EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 26 June 2022 Shift 2>Q 132

MEDIUM

JEE Main

IMPORTANT

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The total number of $3$ -digit numbers, whose greatest common divisor with $36$ is $2$ , is ______.

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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 - 26 June 2022 Shift 2>Q 133

If

a_{1} (> 0), a_{2}, a_{3}, a_{4}, a_{5}

are in a G.P. ,

a_{2} + a_{4} = 2 a_{3} + 1

and

3 a_{2} + a_{3} = 2 a_{4}

, then

a_{2} + a_{4} + 2 a_{5}

is equal to _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 26 June 2022 Shift 1>Q 134

Let

A = \{n \in N : H . C . F . (n, 45) = 1\}

and let

B = \{2 k : k \in \{1, 2, \dots, 100\}\}

. Then the sum of all the elements of

A \cap B

is _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 26 June 2022 Shift 1>Q 135

Let

A = \sum_{i = 1}^{10} \sum_{j = 1}^{10} \min \{i, j\}

and

B = \sum_{i = 1}^{10} \sum_{j = 1}^{10} \max \{i, j\}

. Then

A + B

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 June 2022 Shift 1>Q 136

If

x = \sum_{n = 0}^{\infty} a^{n}, y = \sum_{n = 0}^{\infty} b^{n}, z = \sum_{n = 0}^{\infty} c^{n}

, where

a, b, c

are in A.P. and

|a| < 1, |b| < 1, |c| < 1

,

a b c \neq 0

, then

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 June 2022 Shift 1>Q 137

If the sum of the first ten terms of the series

\frac{1}{5} + \frac{2}{65} + \frac{3}{325} + \frac{4}{1025} + \frac{5}{2501} + \dots .

is

\frac{m}{n}

, where

m

and

n

are co-prime numbers, then

m + n

is equal to ______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 June 2022 Shift 2>Q 138

Let

S = 2 + \frac{6}{7} + \frac{12}{7^{2}} + \frac{20}{7^{3}} + \frac{30}{7^{4}} + \dots . .

then

4 S

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 June 2022 Shift 2>Q 139

If

a_{1}, a_{2}, a_{3} \dots

and

b_{1}, b_{2}, b_{3} \dots .

are A.P. and

a_{1} = 2, a_{10} = 3, a_{1} b_{1} = 1 = a_{10} b_{10}

then

a_{4} b_{4}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 28 June 2022 Shift 1>Q 140

Let

A_{1}, A_{2}, A_{3}, \dots \dots

be an increasing geometric progression of positive real numbers. If

A_{1} A_{3} A_{5} A_{7} = \frac{1}{1296}

and

A_{2} + A_{4} = \frac{7}{36}

, then, the value of

A_{6} + A_{8} + A_{10}

is equal to