x ∈ ℝ : 6 + x - x 2 2 x + 5 ≥ 6 + x - x 2 x + 4 =

( - ∞ , - 4 ] ∪ - 5 2 , - 1

( - ∞ , - 4 ] ∪ [ - 2 , - 1 ]

Let N be the set of positive integers. For all n ∈ N , let f n = n + 1 1 / 3 - n 1 / 3 and A = n ∈ N : f n + 1 < 1 3 n + 1 2 / 3 < f n Then,

the complement of A in N is nonempty, but finite

A and its complement in N are both infinite

If x + 5 ≥ 10 , then

x ∈ ( - ∞ , - 15 ] ∪ [ 5 , ∞ )

x ∈ - ∞ , - 15 ∪ [ 5 , ∞ )

For 0 ≤ p ≤ 1 and for any positive a , b ; let I ( p ) = ( a + b ) p , J ( p ) = a p + b p , then

I ( p ) < J ( p ) in 0 , p 2 and l ( p ) > J ( p ) in p 2 , ∞

I ( p ) < J ( p ) in p 2 , ∞ and J ( p ) < I ( p ) in 0 , p 2

EASY

Earn 100

Read and answer the following question:

‘P ! Q’ means ‘P is not smaller than Q’
‘P @ Q’ means ‘P is neither smaller than nor equal to Q’
‘P # Q’ means ‘P is neither greater than nor equal to Q’
‘P & Q’ means ‘P is neither smaller than nor greater than Q’
‘P * Q’ means ‘P is not greater than Q’

Which of the given symbols can be placed in blank spaces respectively (in the same order from left to right) such that all the three expressions V ! F, T # V and E @ T definitely holds true? H_T_F_E_V

50% studentsanswered this correctly

Important Questions on Inequalities

HARD

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

\{x \in ℝ : \frac{\sqrt{6 + x - x^{2}}}{2 x + 5} \geq \frac{\sqrt{6 + x - x^{2}}}{x + 4}\} =

HARD

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The solution set of the rational inequality

\frac{x + 9}{x - 6} \leq 0

MEDIUM

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

For all

n \in ℕ, n \in ℕ,

, if

1^{2} + 2^{2} + 3^{2} + \dots + n^{2} > x

, then

x =

MEDIUM

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

Let

N

be the set of positive integers. For all

n \in N,

let

f_{n} = {(n + 1)}^{1 / 3} - n^{1 / 3}

and

A = \{n \in N : f_{n + 1} < \frac{1}{3 {(n + 1)}^{2 / 3}} < f_{n}\}

Then,

HARD

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The least positive integer

n

for which

\sqrt[3]{n + 1} - \sqrt[3]{n} < \frac{1}{12}

is-

MEDIUM

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The number of non-negative integer solutions of the equations

6 x + 4 y + z = 200

and

x + y + z = 100

EASY

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The smallest prime number satisfying the inequality

\frac{2 n - 3}{3} \geq \frac{n - 1}{6} + 1

EASY

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

|x + 5| \geq 10

, then

HARD

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

\frac{6 x^{2} - 5 x - 3}{x^{2} - 2 x + 6} \leq 4,

then the least and the highest values of

4 x^{2}

are

MEDIUM

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The number of integers satisfying the inequality

|n^{2} - 100| < 50

HARD

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The number of integral values of

m

for which the quadratic expression

(1 + 2 m) x^{2} - 2 (1 + 3 m) x + 4 (1 + m), x \in R

is always positive, is

HARD

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

Let

a, b, c, d, e

be real numbers such that

a + b < c + d, b + c < d + e, c + d < e + a, d + e < a + b .

Then

MEDIUM

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

Let

x = [\frac{a + 2 b}{a + b}]

and

y = \frac{a}{b}

, where

a

and

b

are positive integers. If

y^{2} > 2

, then

EASY

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

For

0 \leq p \leq 1

and for any positive

a, b;

let

I (p) = (a + b)^{p}, J (p) = a^{p} + b^{p},

then

EASY

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The solution of the inequality

|x^{2} - 4 x| < 5

HARD

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

β

satisfies the equation

x^{2} - x - 6 > 0

, then a value exists for

EASY

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The solution of

\frac{6 x}{4 x - 1} < \frac{1}{2}

MEDIUM

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The maximum value of

z = 7 x + 5 y

subject to

2 x + y \leq 100, 4 x + 3 y \leq 240, x \geq 0, y \geq 0

MEDIUM

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

The least positive integer

n

for which

\sqrt{n + 1} - \sqrt{n - 1} < 0.2

MEDIUM

Mathematics>Algebra>Inequalities>Solution and Representation of Inequalities

5, 5 r, 5 r^{2}

are the lengths of the sides of a triangle, then

r

can not be equal to:

Important Questions on Inequalities

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