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

MEDIUM

JEE Main

IMPORTANT

Earn 100

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 .

50% studentsanswered this correctly

Important Questions on Sequences and Series

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 _______ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 16 March 2021 Shift 2>Q 28

Let

S_{n} (x) = \log_{a^{1 / 2}} x + \log_{a^{1 / 3}} x + \log_{a^{1 / 6}} x + \log_{a^{1 / 11}} x + \log_{a^{1 / 18}} x + \log_{a^{1 / 27}} x + \dots

up to

n

-terms, where

a > 1

. If

S_{24} (x) = 1093

and

S_{12} (2 x) = 265,

then value of

a

is equal to _____ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 17 March 2021 Shift 2>Q 29

If

1, \log_{10} (4^{x} - 2)

and

\log_{10} (4^{x} + \frac{18}{5})

are in arithmetic progression for a real number

x

then the value of the determinant

|\begin{matrix} 2 (x - \frac{1}{2}) & x - 1 & x^{2} \\ 1 & 0 & x \\ x & 1 & 0 \end{matrix}|

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 18 March 2021 Shift 1>Q 30

If

α, β

are natural numbers such that

100^{α} - 199 β = (100) (100) + (99) (101) + (98) (102) + \dots . . + (1) (199),

then the slope of the line passing through

(α, β)

and origin is: