-47186.png

0%
A/G
0%
2A/G
0%
A/G2
0%
A/G2
0%
2A/G2

If A₁ , A₂, G₁, G₂ and H₁ ,H₂ are two AM's, GM's and HM's between two quantities, then the value of
Maths-Sequences and Series-47188.png

0%
0%
2)
0%
0%

0%
f(χ) < 1
0%
f(χ) = 1
0%
1 < f(χ) < 2
0%
f(χ) ≥ 2

Let a, b, c be in AP and |a| < 1, |b| < 1, |c| < 1. If χ = 1 + a + a² + ...+ ∞, y = 1 + b + b² + ...+ ∞, z = 1 + c + c² + ...+ ∞, then χ, y and z are in

0%
AP
0%
GP
0%
HP
0%
None of these

If y = 3^{χ - 1} + 3^{- χ - 1} (χ real), then the least value of y is

0%
2
0%
6
0%
2/3
0%
None of these

The sum of the series 1 + 3χ + 6χ² + 10χ³ + ... ∞ will be

0%
0%
2)
0%
0%

The value of 2^1/4 . 4^1/8 . 8^1/16 ... ∞ is

0%
1
0%
2
0%
3/2
0%
4

0%
16/35
0%
11/8
0%
35/16
0%
7/16

The sum of the series
Maths-Sequences and Series-47206.png

0%
1/17
0%
1/18
0%
1/19
0%
1/20
0%
1/21

Let α, β denote the cube roots of unity other than 1 and α ≠ β.
Maths-Sequences and Series-47208.png

0%
either - 2ω or - 2ω2
0%
either - 2ω or 2ω2
0%
either 2ω or - 2ω2
0%
either 2ω or 2ω2

0%
(n -(2n - 1)
0%
(n +(2n + 1)
0%
(n +(2n - 1)
0%
(n -(2n + 1)

0%
–2, –32
0%
–2, 3
0%
–6, 3
0%
–6, –32

0%
1056
0%
1088
0%
1120
0%
1332
0%
(a,d)

Let the positive numbers a, b, c, d be in A.P. Then abc, abd, acd, bcd are

0%
NOT in A.P./G.P./H.P.
0%
in A.P.
0%
in G.P.
0%
in H.P.

0%
√2
0%
√3
0%
0%

If n is odd positive integer and
Maths-Sequences and Series-47221.png

0%
4n
0%
1
0%
– 1
0%
0

If H_n = 1 + 1/2 + ...+ 1/n, then the value of S_n = 1 + 3/2 + 5/3 + ...+ (2n-1)/n is

0%
Hn + 2n
0%
n - 1 + Hn
0%
Hn– 2n
0%
2n – Hn

Sum of n terms of the following series 1³ + 3³ + 5³ + 7³ + ... is

0%
n2(2n2 – 1)
0%
n3(n – 1)
0%
n3 + 8n + 4
0%
2n4 + 3n2

0%
0%
2)
0%
0%

The value of 1/2! + 2/3! +...+ 999/1000! to

0%
0%
2)
0%
0%
0%

0%
1/2
0%
1
0%
2
0%
4

The sum of the series(1 +(1 + 2 + 2² ) + (1 + 2 + 2² + 2³ ) + ...up to n terms is

0%
2n+2 - n - 4
0%
2(2n -- n
0%
2n+1 - n
0%
2n+1 - 1

The sum of the first n terms of the series 1² + 2 . 2² + 3² + 2 . 4² + 5² + 2 . 6² + .... is (n(n + 1)² )/2, where n is even. when n is odd, the sum is