EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 29 January 2023 Shift 1>Q 101

MEDIUM

JEE Main

IMPORTANT

Earn 100

Let $λ \neq 0$ be a real number. Let $α, β$ be the roots of the equation $14 x^{2} - 31 x + 3 λ = 0$ and $α, γ$ be the roots of the equation $35 x^{2} - 53 x + 4 λ = 0$ . Then $\frac{3 α}{β}$ and $\frac{4 α}{γ}$ are the roots of the equation :

76.19% studentsanswered this correctly

Important Questions on Quadratic Equations

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 29 January 2023 Shift 2>Q 102

Let

α_{1}, α_{2}, \dots, α_{7}

α_{1}, α_{2}, \dots, α_{7}

be the roots of the equation

x^{7} + 3 x^{5} - 13 x^{3} - 15 x = 0

and

|α_{1}| \geq |α_{2}| \geq \dots \geq |α_{7}|

.
Then,

α_{1} α_{2} - α_{3} α_{4} + α_{5} α_{6}

is equal to _______

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 30 January 2023 Shift 2>Q 103

The parabolas :

a x^{2} + 2 b x + c y = 0

and

d^{2} + 2 e x + f y = 0

intersect on the line

y = 1

. If

a, b, c, d, e, f

are positive real numbers and

a, b, c

are in

G . P .

, then

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 30 January 2023 Shift 2>Q 104

If the value of real number

α > 0

for which

x^{2} - 5 α x + 1 = 0

and

x^{2} - α x - 5 = 0

have a common real roots is

\frac{3}{\sqrt{2 β}}

then

β

is equal to ________

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 31 January 2023 Shift 1>Q 105

The number of real roots of the equation

\sqrt{x^{2} - 4 x + 3} + \sqrt{x^{2} - 9} = \sqrt{4 x^{2} - 14 x + 6}

, is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 31 January 2023 Shift 2>Q 106

The equation

e^{4 x} + 8 e^{3 x} + 13 e^{2 x} - 8 e^{x} + 1 = 0, x \in R

has :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 1 February 2023 Shift 1>Q 107

Let

S = \{x : x \in ℝ and {(\sqrt{3} + \sqrt{2})}^{x^{2} - 4} + {(\sqrt{3} - \sqrt{2})}^{x^{2} - 4} = 10\}

. Then

n (S)

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 1 February 2023 Shift 2>Q 108

The number of integral values of

k

, for which one root of the equation

2 x^{2} - 8 x + k = 0

lies in the interval

(1, 2)

and its other root lies in the interval

(2, 3)

, is :