EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 26 August 2021 Shift 2>Q 3

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IMPORTANT

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Let $a_{1}, a_{2}, \dots, a_{10}$ be an $A . P .$ with common difference $- 3$ and $b_{1}, b_{2}, \dots, b_{10}$ be a $G . P .$ with common ratio $2 .$ Let $c_{k} = a_{k} + b_{k}, k = 1, 2, \dots, 10 .$ If $c_{2} = 12$ and $c_{3} = 13,$ then $\sum_{k = 1}^{10} c_{k}$ is equal to ______.

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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 - 26 August 2021 Shift 2>Q 4

The sum of all

3

-digit numbers less than or equal to

500,

that are formed without using the digit

1

and they all are multiple of

11,

is ______.

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 August 2021 Shift 1>Q 5

If $0 < x < 1,$ then $\frac{3}{2} x^{2} + \frac{5}{3} x^{3} + \frac{7}{4} x^{4} + \dots,$ is equal to

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 August 2021 Shift 1>Q 6

If for

x, y \in R, x > 0,

y = \log_{10} x + \log_{10} x^{1 / 3} + \log_{10} x^{1 / 9} + \dots

upto

\infty

terms and

\frac{2 + 4 + 6 + \dots + 2 y}{3 + 6 + 9 + \dots + 3 y} = \frac{4}{\log_{10} x},

then the ordered pair

(x, y)

is equal to

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 August 2021 Shift 2>Q 7

If

0 < x < 1

and

y = \frac{1}{2} x^{2} + \frac{2}{3} x^{3} + \frac{3}{4} x^{4} + \dots \dots

, then the value of

e^{1 + y}

at

x = \frac{1}{2}

is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 31 August 2021 Shift 1>Q 8

The sum of $10$ terms of the series $\frac{3}{1^{2} \times 2^{2}} + \frac{5}{2^{2} \times 3^{2}} + \frac{7}{3^{2} \times 4^{2}} + \dots$ is :

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 31 August 2021 Shift 1>Q 9

Three numbers are in an increasing geometric progression with common ratio

r .

If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference

d .

If the fourth term of GP is

3 r^{2},

then

r^{2} - d

is equal to :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 31 August 2021 Shift 1>Q 10

The mean of

10

numbers

7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, \dots

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 31 August 2021 Shift 2>Q 11

Let

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

be an A.P. If

\frac{a_{1} + a_{2} + \dots + a_{10}}{a_{1} + a_{2} + \dots + a_{p}} = \frac{100}{p^{2}}, p \neq 10,

then

\frac{a_{11}}{a_{10}}

is equal to :