Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 57

EASY

JEE Advanced

IMPORTANT

Earn 100

If the sides of a right angled triangle are in $GP$ , then the cosine of the greater acute angle is

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Important Questions on Sequence and Series

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 58

The consecutive numbers of a three digit number form a

GP

. If we subtract

792

from this number, then we get a number consisting of the same digits written in the reverse order and if we increase the second digit of the required number by

2

, then resulting number forms an

AP

. The number is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 59

Three non-zero numbers

a, b

and

c

are in

AP

. If increasing

a

by

1

or increasing

c

by

2

, the numbers are in

GP

, then

b

equals

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 61

If

x > 0

, then the sum of the series

e^{- x} - e^{- 2 x} + e^{- 3 x} - \dots

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 62

The

n th

term of a

GP

is

128

and the sum to its

n

terms is

255

. If its common ratio is

2

, then its first term is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 64

If

(a, b), (c, d), (e, f)

are the vertices of a triangle such that

a, c, e

are in

GP

with common ratio

r

and

b, d, f

are in

GP

with common ratio

s

, then the area of the triangle is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 65

If sum of all terms of an infinite

GP

is

\frac{1}{5}

times the sum of odd terms. Then, common ratio is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 67

If

{(1.05)}^{50} = 11.658

, then

\sum_{n = 1}^{49} {(1.05)}^{n}

equals

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 68

If the second term of a

GP

is

2

and the sum of its infinite terms is

8

, then its first term is