Mathematics Crash Course JEE Advanced>Chapter 6 - Sequences and Series>Exercise 1>Q 10

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IMPORTANT

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If $\frac{1}{a} + \frac{1}{c} = \frac{1}{2 b - a} + \frac{1}{2 b - c}$ , where $a \neq 2 b$ and $c \neq 2 b$ , then which of the following can be true?

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Important Questions on Sequences and Series

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 6 - Sequences and Series>Exercise 1>Q 11

If

a, b, c

are in

H . P .

then

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 6 - Sequences and Series>Exercise 1>Q 12

If

A_{1}, A_{2}, A_{3}; G_{1}, G_{2}, G_{3}

and

H_{1}, H_{2}, H_{3}

are the three arithmetic, geometric and harmonic means between two positive numbers

a

and

b

(a > b)

, then which of the following is/are true?

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IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 6 - Sequences and Series>Exercise 1>Q 13

Which of the following is true, where

a, b, c > 0 ?

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 6 - Sequences and Series>Exercise 1>Q 14

A straight line through the vertex

P

of a triangle

P Q R

intersects the side

Q R

at the point

S

and the circumcircle of the triangle

P Q R

at the point

T .

if

S

is not the centre of the circumcircle, then

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 6 - Sequences and Series>Exercise 1>Q 15

If

a_{1}, a_{2}, \dots \dots \dots a_{n} \in R^{+}

and

a_{1} \cdot a_{2} \dots \dots a_{n} = 1

then the least value of

(1 + a_{1} + a_{1}^{2}) (1 + a_{2} + a_{2}^{2}) \dots . (1 + a_{n} + a_{n}^{2})

is -

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 6 - Sequences and Series>Exercise 1>Q 16

For the series

2 + (\sqrt{2} + \frac{1}{\sqrt{2}}) + ((2 \sqrt{2} - 1) + \frac{1}{2}) + ((3 \sqrt{2} - 2) + \frac{1}{2 \sqrt{2}}) + \dots \dots

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 6 - Sequences and Series>Exercise 1>Q 20

Let

1, 4, . . . . .

and

9, 16, . . . .

be two arithmetic progressions. The set

S

is the union of the first

2004

terms of each sequence. Suppose there are

' n'

distinct numbers in set

' S',

then find the sum of the digits of

' n'

.

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 6 - Sequences and Series>Exercise 1>Q 21

How many four-digit integers

a b c d,

with

a \neq 0,

have the property that the three two-digit integers

a b < b c < c d

form an increasing arithmetic sequence? One such number is

4692,

where

a = 4, b = 6, c = 9,

and

d = 2 .