Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 28

EASY

CAT

IMPORTANT

Earn 100

Find the maximum and the minimum values of the function $\frac{x^{2} - x + 1}{x^{2} + x + 1}$ for real values of $x$ .

50% studentsanswered this correctly

Important Questions on X+2 Maths

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 29

Consider the equation of the form

x^{2} + bx + c = 0

. The number of such equations that have real roots and have coefficients of

b

and

c

in the set

{1, 2, 3

,

4, 5, 6}

,(

b

may be equal to

c

), is:

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 30

If

a, b, c

and

d

are four consecutive terms of an increasing

A P

, then the roots of the equation

(x - a) (x - c) + 2 (x - b) (x - d) = 0

are

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 31

If

2 a^{- \frac{1}{3}} + 2 a^{\frac{1}{3}} = 5

, then find the value of

a

.

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 32

If

α, β

, and

γ

are the roots of the equation

9 x^{3} - 7 x +

6 = 0

, then the equation whose roots are

3 α + 2, 3 β

+ 2

and

3 γ + 2

is:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 33

If the roots of equation

(q - r) x^{2} + (r - p) x + p - q = 0

are equal, then

p

,

q

,

r

are in:

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 34

Both the roots of the equation

(x - b) (x - c) + (x - a) (x - c) + (x - a) (x - b) = 0

are always

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 35

If

a (b - c) x^{2} + b (c - a) xy + c (a - b) y^{2}

is a perfect square, then,

a

,

b

,

c

are in:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 36

x^{3^{n}} + y^{3^{n}}

is divisible by

x + y,

if