JEE Main Functions Practice Questions With Solutions

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JEE Main Functions Practice Questions with Solutions

Functions are a fundamental part of the Mathematics section in the JEE Main entrance exam. Trigonometry or any topic from calculus can be quite challenging for many students. Usually, 2 to 3 questions may appear in the JEE Main exam’s question paper from functions, which is why, it is a scoring topic. So, it is advised for students to attempt all the questions as possible from this part. The JEE Main Functions Practice Questions with Solutions are a set of questions from functions, intended for students to practice and make themselves familiar with the concepts. The solutions are also provided along with the questions for the students' reference. This section assesses the problem-solving ability of the students. The important topics of the functions chapter from which questions are asked in the JEE Main exam’s question paper are Types of Functions (rational, polynomial, exponential, trigonometric, and logarithmic), Composition of Functions, Transformation of Functions, Inverse Functions, Special Functions, and Graphical Understanding.

Practising the JEE Main Functions Practice Questions with Solutions regularly will improve the students’ knowledge of the functions chapter and help them memorise important formulas and concepts. Questions from all the important topics, and of all difficulty levels, will be present in these practice tests. The questions in the JEE Main Functions practice tests will typically be presented in the form of multiple-choice and assertion-reason types. These practice tests, typically consisting of around 15 to 20 questions from this chapter, are an amazing tool to enhance accuracy and speed, necessary while solving complex mathematical problems. Frequently practising these tests will allow students to understand the format of the question paper and the types of questions asked in this area in the exam. These practice tests will also boost confidence, and improve the students' analytical thinking skills, which are necessary for solving mathematical equations during the JEE Main entrance exam.

JEE Main Mathematics Functions Practice Questions

Chemistry Physics

Question 1.

Let the range of the function $f (x) = \frac{1}{2 + \sin 3 x + \cos 3 x}, x \in R$ be $[a, b]$ . If $α$ and $β$ ar respectively the A.M. and the G.M. of $a$ and $b$ , then $\frac{α}{β}$ is equal to

π

\sqrt{π}

\sqrt{2}

Question 2.

If the domain of the function $f (x) = \sin^{- 1} (\frac{x - 1}{2 x + 3})$ is $R - (α, β)$ , then $12 α β$ is equal to :

Question 3.

Let $f (x) = {\begin{array}{ccc} - a & if & - a \leq x \leq 0 \\ x + a & if & 0 < x \leq a \end{array}$ where $a > 0$ and $g (x) = (f (| x |) - | f (x) |) / 2$ . Then the function $g : [- a, a] \to [- a, a]$ is

neither one-one nor onto.

both one-one and onto.

one-one.

onto

Question 4.

If the function $f (x) = {(\frac{1}{x})}^{2 x}; x > 0$ attains the maximum value at $x = \frac{1}{e}$ then :

e^{π} < π^{e}

e^{2 π} < (2 π)^{e}

(2 e)^{π} > π^{(2 e)}

e^{π} > π^{e}

Question 5.

Let $f (x) = \frac{1}{7 - \sin 5 x}$ be a function defined on $R$ . Then the range of the function $f (x)$ is equal to :

[\frac{1}{8}, \frac{1}{5}]

[\frac{1}{7}, \frac{1}{6}]

[\frac{1}{7}, \frac{1}{5}]

[\frac{1}{8}, \frac{1}{6}]

Question 6.

The function $f (x) = \frac{x^{2} + 2 x - 15}{x^{2} - 4 x + 9}, x \in R$ is

both one-one and onto.

onto but not one-one.

neither one-one nor onto.

one-one but not onto.

Question 7.

Let $f, g : R \to R$ be defined as :

$f (x) = | x - 1 | and g (x) = {\begin{cases} e^{x}, & x \geq 0 \\ x + 1, & x \leq 0 . \end{cases}$

Then the function $f (g (x))$ is

neither one-one nor onto.

one-one but not onto.

both one-one and onto.

onto but not one-one.

Question 8.

Let $A = {1, 3, 7, 9, 11}$ and $B = {2, 4, 5, 7, 8, 10, 12}$ . Then the total number of one-one maps $f : A \to B$ , such that $f (1) + f (3) = 14$ , is :

120

180

240

480

Question 9.

