Functions PYQs - Last 10 Years

JEE Advanced / Mathematics / Calculus / 17 recent questions

MathematicsCalculus2017-2026

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Practice 17 JEE Advanced Mathematics questions from Functions. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

17

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Mathematics / Calculus

2017-2026

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9

Last 5 Years

2022-2026

17

Last 10 Years

2017-2026

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2020

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17PYQs

INTEGER58.8%

MCQM23.5%

MCQ17.6%

Difficulty Mix

#1 Medium9

#2 Hard7

#3 Easy1

9 in last 5 years17 in last 10 years

Last 10 Years Functions Questions

Showing 17 of 17 filtered questions.

Let $\mathbb{N}$ denote the set of all positive integers. Consider the sets
\(A=\{1,2,3,4,5\} \text { and } B=\{1,2,3,4,5,6,7\} .\)
Let $S$ be the set of all functions $f: A \rightarrow B$ such that $f(2) \neq 2$ and $f(4) \neq 4$. Consid...

INTEGER+4 / -02026

Let $\mathbb{R}$ denote the set of all real numbers. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow(0,4)$ be functions defined by
\(f(x)=\log _e\left(x^2+2 x+4\right), \text { and } g(x)=\frac{4}{1+e^{-2 x}}\)
D...

INTEGER+4 / -02025

Let ℝ denote the set of all real numbers. Let f: ℝ → ℝ be a function such that f(x) > 0 for all x ∈ ℝ, and f(x+y) = f(x)f(y) for all x, y ∈ ℝ.
Let the real numbers a₁, a₂, ..., a₅₀ be in an arithmetic progression. If f(a₃₁) = 64f(a₂₅), and
...

INTEGER+4 / -02025

Let ℕ denote the set of all natural numbers, and ℤ denote the set of all integers. Consider the functions f: ℕ → ℤ and g: ℤ → ℕ defined by$$ f(n) = \begin{cases} \frac{(n + 1)}{2} & \text{if } n \text{ is odd,} \\ \frac{(4-n)}{2} & \text{if...

MCQM+4 / -22025

Let the function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by

$$ f(x)=\frac{\sin x}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)}+\frac{2}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+...

INTEGER+4 / -02024

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x+y)=f(x)+f(y)$ for all $x, y \in \mathbb{R}$, and $g: \mathbb{R} \rightarrow(0, \infty)$ be a function such that $g(x+y)=g(x) g(y)$ for all $x, y \in \mathbb{R}$. If $f\...

INTEGER+4 / -02024

Let $f:[0,1] \rightarrow[0,1]$ be the function defined by $f(x)=\frac{x^3}{3}-x^2+\frac{5}{9} x+\frac{17}{36}$. Consider the square region $S=[0,1] \times[0,1]$. Let $G=\{(x, y) \in S: y>f(x)\}$ be called the green region and $R=\{(x, y) \i...

MCQM+4 / -22023

Let $S=(0,1) \cup(1,2) \cup(3,4)$ and $T=\{0,1,2,3\}$. Then which of the following statements is(are) true?

MCQM+4 / -22023

Let \(|M|\) denote the determinant of a square matrix \(M\). Let \(g:\left[0, \frac{\pi}{2}\right] \rightarrow \mathbb{R}\) be the function defined by
\(g(\theta)=\sqrt{f(\theta)-1}+\sqrt{f\left(\frac{\pi}{2}-\theta\right)-1}\)
where
$$
f...

MCQM+4 / -22022

Let the function \(f:(0,\pi ) \to R\) be defined by \(f(\theta ) = {(\sin \theta + \cos \theta )^2} + {(\sin \theta - \cos \theta )^4}\)Suppose the function f has a local minimum at \(\theta\) precisely when $$\theta \in \{ {\lambda _...

INTEGER+4 / -02020

Let the function f : [0, 1] \(\to\) R be defined by\(f(x) = {{{4^x}} \over {{4^x} + 2}}\)Then the value of $$f\left( {{1 \over {40}}} \right) + f\left( {{2 \over {40}}} \right) + f\left( {{3 \over {40}}} \right) + ... + f\left( {{{39} \ov...

INTEGER+4 / -02020

For a polynomial g(x) with real coefficients, let mg denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by $$S = \{ {({x^2} - 1)^2}({a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3}):...

INTEGER+4 / -02020

Let f : [0, 2] \(\to\) R be the function defined by\(f(x) = (3 - \sin (2\pi x))\sin \left( {\pi x - {\pi \over 4}} \right) - \sin \left( {3\pi x + {\pi \over 4}} \right)\)If \(\alpha ,\,\beta \in [0,2]\) are such that $$\{ x \in [0,2]:...

INTEGER+4 / -02020

If the function f : R \(\to\) R is defined by f(x) = |x| (x \(-\) sin x), then which of the following statements is TRUE?

Let \({E_1} = \left\{ {x \in R:x \ne 1\,and\,{x \over {x - 1}} > 0} \right\}\) and $${E_2} = \left\{ \matrix{
x \in {E_1}:{\sin ^{ - 1}}\left( {{{\log }_e}\left( {{x \over {x - 1}}} \right)} \right) \hfill \cr
is\,a\,real\,number \hfil...

Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If \(\alpha\) is the number of one-one functions from X to Y and \(\beta\) is the number of onto functions from Y to X, then the value of $${1 \over {5!}}(\bet...

INTEGER+3 / -02018

Let S = {1, 2, 3, .........., 9}. For k = 1, 2, .........., 5, let Nk be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N1 + N2 + N3 + N4 + N5 =