EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 2nd April 2017>Q 101

HARD

JEE Main

IMPORTANT

Earn 100

For any three positive real numbers $a, b$ and $c$ . If $9 (25 a^{2} + b^{2}) + 25 (c^{2} - 3 a c) = 15 b (3 a + c) .$ Then

34.94% studentsanswered this correctly

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 - 2nd April 2017>Q 102

If, for a positive integer

n

, the quadratic equation,

x (x + 1) + (x + 1) (x + 2) + . .. + (x + \bar{n - 1}) (x + n) = 10 n

has two consecutive integral solutions, then

n

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th April 2017>Q 103

If the arithmetic mean of two numbers $a$ and $b, a > b > 0$ , is five times their geometric mean, then $\frac{a + b}{a - b}$ is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th April 2017>Q 104

If the sum of the first

n

terms of the series

\sqrt{3} + \sqrt{75} + \sqrt{243} + \sqrt{507} + \dots

is

435 \sqrt{3},

then

n

equals:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th April 2017>Q 105

If three positive numbers

a

,

b

and

c

are in A.P. such that

a b c = 8

, then the minimum possible value of

b

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th April 2017>Q 106

Let

S_{n} = \frac{1}{1^{3}} + \frac{1 + 2}{1^{3} + 2^{3}} + \frac{1 + 2 + 3}{1^{3} + 2^{3} + 3^{3}} + \dots + \frac{1 + 2 + \dots, + n}{1^{3} + 2^{3} + \dots n^{3}}

. If

100 S_{n} = n,

then

n

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th April 2016>Q 107

Let

x, y, z

be positive real numbers such that

x + y + z = 12

and

x^{3} y^{4} z^{5} = (0 .1) {(600)}^{3} .

Then

x^{3} + y^{3} + z^{3}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 3rd April 2016>Q 108

If the

2^{n d}, 5^{t h}

and

9^{t h}

terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 3rd April 2016>Q 109

If the sum of the first ten terms of the series

{(1 \frac{3}{5})}^{2} + {(2 \frac{2}{5})}^{2} + {(3 \frac{1}{5})}^{2} + 4^{2} + {(4 \frac{4}{5})}^{2} + \dots .,

is

\frac{16}{5} m

, then

m

is equal to