EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 3 September 2020 Shift 2>Q 46

HARD

JEE Main

IMPORTANT

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If the sum of the series $20 + 19 \frac{3}{5} + 19 \frac{1}{5} + 18 \frac{4}{5} + . . . . . . . . . .$ up to $n^{th}$ term is $488$ and the $n^{th}$ term is negative, then :

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Important Questions on Sequences and Series

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 3 September 2020 Shift 2>Q 47

If

m

arithmetic means (A.Ms) are inserted between

3

and

243

and three geometric means (G.Ms) are inserted between

3

and

243

such that

4^{t h}

A.M. is equal to

2^{n d}

G.M., then

m

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 - 4 September 2020 Shift 1>Q 48

If

1 + (1 - 2^{2} \cdot 1) + (1 - 4^{2} \cdot 3) + (1 - 6^{2} \cdot 5) + \dots \dots + (1 - 20^{2} \cdot 19) = α - 220 β

, then an ordered pair

(α, β)

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 - 4 September 2020 Shift 1>Q 49

Let

α

and

β

be the roots of

x^{2} - 3 x + p = 0

and

γ

and

δ

be the roots of

x^{2} - 6 x + q = 0 .

If

α, β, γ, δ

from a geometric progression. Then ratio

(2 q + p) : (2 q - p)

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 4 September 2020 Shift 2>Q 50

The minimum value of

2^{\sin x} + 2^{\cos x}

is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 4 September 2020 Shift 2>Q 51

Let

a {}_{1}, a_{2}, \dots, a_{n}

be a given

A . P .

whose common difference is an integer and

S_{n} = a_{1} + a_{2} + \dots + a_{n}

. If

a_{1} = 1, a_{n} = 300

and

15 \leq n \leq 50,

then the ordered pair

(S_{n - 4}, a_{n - 4})

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 5 September 2020 Shift 1>Q 52

If

2^{10} + 2^{9} \cdot 3^{1} + 2^{8} \cdot 3^{2} + \dots \dots + 2 \cdot 3^{9} + 3^{10} = S - 2^{11}

, then

S

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 5 September 2020 Shift 1>Q 53

If

3^{2 \sin 2 α - 1}, 14

and

3^{4 - 2 \sin 2 α}

are the first three terms of an A.P. for some

α

, then the sixth term of this A.P. is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 5 September 2020 Shift 1>Q 54

If

S

is the sum of the first 10 terms of the series,

\tan^{- 1} (\frac{1}{3}) + \tan^{- 1} (\frac{1}{7}) + \tan^{- 1} (\frac{1}{13}) + \tan^{- 1} (\frac{1}{21}) + \dots \dots

then

\tan (S)

is equal to :