If the domain of the function

f (x) = \frac{\sqrt{x^{2} - 25}}{(4 - x^{2})} + \log_{10} (x^{2} + 2 x - 15)

(- \infty, α) \cup [β, \infty)

, then

α^{2} + β^{3}

is equal to :

140

175

125

150

Question 10.

Let

f : R \to R

and

g : R \to R

be defined as

f (x) = {\begin{cases} \log_{e} x, & x > 0 \\ e^{- x}, & x \leq 0 \end{cases}

and

g (x) = {\begin{cases} x, & x ⩾ 0 \\ e^{x}, & x < 0 \end{cases}

. Then, gof :

R \to R

is :

one-one but not onto

neither one-one nor onto

onto but not one-one

both one-one and onto

Question 1.

If $f (x) = \frac{4 x + 3}{6 x - 4}, x \neq \frac{2}{3}$ and $(f \circ f) (x) = g (x)$ , where $g : R - {\frac{2}{3}} \to R - {\frac{2}{3}}$ , then $(g o g o g) (4)$ is equal to

- 4

\frac{19}{20}

- \frac{19}{20}

Question 2.

If the domain of the function $f (x) = \log_{e} (\frac{2 x + 3}{4 x^{2} + x - 3}) + \cos^{- 1} (\frac{2 x - 1}{x + 2})$ is $(α, β]$ , then the value of $5 β - 4 α$ is equal to

Question 3.

If the domain of the function $f (x) = \cos^{- 1} (\frac{2 - | x |}{4}) + {\log_{e} (3 - x)}^{- 1}$ is $[- α, β) - {γ}$ , then $α + β + γ$ is equal to :

Question 4.

If $f (x) = {\begin{array}{cc} 2 + 2 x, & - 1 \leq x < 0 \\ 1 - \frac{x}{3}, & 0 \leq x \leq 3 \end{array}; g (x) = {\begin{array}{cc} - x, & - 3 \leq x \leq 0 \\ x, & 0 < x \leq 1 \end{array}$ , then range of $(f o g) (x)$ is

[0, 1)

[0, 3)

(0, 1]

[0, 1]

Question 5.

Let $f : R - {\frac{- 1}{2}} \to R$ and $g : R - {\frac{- 5}{2}} \to R$ be defined as $f (x) = \frac{2 x + 3}{2 x + 1}$ and $g (x) = \frac{| x | + 1}{2 x + 5}$ . Then, the domain of the function fog is :

R - {- \frac{7}{4}}

R

R - {- \frac{5}{2}, - \frac{7}{4}}

R - {- \frac{5}{2}}

Question 6.

The function

f : N - {1} \to N

; defined by

f (n) =

the highest prime factor of

n

, is :

one-one only

neither one-one nor onto

onto only

both one-one and onto

Question 7.

The range of $f (x) = 4 \sin^{- 1} (\frac{x^{2}}{x^{2} + 1})$ is

[0, 2 π]

[0, 2 π)

[0, π)

[0, π]

Question 8.

For $x \in R$ , two real valued functions $f (x)$ and $g (x)$ are such that, $g (x) = \sqrt{x} + 1$ and $f \circ g (x) = x + 3 - \sqrt{x}$ . Then $f (0)$ is equal to

-

Question 9.

Let $D$ be the domain of the function $f (x) = \sin^{- 1} (\log_{3 x} (\frac{6 + 2 \log_{3} x}{- 5 x}))$ . If the range of the function $g : D \to R$ defined by $g (x) = x - [x], ([x]$ is the greatest integer function), is $(α, β)$ , then $α^{2} + \frac{5}{β}$ is equal to

136

nearly 135

Question 10.

The domain of the function $f (x) = \frac{1}{\sqrt{[x]^{2} - 3 [x] - 10}}$ is : ( where $[x]$ denotes the greatest integer less than or equal to $x$ )

(- \infty, - 2) \cup [6, \infty)

(- \infty, - 3] \cup [6, \infty)

(- \infty, - 2) \cup (5, \infty)

(- \infty, - 3] \cup (5, \infty)

JEE Main Functions Practice Questions With Solutions

JEE Main Functions Practice Questions with Solutions

JEE Main Mathematics Functions Practice Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

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