Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 5 - Inequalities Involving Means>DPP>Q 2

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IMPORTANT

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Let $a, b \in R$ and $a b = 1$ , then the minimum value of $\frac{1}{a^{4}} + \frac{1}{4 b^{4}}$ is

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Important Questions on Inequalities Involving Means

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 5 - Inequalities Involving Means>DPP>Q 3

If

x > 0, y > 0, z > 0,

then least value of

x^{\log_{e} y - \log_{e} z} + y^{\log_{e} z - \log_{e} x} + z^{\log_{e} x - \log_{e} y}

is

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 5 - Inequalities Involving Means>DPP>Q 4

Let

p, q, r \in R^{+}

and

27 p q r \geq {(p + q + r)}^{3}

and

3 p + 4 q + 5 r

= 12

. Then the value of

8 p + 4 q - 7 r =

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 5 - Inequalities Involving Means>DPP>Q 5

The minimum value of

f (x) = \cos^{2} x + \frac{\sec x}{4}, x \in (- \frac{π}{2}, \frac{π}{2})

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 5 - Inequalities Involving Means>DPP>Q 6

Let $x, y, z \in R^{+}$ and $2 x y + 3 y z + 4 x z = 18$ . If $α, β$ and $γ$ be the values of $x, y$ and $z$ respectively, for which $x y z$ attains its maximum value, then find the value of $2 α + β + γ$ .

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 5 - Inequalities Involving Means>DPP>Q 7

The minimum value of

\frac{x^{4} + y^{4} + z^{2}}{x y z}

for positive real numbers

x, y, z

is

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 5 - Inequalities Involving Means>DPP>Q 8

If

n_{1}, n_{2}, n_{3}, \dots, n_{100}

are positive real numbers such that

n_{1} + n_{2} + n_{3} + \dots + n_{100} = 20

and

k = n_{1} (n_{2} + n_{3} + n_{4}) (n_{5} + n_{6} + . . \dots + n_{9}) (n_{10} + \dots + n_{16}) \dots (\dots + n_{100})

, then

k

belongs to

HARD

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 5 - Inequalities Involving Means>DPP>Q 9

If

a, b, c

are the sides of a triangle, then the least value of

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

is

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 5 - Inequalities Involving Means>DPP>Q 10

If

x > 0, n \in N

then

, \frac{x^{n}}{1 + x + x^{2} + . . . + x^{2 n}}

is