CAT Functions, Graphs and Statistics Questions & Solutions

A sample of real CAT Functions, Graphs and Statistics past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 93 Functions, Graphs and Statistics questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   If $f(x)= (x^{2} + 3x)(x^{2}+ 3x+2)$ then the sum of all real roots of the equation $\sqrt{f(x)+1}= 9701$, is

   • -6

   • 6

   • 3

   • -3

2. Q2.CAT 2023

   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

   Answer: 3

3. Q3.CAT 2020

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

   • 1

   • 2

   • infinite

   • 0

4. Q4.CAT 2019

   Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals

   Answer: 12

5. Q5.CAT 2017

   If $f_{1}(x)=x^{2}+11x+n$ and $f_{2}(x)=x$, then the largest positive integer n for which the equation $f_{1}(x)=f_{2}(x)$ has two distinct real roots is
   

   Answer: 24

6. Q6.CAT 2008

   Let $f(x)\neq0$ for any 'x' be a function satisfying $f(x)f(y) = f(xy)$ for all real x, y. If $f(2) = 4$, then what is the value of $f(\frac{1}{2})$?

   • 0

   • $\frac{1}{4}$

   • $\frac{1}{2}$

   • 1

   • cannot be determined

7. Q7.CAT 2006

   The graph of y - x (on the y axis) against y + x (on the x axis) is as shown below. (All graphs in this question are drawn to scale and the same scale and the same scale has been used on each axis.)

   Which of the following shows the graph of y against x?
8. Q8.CAT 2004

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

   • $\frac{1}{2}$

   • -1

   • $\frac{1}{2}$ or -1

   • $\frac{-1}{2}$ or -1

9. Q9.CAT 2002

   Suppose for any real number x, [x] denotes the greatest integer less than or equal to x. Let L(x, y) = [x] + [y] + [x + y] and R(x, y) = [2x] + [2y]. Then it is impossible to find any two positive real numbers x and y for which

   • $L(x, y) = R(x, y)$

   • L(x, y) $\neq$ R(x, y)

   • $L(x, y) < R(x, y)$

   • $L(x, y) > R(x, y)$

10. Passage

    Directions for the next 3 questions: For three distinct real positive numbers x, y and z, let

    f(x, y, z) = min (max(x, y), max (y, z), max (z, x))

    g(x, y, z) = max (min(x, y), min (y, z), min (z, x))

    h(x, y, z) = max (max(x, y), max(y, z), max (z, x))

    j(x, y, z) = min (min (x, y), min(y, z), min (z, x))

    m(x, y, z) = max (x, y, z)

    n(x, y, z) = min (x, y, z)

    Q10.CAT 2000

    Which of the following expressions is indeterminate?

    • (f(x, y, z)-h(x, y, z))/(g(x, y, z) —j(x, y, z))

    • [f(x,y,z)+h(x,y,z)+g(x,y,z)+j(x,y, z)]/[j(x, y, z) + h(x, y, z)-m(x, y, z) - n(x, y, z)]

    • [g(x, y, z)-j(x, y, z)]/[f(x, y, z)-h(x, y, z)]

    • [h(x, y, z) fix, y, z)]/[n(x, y, z) - g(x, y, z)]

11. Q11.CAT 1999

    For two positive integers a and b define the function h(a,b):as the greatest common factor (G.C.F) of a, b. Let A be a set of n positive integers. G(A), the GCF of the elements of set A is computed by repeatedly using the function h.
    The minimum number of times h is required to be used to compute G is:

    • $\frac{1}{2}$ n

    • (n - 1)

    • n

    • None of these

12. Passage

    DIRECTIONS for the following questions: These questions are based on the situation given below: Let x and y be real numbers

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

    F(f(x, y)) = -f(x, y)

    G(f(x, y)) = -F(f(x, y))

    Q12.CAT 1999

    What is the value of f(G(f(1, 0)), f(F(f(1, 2)), G(f(1, 2))))?

    • 3

    • 2

    • 1

    • 0

CAT Functions, Graphs and Statistics previous year questions with solutions — AthenaPrep