EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 22 July 2021 Shift 1>Q 19

HARD

JEE Main

IMPORTANT

Earn 100

Let $S_{n}$ denote the sum of first $n$ -terms of an arithmetic progression. If $S_{10} = 530, S_{5} = 140,$ then $S_{20} - S_{6}$ is equal to:

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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 - 22 July 2021 Shift 1>Q 20

The sum of all the elements in the set

{n \in {1, 2, \dots \dots, 100} ∣

H.C.F. of

n

and

2040

is

1

} is equal to __________.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 25 July 2021 Shift 1>Q 21

Let

S_{n}

be the sum of the first

n

terms of an arithmetic progression. If

S_{3 n} = 3 S_{2 n}

, then the value of

\frac{S_{4 n}}{S_{2 n}}

is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 25 July 2021 Shift 1>Q 22

If the value of ${(1 + \frac{2}{3} + \frac{6}{3^{2}} + \frac{10}{3^{3}} + \dots . . upto \infty)}^{\log_{(0.25)} (\frac{1}{3} + \frac{1}{3^{2}} + \frac{1}{3^{3}} + \dots . upto \infty)}$ is $l$ , then $l^{2}$ is equal to .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 25 July 2021 Shift 2>Q 23

If

[x]

be the greatest integer less than or equal to

x,

then

\sum_{n = 8}^{100} [\frac{{(- 1)}^{n} n}{2}]

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 July 2021 Shift 1>Q 24

If

\log_{3} 2, \log_{3} (2^{x} - 5), \log_{3} (2^{x} - \frac{7}{2})

are in an arithmetic progression, then the value of

x

is equal to _____.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 July 2021 Shift 2>Q 25

If

\tan (\frac{π}{9}), x, \tan (\frac{7 π}{18})

are in arithmetic progression and

\tan (\frac{π}{9}), y, \tan (\frac{5 π}{18})

are also in arithmetic progression, then

|x - 2 y|

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 16 March 2021 Shift 1>Q 26

Consider an arithmetic series and a geometric series having four initial terms from the set

\{11, 8, 21, 16, 26, 32, 4\}

. If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these two series is equal to _______.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 16 March 2021 Shift 2>Q 27

Let

\frac{1}{16}, a

and

b

be in G.P. and

\frac{1}{a}, \frac{1}{b}, 6

be in A.P., where

a, b > 0

. Then

72 (a + b)

is equal to _______ .