EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th January 2020 Shift 2>Q 65

EASY

JEE Main

IMPORTANT

Earn 100

If the $10^{t h}$ term of an $A . P .$ is $\frac{1}{20}$ and its $20^{t h}$ term is $\frac{1}{10}$ , then the sum of its first $200$ terms is

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Important Questions on Sequences and Series

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th January 2020 Shift 2>Q 66

The sum,

\sum_{n = 1}^{7} \frac{n (n + 1) (2 n + 1)}{4}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2020 Shift 1>Q 67

The product

2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot . . . .

to

\infty

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2020 Shift 2>Q 68

Let

a_{n}

be the

n^{t h}

term of a G.P. of positive terms. If

\sum_{n = 1}^{100} a_{2 n + 1} = 200

and

\sum_{n = 1}^{100} a_{2 n} = 100,

then

\sum_{n = 1}^{200} a_{n}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2020 Shift 2>Q 69

If

x = \sum_{n = 0}^{\infty} {(- 1)}^{n} \tan^{2 n} θ

and

y = \sum_{n = 0}^{\infty} \cos^{2 n} θ,

for

0 < θ < \frac{π}{4},

then:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2020 Shift 2>Q 70

The number of terms common to the two A.P.’s

3, 7, 11, \dots, 407

and

2, 9, 16, \dots, 709

is ____________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th April 2019 Shift 1>Q 71

Let the sum of the first

n

terms of a non-constant

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

be

50 n + \frac{n (n - 7)}{2} A,

where

A

is a constant. If

d

is the common difference of this

A . P .

, then the ordered pair

(d, a_{50})

is equal to

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th April 2019 Shift 2>Q 72

The sum of the series

1 + 2 \times 3 + 3 \times 5 + 4 \times 7 + \dots

upto

11^{t h}

term is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th April 2019 Shift 2>Q 73

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If

99

more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square, whose each side contains exactly

2

balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is