Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 117

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

The constant term of the quadratic expression $\sum_{k = 2}^{n} (x - \frac{1}{k - 1}) (x - \frac{1}{k})$ , as $n \to \infty$ 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>Target Exercises>Q 118

The system

y^{(x^{2} + 7 x + 12)} = 1

and

x + y = 6, y > 0

has

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 119

The curve

y = (λ + 1) x^{2} + 2

intersects the curve

y = λ x + 3

in exactly one point, if

λ

equals

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 120

If the expression

x^{2} + 2 (a + b + c) x

+ 3 (b c + c a + a b)

is a perfect square, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 121

Sum of the non-real roots of

(x^{2} + x - 2) (x^{2} + x - 3) = 12

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 122

The number of irrational roots of the equation

\frac{4 x}{(x^{2} + x + 3)} + \frac{5 x}{(x^{2} - 5 x + 3)} = - \frac{3}{2}

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 123

If

α

and

β

are the roots of the equation

x^{2} - 2 x + 3 = 0

, then the equation whose roots are

P = α^{3} - 3 α^{2} + 5 α - 2

and

Q = β^{3} - β^{2} + β + 5

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 124

If

α

and

β

are the roots of the equation

2 x^{2} - 35 x + 2 = 0, α, β \neq 0

then the value of

{(2 α - 35)}^{3} {(2 β - 35)}^{3}

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 125

The sum of values of

x

satisfying the equation

{(31 + 8 \sqrt{15})}^{x^{2} - 3} + 1 = {(32 + 8 \sqrt{15})}^{x^{2} - 3}

is