Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 9

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JEE Advanced

IMPORTANT

Earn 100

If $m$ is the $AM$ of two distinct real numbers $l$ and $n (l, n > 1)$ and $G_{1}, G_{2}$ and $G_{3}$ are three geometric means between $l$ and $n$ , then $G_{1}^{4} + 2 G_{2}^{4} + G_{3}^{4}$ equals

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Important Questions on Sequence and Series

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 10

The sum of first

9

terms of the series

\frac{1^{3}}{1} + \frac{1^{3} + 2^{3}}{1 + 3} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 3 + 5} + \dots

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 11

Let

α

and

β

be the roots of equation

p x^{2} + q x + r = 0, p \neq 0

. If

p, q

and

r

are in

AP

and

\frac{1}{α} + \frac{1}{β} = 4

, then the value of

| α - β |

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 12

If

{(10)}^{9} + 2 {(11)}^{1} {(10)}^{8} + 3 {(11)}^{2} {(10)}^{7} + \dots + 10 {(11)}^{9} = k {(10)}^{9}

, then

k

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 13

Three positive numbers form an increasing

GP

. If the middle term in this

GP

is doubled, then new numbers are in

AP

. Then, the common ratio of a

GP

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 14

The sum of first

20

terms of the sequence

0.7, 0.77, 0.777, . . .

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 15

If

100

times the

100 th

term of an

AP

with non-zero common difference equal to

50

times its

50 th

term, then the

150 th

term of this

AP

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 17

A man saves

Rs . 200

in each of the first three months of his service. In each of the subsequent months, his savings increases by

Rs . 40

more than the savings of immediately previous month. His total saving from the start of service will be

Rs . 11040

after

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 18

A person is to count

4500

currency notes. Let

a_{n}

denotes the number of notes he counts in the

n th

minute. If

a_{1} = a_{2} = \dots = a_{10} = 150

and

a_{10}, a_{11}, \dots

are in

AP

with common difference

- 2

, then the time taken by him to count all notes, is