The CAT QA section requires speed and accuracy, along with a thorough understanding of the Functions. This article provides a set of MCQs on Functions to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
CAT MCQs on Functions
1. Let \(f(x)=x^2+ax+b\) and \(g(x)=f(x+1)-f(x-1)\). If \(f(x)≥0\) for all real \(x\), and \(g(20)=72\), then the smallest possible value of \(b\) is
View Solution
2. 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
View Solution
3. If \(f(x)=\frac{5x+2 }{3x-5}\) and \(g(x)=x^2-2x-1\),then the value of \(g(f(f(3)))\) is
View Solution
4. Let f(x) = x2 and g(x) = 2X , for all real x. Then the value of f( f(g(x)) + g(f(x)) ) at x = 1 is
View Solution
5. If 9x-1/2-22x-2=4x-32x-3, then x is
View Solution
6. If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(l) is
View Solution
7. A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is
View Solution
8. For any non-zero real number x, let\( f(x) + 2f\left(\frac{1}{x}\right) = 3x.\)Then, the sum of all possible values of x for which f(x) = 3, is
View Solution
9. If \( g(x) = p(x) = qx^n \), and \( p \) and \( q \) are constants, then at \( x = 0 \), \( g(x) \) will be:
A
Maximum when \( p>0, q>0 \)
B
Minimum when \( p>0, q<0 \)
C
Minimum when \( p>0, q>0 \)
D
Maximum when \( p>0, q<0 \)
View Solution
10.
Let \( f \) be an injective map with domain x, y, z and range 1, 2, 3 such that exactly one of the following statements is correct and the remaining are false.}
[I.] \( f(x) = 1 \Rightarrow f(y) = 1, f(z) = 2 \)
[II.] \( f(x) = 2 \Rightarrow f(y) = 1, f(z) = 1 \)
[III.] \( f(x) = 1, f(y) = 1, f(z) = 2 \) Then the value of \( f(1) \) is:
View Solution
11. If \( f\left(x + \frac{y}{8}, y - \frac{x}{8}\right) = xy \), then \( f(m,n) + f(n,m) = 0 \) is true:
D
for all \( m \) and \( n \)
View Solution
12. Let \(f(x)\) 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 \(f\left( \frac12 \right)\)?
View Solution
13. Let $g(x)$ be a function such that $g(x+1)+g(x-1) = g(x)$ for all real $x$. For what $p$ does $g(x+p) = g(x)$ hold for all $x$?
View Solution
14. A function \( f(x) \) satisfies \( f(1) = 3600 \) and \( f(1) + f(2) + \ldots + f(n) = n^2 f(n) \) for all positive integers \( n>1 \). What is the value of \( f(9) \)?
View Solution
Comments