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

HARD

JEE Advanced

IMPORTANT

Earn 100

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

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Important Questions on Sequence and Series

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

MEDIUM

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

MEDIUM

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

MEDIUM

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

MEDIUM

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

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 19

The sum of the series

1 + \frac{2}{3} + \frac{6}{3^{2}} + \frac{10}{3^{3}} + \frac{14}{3^{4}} + \dots

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 20

The first two terms of a geometric progression add up to

12

. The sum of the third and fourth terms is

48

. If the terms of the geometric progression are alternately positive and negative, then the first term is