CAT 2023 Functions, Graphs and Statistics Questions with Answers

Functions, Graphs and Statistics

Functions, graphs, and statistics cover odd-even functions, into-onto functions, shifting of graphs, mean, median, mode, and other related topics. Solve the sample questions provided below and go through the detailed solutions and video explanations to learn the topics. 

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For the following questions answer them individually

Question 1

If f(x) + 2 f(1/x)=2x, find the value of f(0.25)

Question 2

A function F is defined on natural numbers such that, F(n) = 2F(n-1) if n is even and F(n) = F(n-1)/2 is n is odd. If F(1) is 20, what is the average of F(1),F(2),...,F(100)

Question 3

If a, b, and c are real numbers such that a+b+c=30 and ab+bc+ca=192. Find the maximum value of a.

Question 4

What is the range of the function 3sinx+4cosx?

Question 5

For every odd number, x greater than 5, F(x) = (x-1)x(x+1). A set K is formed with all such F(x). What is the HCF of all the elements of K?

Question 6

Let f(x) = $$ax^2+bx+c$$; a,b,c are constants and a not equal to 0. It is given that f(5) = -4*f(2) and 7 is a root of the equation. What is the value of a+b+c?

Question 7

Find the minimum value of f(a)*f(b)*f(c) such that f(x) = $$\frac{6}{x} - 1$$, a + b + c = 6 and a, b and c are positive real numbers.

Question 8

If $$(x^3 + 2x^2 + 2x + 1)^6$$ is expressed as $$a_0+a_1x+a_2x^2+...+a_{18}x^{18}$$, find the value of the expression: $$a_0+a_2+a_4+...+a_{18}$$ ?

Question 9

For all natural numbers n, suppose f(n) = n + sum of the digits of n. Then,

Question 10

Select the best option which satisfies the condition that g(x) = g(1 - x) for all x?

Question 11

Find the domain of the function f(x) =$$\frac{log(x^2-8)}{|x-5|}$$ if f(x) is a real function

Question 12

f(x) = $$x^4 - 6x^3 + 4x^2 - 2x + p^2$$; If f(1) and f(2) are not of the same sign, then how many integral values of p will satisfy the conditions?

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Question 13

Function g(x) is obtained by the reflection of f(x) in the line y=1. The function h(x) is obtained by the reflection of g(x) in the line x=1. Then, reflection of h(x) in which of the following would result in f(x).

Question 14

Find the number of onto functions from the set P = {1, 2, 3, 4, 5} to R = {x, y, z}.

Question 15

Consider the following fns: $$f(x)=x+1$$ if $$-2 \leq x \leq 0$$, $$1-x$$ if $$0< x \leq 2$$, $$-1$$ otherwise, $$g(x)=-f(x)$$, $$h(x)=g(-x)$$, $$i(x)=-h(x)$$, then which of the following equations would necessarily be true

Question 16

What is the minimum value of the function f(x) = max{2x + 1, 4x - 3, 5 - 2x}

Question 17

f(x)=2f(x-1)+3 and f(1)=1. What is the value of f(25)-f(22)?

Question 18

Find the domain of the function $$f(x) = \log(2-x) + 1/\sqrt{16-x^2}$$ if f(x) is a real function

Question 19

Two functions A(x) and B(x) are such that $$ 4A^{2}(x)-2B(x)B(-x)=B^{2}(x)+B^{2}(-x)$$. If $$A(4) = 24$$ what is the value of $$A(-4)$$?

Question 20

$$h(1) + h(2) + h(3) + .... + h(x) = x^2h(x)$$ where x is a positive integer. Find the value of h(5) if h(1) is equal to 14400.

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