Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 4

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If $x, y, z$ are positive reals satisfying $4 x y + 6 y z + 8 z x = 9$ , then the greatest possible value of the product $x y z$ is

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Important Questions on Sequences and Series

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 5

If

a + b + c = 3

and

a > 0, b > 0, c > 0

, then the greatest value of

a^{2} b^{3} c^{2}

is -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 6

Let

C

be a circle with centre

P_{0}

and

A B

be a diameter of

C

. Suppose

P_{1}

is the midpoint of line segment

P_{0} B, P_{2}

the midpoint of line segment

P_{1} B

and so on. Let

C_{1}, C_{2}, C_{3}

be circles with diameters

P_{0} P_{1}, P_{1} P_{2}, P_{2} P_{3}, . . . .

respectively Suppose the circles

C_{1}, C_{2}, C_{3} . . .

are all shaded. The ratio of the area of the unshaded portion of

C

to that of the original circle is

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 7

If

b - c, 2 b - x

and

b - a

are in H.P., then

a - (x / 2), b - (x / 2)

and

c - (x / 2)

are in

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 8

The numbers

\log_{180} 12, \log_{2160} 12, \log_{25920} 12

are in

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 9

The values of

x

such that

\log_{\frac{1}{2}} x > \log_{\frac{1}{3}} x

, is/are

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 10

If sum of

n

-terms of a series is

5 n^{2} + 2 n

then second term is -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 11

If

a, b, c

are in

H . P .

then

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

equals -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 12

The number of numbers lying between

100

and

500

that are divisible by

7

but not by

21

, is