Functions (IPMAT/JIPMAT) - Free PYQs + Solutions

Q1:

Indore 2024

Algebra

>

Functions

Medium

Q1:

Let

f

and

g

be two functions defined by

f(x) = |x + |x||

and

g(x) = \frac{1}{x}

for

x \neq 0

. If

f(a) + g(f(a)) = \frac{13}{6}

for some real

a

, then the maximum possible value of

f(g(a))

is:

Entered answer:

Correct Answer

6

Correct Answer

Explanation →

Q2:

Indore 2023

Algebra

>

Functions

Medium

Q2:

If

f(1) = 1

and

f(n) = 3n - f(n - 1)

for all integers

n > 1

, then the value of

f(2023)

is

Entered answer:

Correct Answer

3034

Correct Answer

Explanation →

Q3:

Indore 2022

Algebra

>

Functions

Medium

Q3:

Let

A=\{1,2,3\}

and

B=\{a, b\}

. Assuming all relations from set

A

to set

B

are equally likely, what is the probability that a relation from

A

to

B

is also a function?

\frac{1}{8}

\frac{1}{2}

1

\frac{3^{2}}{2^{6}}

Correct Answer

Option: 1

Correct Answer

Explanation →

Q4:

Indore 2022

Algebra

>

Functions

Easy

Q4:

A set of all possible values the function

f(x)=\dfrac{x}{|x|}

, where

x \neq 0

, takes is

\{1\}

\{1,-1\}

\{1,0\}

\{1,0,-1\}

Correct Answer

Option: 2

Correct Answer

Explanation →

Q5:

Indore 2022

Algebra

>

Functions

Hard

Q5:

If

f\left(x^{2}+f(y)\right)=x f(x)+y

for all non-negative integers

x

and

y

, then the value of

[f(0)]^{2}+f(0)

equals _________.

2

0

6

1

Correct Answer

Option: 2

Correct Answer

Explanation →

Q6:

Indore 2021

Algebra

>

Functions

Medium

Q6:

Suppose that a real-valued function

f(x)

of real numbers satisfies

f(x + xy) = f(x) + f(xy

) for all real

x, y,

and that

f(2020) = 1

. Compute

f(2021)

.

\frac{2021}{2020}

\frac{2020}{2019}

1

\frac{2020}{2021}

Correct Answer

Option: 1

Correct Answer

Explanation →

Q7:

Indore 2021

Algebra

>

Functions

Medium

Q7:

If a function

f(a) = max (a, 0)

then the smallest integer value of

x

for which the equation

f(x - 3) + 2f(x + 1) = 8

holds true is _______.

Entered answer:

Correct Answer

3

Correct Answer

Explanation →

Q8:

Indore 2020

Algebra

>

Functions

Easy

Q8:

Given

f(x) = x^2 + \log_3 x

and

g(y) = 2y + f(y)

, then the value of

g(3)

equals

16

15

25

26

Correct Answer

Option: 1

Correct Answer

Explanation →

Q9:

Indore 2019

Algebra

>

Functions

Hard

Q9:

The function

f(x) = \dfrac{x^3 - 5x^2 - 8x}{3}

is

positive and monotonically increasing for x

\in (-\infty, \frac{5-\sqrt{57}}{2})

and x

\in (\frac{5+\sqrt{57}}{2}, +\infty)

negative and monotonically decreasing for x

\in (-\infty, \frac{5-\sqrt{57}}{2})

and x

\in (\frac{5+\sqrt{57}}{2},+\infty)

negative and monotonically increasing for x

\in (-\infty, \frac{5-\sqrt{57}}{2})

and positive and monotonically increasing for x

\in (\frac{5+\sqrt{57}}{2},+\infty)

positive and monotonically increasing for x

\in (-\infty, \frac{5-\sqrt{57}}{2})

and negative and monotonically decreasing for x

\in (\frac{5+\sqrt{57}}{2},+\infty)

Correct Answer

Option: 3

Correct Answer

Explanation →

Q10:

Indore 2019

Algebra

>

Functions

Hard

Q10:

A real-valued function

f

satisfies the relation

f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y

, for all real numbers

x

and

y

, then the value of

f(8)

is

Entered answer:

Correct Answer

19

Correct Answer

Explanation →

Functions - Past Year Questions

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Functions - Past Year Questions (Free PDF Download)