Functions — JEE Main Previous Year Questions

How many JEE Main questions come from Functions?

Functions has contributed 155 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 14 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 155 questions carries a written, step-by-step solution, and each is tagged to Functions within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Functions questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 155 Functions questions (with full written solutions) are available in practice.

1. Question 1 · JEE Main 2019

   The number of functions f from {1, 2, 3, ...., 20} onto {1, 2, 3, ...., 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :
   1. (A)$$65\times (15)!$$
   2. (B)$$56\times 15$$
   3. (C)$$(15)!\times 6!$$
   4. (D)$$5!\times 6!$$
   Show answerAnswer

   Answer: $(C)(15)!\times 6!$

2. Question 2 · JEE Main 2019

   Let ƒ(x) = a x (a > 0) be written as ƒ(x) = ƒ 1 (x) + ƒ 2 (x), where ƒ 1 (x) is an even function and ƒ 2 (x) is an odd function. Then ƒ 1 (x + y) + ƒ 1 (x – y) equals
   1. (A)2ƒ 1 (x)ƒ 1 (y)
   2. (B)2ƒ 1 (x + y)ƒ 1 (x – y)
   3. (C)2ƒ 1 (x)ƒ 2 (y)
   4. (D)2ƒ 1 (x + y)ƒ 2 (x – y)
   Show answerAnswer

   Answer: (A) 2ƒ 1 (x)ƒ 1 (y)

3. Question 3 · JEE Main 2026

   The number of functions $f:\{1,2,3,4\}\to \{a,b,c\}$, which are not onto, is :
   1. (A)48
   2. (B)45
   3. (C)51
   4. (D)35
   Show answerAnswer

   Answer: (B) 45

4. Question 4 · JEE Main 2026

   If $g(x)=3x^2+2x-3,f(0)=-3$ and $4g(f(x))=3x^2-32x+72$, then $f(g(2))$ is equal to:
   1. (A)$\frac{7}{2}$
   2. (B)$-\frac{25}{6}$
   3. (C)$\frac{25}{6}$
   4. (D)$-\frac{7}{2}$
   Show answerAnswer

   Answer: (A) $\frac{7}{2}$

5. Question 5 · JEE Main 2026

   Let $f(x)=[x{]}^2-[x+3]-3,x\in \mathbf{R}$, where [.] is the greatest integer function. Then
   1. (A)$f(x)=0$ for finitely many values of $x$
   2. (B)$f(x)
   3. (C)$\underset{0}{\overset{2}{\int }}f(x)\mathrm{d}x=-6$
   4. (D)$f(x)>0$ only for $x\in [4,\infty )$
   Show answerAnswer

   Answer: (B) $f(x)

Functions questions by year

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