JEE Questions for Maths Sequences And Series Quiz 4

If the first, second and last terms of an arithmetic series are a, b and c respectively, then the number of terms is

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0%
2)
0%
0%

If a₁ ,a₂,...,a_n, are in AP with common difference d ≠ 0, then (sin d)[sec a₁ sec a₂ + sec a₂ sec a₃ + ... + sec a_n-1 sec a_n] is equal to

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cot an - cot a1
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cot a1 - cot an
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tan an - tan a1
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tan an - tan an-1
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tan a1 - tan an

If three positive real numbers a, b and c are in AP and abc = 4, then the minimum possible value of b is

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23/2
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22/3
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21/3
0%
25/2

The sum of all odd numbers between 1 and 1000 which are divisible by 3, is

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83667
0%
90000
0%
83660
0%
None of these

If a₁ , a₂...a_n an are in arithmetic progression, where a₁ > 0 for all i. Then,
Maths-Sequences and Series-47403.png

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0%
2)
0%
0%
None of these

In an arithmetic progression, the 24th term is 100. Then, the sum of the first 47 terms of the arithmetic progression is

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2300
0%
2350
0%
2400
0%
4600
0%
4700

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

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53 : 155
0%
27 : 87
0%
29 : 83
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31 : 89

IF (10)⁹ + 2(11)¹ (10)⁸ + 3(11)² (10)⁷ + ...+ 10(11)⁹ = k(10)⁹, then k is equal to

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121/100
0%
441/100
0%
100
0%
110

If the second and fifth terms of a GP are 24 and 3 respectively,then the sum of first six terms is

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181
0%
181/2
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189
0%
189/2
0%
191

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,..., is

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7/81 (179 - 10-20)
0%
7/9 (99 - 10-20)
0%
7/81 (179 + 10-20)
0%
7/9 (99 + 10-20 )

If sum of an infinite geometric series is 4/3 and 1st term is 3/4, then its common ratio is

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7/16
0%
9/16
0%
1/9
0%
7/9

The value of n for which
Maths-Sequences and Series-47414.png

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n = -1/2
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n = 1/2
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n = 1
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n = -1

If I + sin χ + sin² χ+.. upto ∞ = 4 + 2√3, 0 < χ < π and x # π/2, then χ is equal to 2

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π/3 , 5π/6
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2π/3, π/6
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π/3, 2π/3
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π/6, π/3

If G is the GM of the product of r set of observations with geometric means G₁ , G₂ , , G_r respectively, then G is equal to

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log G1 + log G2 +...+ log Gn
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G1, G2,...,Gr
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log G1, log G2 ,..., log Gn
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None of the above

The value of
Maths-Sequences and Series-47418.png

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1
0%
0
0%
- 1
0%
None of these

The first two terms of a geometric progression add upto 12. The sum of the third and the fourth terms is 48. If tenris of the geometric progression are alternately positive and negative, then the first term is

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4
0%
- 4
0%
- 12
0%
12

Geometric mean of 7, 7², 7³, ..., 7ⁿ is

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7(n+1)/2
0%
7
0%
7n/2
0%
7n

In an infinite geometric series, the first term is a and common ratio is r. If the sum of the series is 4 and the second term is 3/4, then (a,r)is

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(4/7 , 3/7)
0%
(2, 3/8)
0%
(3/2, 1/2)
0%
(3, 1/4)
0%
(4, 3/4)

Ifχ = 1+ a+ a² +... ∞ and y=1+b+b²+...∞, where a and b are proper fractions, then 1+ ab + a² b² +... ∞ equals

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0%
2)
0%
0%
None of these

In a geometric progression the ratio of the sum of the first three terms and first six terms is 125 : 152. The common

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1/5
0%
2/5
0%
4/5
0%
3/5

If a, b, c, d and p are distinct real numbers such that (a² + b² + c²)p² - 2(ab + bc + cd)p + (b² + c² + d²) ≤ 0, then a, b, c and d

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are in AP
0%
are in GP
0%
are in HP
0%
satisfy ab = cd

The value of
Maths-Sequences and Series-47429.png

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37/1000
0%
37/990
0%
1/37
0%
1/27

If three real numbers a, b and c are in harmonic progression, then which of the following is true ?

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0%
2)
0%
ab, bc, ca are in HP
0%

Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

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√2 + √3
0%
3 + √2
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2 - √3
0%
2 + √2

If p, q, r and s are positive real numbers such that p + q + r + s = 2, then M = (p + q) (r + s) satisfies the relation

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0 < M ≤ 1
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1 ≤ M ≤ 2
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2 ≤ M ≤ 3
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3 ≤ M ≤ 4

If a is a positive number such that the arithmetic mean of a and 2 exceeds their geometric mean by 1. Then, the value of a is

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3
0%
5
0%
9
0%
8
0%
10

If the AM of two numbers is A and GM is G, then the numbers will be

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A ± (A2 -G2 )
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2)
0%
0%

If a,b, c are in AP, b - a, c - b and a are in GP, then a : b : c is

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1 : 2 : 3
0%
1 : 3 : 5
0%
2 : 3 : 4
0%
1 : 2 : 4

If p,q,r are in GP and tan^-1 p, tan^-1 q, tan^-1 rare in AP, then p, q, r satisfies the relation

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p = q = r
0%
p # q # r
0%
p + q = r
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None of these

Let α, β, γ and δ be four positive real numbers such that their product is unity, then the least value of (1 +α) (1+β) (1 + γ) (1 +δ ) is

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6
0%
16
0%
0
0%
32

If AM and GM of χ and y are in the ratio p : q, then χ : y is

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0%
2)
0%
P : q
0%
0%

If |χ| < 1, then the sum of the series 1 + 2χ + 3χ² + 4χ³ +... ∞ will be

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0%
2)
0%
0%

Statement I : the sum of series 1 + (1 + 2 ++ (4 + 6 ++ (9 + 12 ++...+ (361 + 380 +is 8000.

Maths-Sequences and Series-47455.png

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Statement I is correct, statement II is correct
0%
Statement I is in; statement II is a correct explanation for statement Icorrect, statement II is correct
0%
Statement I is correct, statement II is correct; statement II is not a correct explanation for statement I
0%
Statement I is correct, statement II is incorrect