EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 8th January 2020 Shift 2>Q 42

EASY

JEE Main

IMPORTANT

Earn 100

Let $S$ be the set of all real roots of the equation $3^{x} (3^{x} - 1) + 2 = |3^{x} - 1| + |3^{x} - 2|$ , then

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Important Questions on Quadratic Equations

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th January 2020 Shift 1>Q 43

The number of real roots of the equation,

e^{4 x} + e^{3 x} - 4 e^{2 x} + e^{x} + 1 = 0

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th January 2020 Shift 1>Q 44

The number of distinct solutions of the equation,

\log_{\frac{1}{2}} |\sin x| = 2 - \log_{\frac{1}{2}} |\cos x|

in the interval

[0, 2 π],

is ________

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th January 2020 Shift 2>Q 45

Let

a, b \in R, a \neq 0

be such that the equation,

a x^{2} - 2 b x + 5 = 0

has a repeated root

α,

which is also a root of the equation,

x^{2} - 2 b x - 10 = 0 .

If

β

is the other root of this equation, then

α^{2} + β^{2}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th April 2019 Shift 1>Q 46

Let

p, q \in Q .

If

2 - \sqrt{3}

is a root of the quadratic equation

x^{2} + p x + q = 0,

then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th April 2019 Shift 2>Q 47

If

m

is chosen in the quadratic equation

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

such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th January 2019 Shift 2>Q 48

The number of all possible positive integral value of

α

for which the roots of the quadratic equation

6 x^{2} - 11 x + α = 0

are rational numbers is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th January 2019 Shift 2>Q 49

If both the roots of the quadratic equation

x^{2} - m x + 4 = 0

are real and distinct and they lie in the interval

(1, 5),

then

m

lies in the interval:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 8th April 2019 Shift 1>Q 50

The sum of the solutions of the equation

|\sqrt{x} - 2| + \sqrt{x} (\sqrt{x} - 4) + 2 = 0, (x > 0)

is equal to