EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 7th January 2020 Shift 2>Q 62

HARD

JEE Main

IMPORTANT

Earn 100

If the sum of the first $40$ terms of the series, $3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + . . . .$ is $102 m,$ then $m$ is equal to

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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 January 2020 Shift 1>Q 63

Let

f : R \to R

be such that for all

x \in R (2^{1 + x} + 2^{1 - x}), f (x)

and

(3^{x} + 3^{- x})

are in A.P., then the minimum value of

f (x)

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th January 2020 Shift 1>Q 64

The sum

\sum_{k = 1}^{20} (1 + 2 + 3 + \dots + k)

is ___________.

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 65

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

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:

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 70

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

3, 7, 11, \dots, 407

and

2, 9, 16, \dots, 709

is ____________.