EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2019 Shift 1>Q 75

MEDIUM

JEE Main

IMPORTANT

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If $a, b$ and $c$ be three distinct real numbers in G.P. and $a + b + c = x b,$ then $x$ cannot be:

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Important Questions on Sequences and Series

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2019 Shift 1>Q 76

Let

a_{1}, a_{2}, \dots, a_{30}

be an A.P.,

S = \sum_{i = 1}^{30} a_{i}

and

T = \sum_{i = 1}^{15} a_{(2 i - 1)} .

If

a_{5} = 27

and

S - 2 T = 75,

then

a_{10}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2019 Shift 2>Q 77

The sum of the following series

1 + 6 + \frac{9 (1^{2} + 2^{2} + 3^{2})}{7} + \frac{12 (1^{2} + 2^{2} + 3^{2} + 4^{2})}{9} + \frac{15 (1^{2} + 2^{2} + \dots + 5^{2})}{11} + . . . .

up to

15

terms, is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2019 Shift 2>Q 78

Let

a, b

and

c

be the

7^{t h}, 11^{t h}

and

13^{t h}

terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then

\frac{a}{c}

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th April 2019 Shift 1>Q 79

The sum of all natural numbers

n

such that

100 < n < 200

and

H . C . F .

(91, n) > 1

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th April 2019 Shift 2>Q 80

If three distinct numbers

a, b, c

are in G.P. and the equations

a x^{2} + 2 b x + c = 0

and

d x^{2} + 2 e x + f = 0

have a common root, then which one of the following statements is correct?

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th April 2019 Shift 2>Q 81

The sum

\sum_{k = 1}^{20} k \frac{1}{2^{k}}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 10th April 2019 Shift 1>Q 82

If

a_{1}, a_{2}, a_{3} . . . . . . . . ., a_{n}

are in

A . P .

and

a_{1} + a_{4} + a_{7} . . . . . . . . . + a_{16} = 114

, then

a_{1} + a_{6} + a_{11} + a_{16}

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 10th April 2019 Shift 1>Q 83

The sum

\frac{3 \times 1^{3}}{1^{2}} + \frac{5 \times (1^{3} + 2^{3})}{1^{2} + 2^{2}} + \frac{7 \times (1^{3} + 2^{3} + 3^{3})}{1^{2} + 2^{2} + 3^{2}} + . . . . .

upto

10^{t h}

term is