EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 31 August 2021 Shift 2>Q 12

MEDIUM

JEE Main

IMPORTANT

Earn 100

The number of $4$ -digit numbers which are neither multiple of $7$ nor multiple of $3$ is .

50% studentsanswered this correctly

Important Questions on Sequences and Series

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 31 August 2021 Shift 2>Q 13

If

S = \frac{7}{5} + \frac{9}{5^{2}} + \frac{13}{5^{3}} + \frac{19}{5^{4}} + \dots,

then

160 S

is equal to .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 1 September 2021 Shift 2>Q 14

$Let S_{n} = 1 \cdot (n - 1) + 2 \cdot (n - 2) + 3 \cdot (n - 3) + \dots + (n - 1) \cdot 1, n ⩾ 4 .$

$The sum \sum_{n = 4}^{\infty} (\frac{2 S_{n}}{n!} - \frac{1}{(n - 2)!}) is equal to :$

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 1 September 2021 Shift 2>Q 15

Let

a_{1}, a_{2}, \dots, a_{21}

be an

A . P .

such that

\sum_{n = 1}^{20} \frac{1}{a_{n} a_{n + 1}} = \frac{4}{9} .

If the sum of this

A . P .

is

189,

then

a_{6} a_{16}

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 20 July 2021 Shift 2>Q 16

If sum of the first

21

terms of the series

\log_{9^{1 / 2}} x + \log_{9^{1 / 3}} x + \log_{9^{1 / 4}} x + \dots . .

where

x > 0

is

504,

then

x

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 20 July 2021 Shift 2>Q 17

For

k \in N,

let

\frac{1}{α (α + 1) (α + 2) \dots \dots . (α + 20)} = \sum_{K = 0}^{20} \frac{A_{k}}{α + k},

where

α > 0 .

Then the value of

100 {(\frac{A_{14} + A_{15}}{A_{13}})}^{2}

is equal to ____________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 20 July 2021 Shift 2>Q 18

Let

{\{a_{n}\}}_{n = 1}^{\infty}

be a sequence such that

a_{1} = 1, a_{2} = 1

and

a_{n + 2} = 2 a_{n + 1} + a_{n}

for all

n \geq 1

. Then the value of

47 \sum_{n = 1}^{\infty} (\frac{a_{n}}{2^{3 n}})

is equal to ________.

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 19

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:

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 __________.