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

EASY

CAT

IMPORTANT

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Let $f (x)$ be the greatest integer function and $g (x)$ be the modulus function, then what is the value of $(g \circ f) (- \frac{5}{3}) + (f \circ g) (- \frac{5}{3}) ?$

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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 35

Part of the graph of $f (x) = {ax}^{3} + {bx}^{2} + cx + d$ is shown. What is b?

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HARD

CAT

IMPORTANT

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

In the sequence

2001, 2002, 2003,

..... each term after the third is found by subtracting the previous term from the sum of the two terms that precede that term. For example, the fourth term is

2001 + 2002 - 2003 = 2000 .

What is the

2004^{th}

term in this sequence?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 37

If f (x) = \log (\frac{1 + x}{1 - x}), then f (x) + f (y) is:

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 38

Let,

f (x, y) = | x + y |

g (x, y) = | x - y |

and, then how many ordered pairs of the from

(x, y)

would satisfy

f (x, y) = g (x, y)

?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 39

f (x) = y + \frac{1}{y}

, where

y > 0

. If y increases in value, then

f (x)

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 40

A function H is defined for all the positive integers that satisfy the following condition:

$H (1) + H (2) + H (3) + \dots + H (x) = x^{2} H (x)$ .

If

H (1) = 2006

, then find the value of

H (2005)

.

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 1

If

a < b < c < d < e

and

f (x) = (x - a)^{2} (x - b) (x - c) (x - d) (x - e)

, then which of the following is true?

EASY

CAT

IMPORTANT

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

[x]

is defined as the greatest integer less than or equal to x, and

{x}

is defined as the least integer greater than or equal to x, for all real values of x. Consider the four statements.

$1$ . $[x] + [- x] = - 1$ , if x is not an integer.

$2$ . ${x} + [- x] = 0$

$3$ . ${[x]} - [{x}] = - 1$

$4$ . $[2 x] + {3 x} \leq 5 x$

How many of the above statements are always true for all the real values of x?