Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 5

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The sum of the arithmetic mean and the geometric mean of two positive numbers is $200$ . The sum of the positive square roots of the two numbers is

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Important Questions on Sequences and Series

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Agniveer Vayu

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 6

If

a, b, c, d

are four positive real numbers such that

a b c d = 1

then least value of

(a + 4) (b + 4) (c + 4) (d + 4)

is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 7

The minimum value of

7^{\sin θ} + 7^{\cos θ}

is equal to

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 8

If

a, b, c

and

d

are four positive real numbers such that

a b c d = 1

, the minimum value of

(1 + a) (1 + b) (1 + c) (1 + d)

is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 9

If

\log_{2} (a + b) + \log_{2} (c + d) \geq 4

. Then the min. value of the expression

a + b + c + d

is -

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 10

The minimum value of

4^{x} + 4^{1 - x}, x \in R,

is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 11

If

a_{n} > 1

for all

n \in N

then

\log_{a_{2}} a_{1} + \log_{a_{3}} a_{2} + \dots + \log_{a_{n}} a_{n - 1} + \log_{a_{1}} a_{n}

has the minimum value

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 12

The minimum value of

\frac{x^{4} + y^{4} + z^{4}}{x y z}

for positive reals

x, y, z

is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 13

If

α \in (0, \frac{π}{2})

, then

\sqrt{x^{2} + x} + \frac{\tan^{2} α}{\sqrt{x^{2} + x}}

is always greater than or equal to