JEE Main Functions Practice Questions With Solutions

Practising JEE Main mock tests is crucial for effective exam preparation. These tests help students understand the exam pattern, improve time management, and identify strengths and weaknesses. Regular practice boosts confidence, enhances problem-solving speed, and ensures better performance in the actual 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)

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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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