Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 16

EASY

CAT

IMPORTANT

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For any real number x, let $(x)$ denote the largest integer less than or equal to x and $⟨ x ⟩ = x - [x]$ , that is, the fractional part of x. For arbitrary real numbers x, y, and z, only one of the following statements is correct. Which one is it?

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Important Questions on X+2 Maths

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 17

The domain of the function

f (x) = {}^{16 x}C_{2 x - 1} + {}^{20 - 3 x}P_{4 x - 5}

Where the symbols have their usual meanings is the set:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 18

The domain of the real valued function

f (x) = \log_{e} |\log_{e} x|

is:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 19

The domain of the function

f (x) = \log_{e} (x - [x])

is { where [.] denotes greatest integer function}

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 20

Let

f (x) = \log_{x^{2}} 25

and

g (x) = \log_{x} 5

, then

f (x) = g (x)

holds for x belonging to:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 21

Let

f (x) = | x - 2 | + | x - 3 | + | x - 4 |

and

g (x) = f (x + 1)

. Then:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 22

If

f (x) = x^{n}, n \in N

and

(gof) (x) = n g (x)

, then

g (x)

can be

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 23

The inverse function of the function

f (x) = f (x) = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}

is:

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 24

The graph of the function

y = f (x)

is symmetrical about the line

x = 2

, then :