# Top 20 CAT Quant Functions and Graphs Questions PDF

by Naveen Neredimalli Wed 29 May 2024 05:41 PM 21

Check out the Top 20 Functions and Graphs Questions for CAT 2024 preparation. Questions related to functions and graphs are quite common in the quantitative aptitude section of CAT and require a strong understanding of mathematical concepts and problem-solving skills.

Download PDF is designed to help you enhance your proficiency in solving CAT Quant questions related to functions and graphs. Practising these top 20 questions will strengthen your grasp of fundamental concepts and develop strategies to tackle complex problems efficiently. Each question in this PDF is carefully curated to reflect the diverse range of topics and difficulty levels you may encounter in the CAT exam. These CAT questions will test your analytical reasoning and mathematical abilities, from essential functions to advanced graphical representations.

#### Question 1

Let $$f(x)$$ be a quadratic polynomial in $$x$$ such that $$f(x) \geq 0$$ for all real numbers $$x$$. If f(2) = 0 and f( 4) = 6, then f(-2) is equal to

#### Question 2

Suppose for all integers x, there are two functions f and g such that $$f(x) + f (x - 1) - 1 = 0$$ and $$g(x ) = x^{2}$$. If $$f\left(x^{2} - x \right) = 5$$, then the value of the sum f(g(5)) + g(f(5)) is

#### Question 3

The number of real-valued solutions of the equation $$2^{x}+2^{-x}=2-(x-2)^{2}$$ is:

#### Question 4

Let $$f(x)=x^{2}+ax+b$$ and $$g(x)=f(x+1)-f(x-1)$$. If $$f(x)\geq0$$ for all real x, and $$g(20)=72$$. then the smallest possible value of b is

#### Question 5

For any real number x, let [x] be the largest integer less than or equal to x. If $$\sum_{n=1}^N \left[\frac{1}{5} + \frac{n}{25}\right] = 25$$ then N is

#### Question 6

The area of the quadrilateral bounded by the Y-axis, the line x = 5, and the lines $$\mid x-y\mid-\mid x-5\mid=2$$, is

#### Question 7

In how many ways can a pair of integers (x , a) be chosen such that $$x^{2}-2\mid x\mid+\mid a-2\mid=0$$ ?

#### Question 8

Let S be the set of all points (x, y) in the x-y plane such that $$\mid x \mid + \mid y \mid \leq 2$$ and $$\mid x \mid \geq 1.$$ Then, the area, in square units, of the region represented by S equals

#### Question 9

For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n) = n + 3 if n is odd. If m is a positive integer such that 8f(m + 1) - f(m) = 2, then m equals

#### Question 10

In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

#### Question 11

The area, in sq. units, enclosed by the lines $$x=2,y=\mid x-2\mid+4$$, the X-axis and the Y-axis is equal to

#### Question 12

Let r be a real number and $$f(x) = \begin{cases}2x -r & ifx \geq r\\ r &ifx; < r\end{cases}$$. Then, the equation $$f(x) = f(f(x))$$ holds for all real values of $$x$$ where

#### Question 13

If $$f(5+x)=f(5-x)$$ for every real x, and $$f(x)=0$$ has four distinct real roots, then the sum of these roots is

#### Question 14

The number of the real roots of the equation $$2 \cos (x(x + 1)) = 2^x + 2^{-x}$$ is

#### Question 15

The area of the region satisfying the inequalities $$\mid x\mid-y\leq1,y\geq0$$ and $$y\leq1$$ is

#### Question 16

If $$f(x+y)=f(x)f(y)$$ and $$f(5)=4$$, then $$f(10)-f(-10)$$ is equal to

#### Question 17

Let $$0 \leq a \leq x \leq 100$$ and $$f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$$. Then the maximum value of f(x) becomes 100 when a is equal to

#### Question 18

Suppose f(x, y) is a real-valued function such that f(3x + 2y, 2x - 5y) = 19x, for all real numbers x and y. The value of x for which f(x, 2x) = 27, is

#### Question 19

If $$f(x)=x^{2}-7x$$ and $$g(x)=x+3$$, then the minimum value of $$f(g(x))-3x$$ is:

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