Functions, Graphs and statistics is the one of the topic in CAT quantitative aptitude section, where the questions are mostly tricky. We have provided one solved set of questions on functions and graphs topic.

**Functions Questions for CAT PDF:**

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**Question 1:**

Suppose, the seed of any positive integer n is defined as follows:

seed(n) = n, if n < 10

seed(n) = seed(s(n)), otherwise, where s(n) indicates the sum of digits of n.

For example, seed(7) = 7,

seed(248) = seed(2 + 4 + 8) = seed(14) = seed (1 + 4) = seed (5) = 5 etc.

How many positive integers n, such that n < 500, will have seed (n) = 9?

a) 39

b) 72

c) 81

d) 108

e) 55

**Question 2:**

The function f(x) = |x â€“ 2| + |2.5 â€“ x| + |3.6 â€“ x|, where x is a real number, attains a minimum at

a) x = 2.3

b) x = 2.5

c) x = 2.7

d) None of the above

**Question 3:**

Consider the following two curves in the x-y plane:

$y = x^3 + x^2 + 5$

$y = x^2 + x + 5$

Which of following statements is true for $-2 \leq x \leq 2$ ?

a) The two curves intersect once.

b) The two curves intersect twice.

c) The two curves do not intersect

d) The two curves intersect thrice.

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**Question 4:**

If $f(x)=x^3-4x+p$ , and f(0) and f(1) are of opposite signs, then which of the following is necessarily true

a) -1 < p < 2

b) 0 < p < 3

c) -2 < p < 1

d) -3 < p < 0

**Question 5:**

If $\frac{a}{b+c}=\frac{b}{a+c} =\frac{c}{b+a} =r$, then r cannot take any value except

a) 1/2

b) -1

c) 1/2 or -1

d) -1/2 or -1

**Answers and Solutions for Functions Questions for CAT PDF:**

**1)** Answer (E)

For seed (n) = 9, all the numbers below 500 must have a digit sum of 9.

These numbers are all divisible by 9.

So total number of numbers below 500 and divisible by 9 is 55.

**2)** Answer (B)

f(x) = |x â€“ 2| + |2.5 â€“ x| + |3.6 â€“ x|

For x belonging to (-infinity to 2), f(x) = 2-x + 2.5-x + 3.6-x = 8.1-3x

This attains the minimum value at x=2. Value = 2.1

For x belonging to (2 to 2.5), f(x) = x-2 + 2.5-x + 3.6-x = 4.1-x

Attains the minimum value at x = 2.5. Value = 1.6

For x belonging to (2.5 to 3.6), f(x) = x-2 + x-2.5 + 3.6-x = x-0.9

Attains the minimum at x=2.5, value = 1.6

For x > 3.6, f(x) = x-2+x-2.5+x-3.6 = 3x – 8.1

Attains the minimum at x= 3.6, value = 2.7

So, min value of the function is 1.6 at x=2.5

**3)** Answer (D)

Equate the 2 equations we get value of x = 1 and -1 . Also we notice that there is intersection at x=0 . hence D

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**4)** Answer (B)

f(1) = 1-4+p = p-3

f(0) = p

Since they are of opposite signs, p(p-3) < 0

=> 0 < p < 3

**5)** Answer (C)

a = r(b+c)

b = r(a+c)

c = r(a+b)

On adding all the equations,

a+b+c = 2r(a+b+c)

If r = 1/2, a+b+c = a+b+c (valid)

If r = -1, a+b+c = -2(a+b+c) => a+b+c = 0 => b+c = -a and a/(b+c) = a/(-a) = -1 (valid)

So, r can take the values 1/2 or -1.

We hope that this Functions for CAT PDF is useful to you.