EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th April 2019 Shift 2>Q 80

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JEE Main

IMPORTANT

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If three distinct numbers $a, b, c$ are in G.P. and the equations $a x^{2} + 2 b x + c = 0$ and $d x^{2} + 2 e x + f = 0$ have a common root, then which one of the following statements is correct?

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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 - 8th April 2019 Shift 2>Q 81

The sum

\sum_{k = 1}^{20} k \frac{1}{2^{k}}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 10th April 2019 Shift 1>Q 82

If

a_{1}, a_{2}, a_{3} . . . . . . . . ., a_{n}

are in

A . P .

and

a_{1} + a_{4} + a_{7} . . . . . . . . . + a_{16} = 114

, then

a_{1} + a_{6} + a_{11} + a_{16}

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 - 10th April 2019 Shift 1>Q 83

The sum

\frac{3 \times 1^{3}}{1^{2}} + \frac{5 \times (1^{3} + 2^{3})}{1^{2} + 2^{2}} + \frac{7 \times (1^{3} + 2^{3} + 3^{3})}{1^{2} + 2^{2} + 3^{2}} + . . . . .

upto

10^{t h}

term is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 10th April 2019 Shift 2>Q 84

The sum

1 + \frac{1^{3} + 2^{3}}{1 + 2} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 2 + 3} + . . . + \frac{1^{3} + 2^{3} + 3^{3} + . . . + 15^{3}}{1 + 2 + 3 + . . . + 15} - \frac{1}{2} (1 + 2 + 3 + . . . + 15)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 10th April 2019 Shift 2>Q 85

Let

a_{1}, a_{2}, a_{3} . . .

be an

A . P .

with

a_{6} = 2 .

Then, the common difference of this

A . P .,

which maximise the product

a_{1} \cdot a_{4} \cdot a_{5},

is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 10th April 2019 Shift 2>Q 86

Let

a, b

and

c

be in

G . P .

with common ratio

r,

where

a \neq 0

and

0 < r \leq \frac{1}{2} .

If

3 a, 7 b

and

15 c

are the first three terms of an

A . P .,

then the

4^{t h}

term of this

A . P .

is :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 10th January 2019 Shift 1>Q 87

The sum of all two digit positive numbers which when divided by

7

yield

2

or

5

as remainder is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 12th April 2019 Shift 1>Q 88

Let

S_{n}

denote the sum of the first

n

terms of an

A . P .

. If

S_{4} = 16

and

S_{6} = - 48

, then

S_{10}

is equal to: