EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 16 March 2021 Shift 2>Q 27

EASY

JEE Main

IMPORTANT

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Let $\frac{1}{16}, a$ and $b$ be in G.P. and $\frac{1}{a}, \frac{1}{b}, 6$ be in A.P., where $a, b > 0$ . Then $72 (a + b)$ is equal to _______ .

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Important Questions on Sequences and Series

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 16 March 2021 Shift 2>Q 28

Let

S_{n} (x) = \log_{a^{1 / 2}} x + \log_{a^{1 / 3}} x + \log_{a^{1 / 6}} x + \log_{a^{1 / 11}} x + \log_{a^{1 / 18}} x + \log_{a^{1 / 27}} x + \dots

up to

n

-terms, where

a > 1

. If

S_{24} (x) = 1093

and

S_{12} (2 x) = 265,

then value of

a

is equal to _____ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 17 March 2021 Shift 2>Q 29

If

1, \log_{10} (4^{x} - 2)

and

\log_{10} (4^{x} + \frac{18}{5})

are in arithmetic progression for a real number

x

then the value of the determinant

|\begin{matrix} 2 (x - \frac{1}{2}) & x - 1 & x^{2} \\ 1 & 0 & x \\ x & 1 & 0 \end{matrix}|

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 18 March 2021 Shift 1>Q 30

If

α, β

are natural numbers such that

100^{α} - 199 β = (100) (100) + (99) (101) + (98) (102) + \dots . . + (1) (199),

then the slope of the line passing through

(α, β)

and origin is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 18 March 2021 Shift 1>Q 31

\frac{1}{3^{2} - 1} + \frac{1}{5^{2} - 1} + \frac{1}{7^{2} - 1} + \dots + \frac{1}{(201)^{2} - 1}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main 18 March 2021 Shift 2>Q 32

Let

S_{1}

be the sum of first

2 n

terms of an arithmetic progression. Let

S_{2}

be the sum of first

4 n

terms of the same arithmetic progression. If

(S_{2} - S_{1})

is

1000

, then the sum of the first

6 n

terms of the arithmetic progression is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 24 Feb 2021 Shift 1>Q 33

If

e^{(\cos^{2} x + \cos^{4} x + \cos^{6} x + . . . . \infty) \log_{e} 2}

satisfies the equation

t^{2} - 9 t + 8 = 0

, then the value of

\frac{2 \sin x}{\sin x + \sqrt{3} \cos x}

, where

0 < x < \frac{π}{2}

, is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 24 Feb 2021 Shift 2>Q 34

The sum of first four terms of a geometric progression

(G . P .)

is

\frac{65}{12}

and the sum of their respective reciprocals is

\frac{65}{18} .

If the product of first three terms of the

G . P .

is

1,

and the third term is

α,

then

2 α

is _________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 25 Feb 2021 Shift 1>Q 35

If

0 < θ, ϕ < \frac{π}{2}, x = \sum_{n = 0}^{\infty} \cos^{2 n} θ, y = \sum_{n = 0}^{\infty} \sin^{2 n} ϕ

and

z = \sum_{n = 0}^{\infty} \cos^{2 n} θ \cdot \sin^{2 n} ϕ

then :