EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 4 September 2020 Shift 1>Q 49

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JEE Main

IMPORTANT

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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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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 - 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

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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 :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 5 September 2020 Shift 2>Q 55

If the sum of the second, third and fourth terms of a positive term G.P. is

3

and the sum of its sixth, seventh and eighth terms is

243

, then the sum of the first

50

terms of this G.P. is :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 5 September 2020 Shift 2>Q 56

If the sum of the first

20

terms of the series

\log_{(7^{1 / 2})} x + \log_{(7^{1 / 3})} x + \log_{(7^{1 / 4})} x + \dots

is

460

, then

x

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 6 September 2020 Shift 1>Q 57

Let

a, b, c, d and p

be non-zero distinct real numbers such that

(a^{2} + b^{2} + c^{2}) p^{2} - 2 (a b + b c + c d) p + (b^{2} + c^{2} + d^{2}) = 0

. Then