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

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IMPORTANT

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If 0 < x < 1000 and $[\frac{x}{2}] + [\frac{x}{3}] + [\frac{x}{5}] = \frac{31}{30} x$ , where [ x ] is greatest integer function less than or equal to x, then the number of possible values of x is

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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 7

If

f (x) = 1 / x, x \neq 0; f^{n + 1} (x) = f^{n} (f (x))

, find the value of the product

f^{13} (1) \times f^{15} (1) \times f^{19} (1) f^{21} (1)

.

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

The set of real values of

x

, satisfying

||x - 1| - 1| \leq 1

is

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

A function is defined as

f^{n} (x) = f \{f^{n - k} (x)\}

If n is odd, $k = 1$ .

If n is even, $k = 2$ and $f^{0} (x) = 1$ .

Find

f^{⌝} (x)

at

x = 1

, if

f (x) = x^{2} + 1

.

EASY

CAT

IMPORTANT

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

(x^{2} - 1)

is a factor of

f (x) = (x^{5} + {ax}^{4} + {bx}^{3} + {cx}^{2} + x + d)

. The graph of

f (x)

intersects y axis at

(0, - 3)

. Find the value of

(a + c)

.

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

Let

F (x)

denote the sum of the digits of the positive integer

x .

For example,

F (8) = 8

and

F (123) = 1 + 2 + 3 = 6 .

For how many two-digit values of

x

is

F (F (x)) = 3

?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 12

If

f (x + 1) + f (x - 1) = 2 f (x)

and

f (0) = 0

, then

f (n), n \in

N is:

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 13

Let

f (x) = 1 + | x |, x < - 1

[x], x \geq - 1

, where [.] denotes the greatest integer function. Then,

f {f (- 2.3)}

is equal to:

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Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 14

The largest set of real values of

x

for which

f (x) = \sqrt{(x + 2) (5 - x)} - \frac{1}{\sqrt{x^{2} - 4}}

is a real function is