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

HARD

CAT

IMPORTANT

Earn 100

Let $f (x) = | x - a | + | x - 2 a | + | x - 3 a |$ , where $a > 0$ . Let the minimum value of $f (x)$ be denoted by $m$ and the corresponding value of $x$ be denoted by $b$ . Which of the following is true?

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Important Questions on X+2 Maths

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 4

The minimum of

f (x) = | x - 1 | + | x - 4 | + | x - 5 |

is attained at

x =

_____.

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 5

Let

y = k^{2} (x^{2} + 1) + 2 k (3 x + 4) + 27

. If

k

and

x

are real numbers, what is the minimum value of

y

?

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 6

If

x < - 3

and

y > 2

, then which of the following is true for all real values of

x

and

y

?

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 7

If

a_{1}, a_{2}, \dots, a_{n}

are

n

integers such that

a_{1} a_{2} \dots a_{n} = 1

, then which of the following must be true?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 8

If a and b are positive real values, and

a b + 2 (a + b) = 21

, what is the minimum value of

(a + b)

?

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 9

The least integral value of

k

for which

(k - 2) x^{2} + 8 x + k + 4 > 0, \forall x \in R

is

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 10

If

f (x) = 2 x^{2} + 3 x + 4

and

g (x) = 5 - x^{2}

, then,

minimum [f (x)] - maximum [g (x)]

is equal to:

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 11

If

a + b + c = 20

and

(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) = 30

, then the value of

(\frac{a}{b} + \frac{b}{a} + \frac{a}{c} + \frac{c}{a} + \frac{b}{c} + \frac{c}{b})

is: