Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 4 - Sequence & Series>Exercise>Q 7

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IMPORTANT

Earn 100

The sum of all two digit numbers which are not divisible by $2$ or $3$ is

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Important Questions on Sequence & Series

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KVPY Aptitude Test - Stream SA

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 4 - Sequence & Series>Exercise>Q 8

In a sequence of

21

terms first

11

terms are in A.P. with common difference

2

and last

11

terms are in G.P. with common ratio

2 .

If middle term of A.P. is equal to middle term of G.P. then, middle term in the complete sequence is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 4 - Sequence & Series>Exercise>Q 9

If

a, b, c

are real numbers forming an A.P. and

3 + a, 2 + b, 3 + c

are in GP, then the minimum value of

a c

is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 4 - Sequence & Series>Exercise>Q 10

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 the quadratic equation whose roots are

\frac{1}{a}

and

\frac{1}{b}

is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 4 - Sequence & Series>Exercise>Q 11

Harmonic mean of the reciprocal of even numbers from

12

to

190

is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 4 - Sequence & Series>Exercise>Q 12

If

\log_{10} (x^{3} + y^{3}) - \log_{10} (x^{2} + y^{2} - x y) \leq 2,

where

x and y

are positive real numbers. Then the maximum value of

x y

is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 4 - Sequence & Series>Exercise>Q 13

If

a + b + c + d + e + f = 12

, then the maximum value of

a b + b c + c d + d e + e f + f a .

(

a, b, c, d, e, f

are non-negative real numbers)

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 4 - Sequence & Series>Exercise>Q 14

If

a_{1} + a_{2} + a_{3} + a_{4} + a_{5} + \dots \dots . + a_{n} = 1

for all

a_{i} > 0, i = 1, 2, 3 \dots \dots . . n .

Then the maximum value of

a_{1} {}^{2}a_{2} a_{3} a_{4} a_{5} \dots \dots \dots a_{n}

is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 4 - Sequence & Series>Exercise>Q 15

The maximum value of the expression,

f (x, y, z) = x y z (4 d - a x - b y - c z)

, where

a, b, c, d

are positive constants,

x, y, z

are positive variables and

4 d - a x - b y - c z > 0

is