Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 26

HARD

JEE Main/Advance

IMPORTANT

Earn 100

In the 20th row of the triangle

1

2 3

4 5 6

$⋰$ $⋮$ $⋱$

50% studentsanswered this correctly

Important Questions on Progression and Series

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 27

Given that

x + y + z = 15

when

a, x, y, z, b

are in A.P. and

\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{5}{3}

when

a, x, y, z, b

are in H.P. Then

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 28

If

a, b,

and

c

are in H.P.., then the value of

\frac{(a c + a b - b c) (a b + b c - a c)}{{(a b c)}^{2}}

is

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 29

If $p, q,$ and $r$ are in A.P. then which of the following is/are true?

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 30

If

x^{2} + 9 y^{2} + 25 z^{2} = x y z (\frac{15}{x} + \frac{5}{y} + \frac{3}{z})

, then

HARD

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 31

If

A_{1}, A_{2}, G_{1}, G_{2}

and

H_{1}, H_{2}

are two arithemetic, geometric and harmonic means, respectively, between two qualities

a

and

b

, then

a b

is equal to

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 32

If

\frac{1}{b - a} + \frac{1}{b - c} = \frac{1}{a} + \frac{1}{c}

, then which of the following is/are possible?

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 33

If

a, b, c

are three distinct numbers in G.P.,

b, c, a

are in A.P., and

a, b c, a b c

are in H.P., then the possible value of

b

is

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 34

If $a, b, c$ are in A.P. and $a^{2}, b^{2}, c^{2}$ are in H.P. Then, which is of the following is/are possible?