Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 33

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JEE Advanced

IMPORTANT

Earn 100

The number of the real solutions of the equation $x^{2} - 3 |x| + 2 = 0$ is

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Important Questions on Inequalities and Quadratic Equation

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 34

The value of

a

for which one root of the quadratic equation

(a^{2} - 5 a + 3) x^{2} + (3 a - 1) x + 2 = 0

is twice as large as the other, is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 35

If

α \neq β

and

α^{2} = 5 α - 3, β^{2} = 5 β - 3,

then the equation having

\frac{α}{β}

and

\frac{β}{α}

as its roots, is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 36

The number of real roots of

3^{2 x^{2} - 7 x + 7} = 9

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 37

The number of digits in

20^{301}

(

given

\log_{10} 2 = 0.3010)

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 38

The number of solutions of the equation

\log_{101} \log_{7} (\sqrt{x + 7} + \sqrt{x}) = 0

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 39

The value of

a

, so that the sum of squares of the roots of the equation

x^{2} - (a - 2) x - a + 1 = 0

assume the least value, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 40

If the roots of

x^{2} - a x + b = 0

are two consecutive odd integers, then

a^{2} - 4 b

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 41

If

α

and

β

are the roots of

x^{2} - a x + b^{2} = 0,

then

α^{2} + β^{2}

is equal to