Functions Test 54

Result

Functions Test 54

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The domain of definition of the function $$y=\dfrac { 325 }{ 197 } \left[ \dfrac { \sqrt { { x }^{ 2 }-1 } }{ \sqrt { { x-1 } } } \right] $$

A
$$\left(1,\infty\right)$$

B
$$\left[1,\infty\right)$$

C
Set of all real numbers

D
$$\left(-\infty,-1\right)\cup \left( 1,\infty \right) $$

Solution

$$y=\dfrac{325}{197}\left[\dfrac{\sqrt{x^{2}-1}}{\sqrt{x-1}}\right] \\$$
$$\text { For y to be defined, } \\$$
$$\sqrt{x-1} \neq 0 \\$$
$$x \neq 1 \\$$
$$x \in R-\{1\}-(i) \\$$
$$x-1>0 \\$$
$$x>1 \\$$
$$x \in(1, \infty)-(i i) \\$$
$$x^{2}-1>0 \\$$
$$x^{2}>1 \\$$
$$x \in(-\infty,-1) \cup(1, \infty)-(iii) \\$$
All above the conditions must satisfy
$$x \in(1, \infty)$$
Question 2
1 / -0

The domain of the function $$f\left( x \right) =3\sqrt { \dfrac { x }{ 1-\left| x \right| } } $$

A
$$\left( -\infty ,1 \right) \bigcup \left( -1,1 \right) \bigcup \left( 1,\infty \right) $$

B
$$\left( -\infty ,1 \right) $$

C
$$\left( 0,\infty\right) $$

D
$$none\ of\ these$$
Question 3
1 / -0

Let n(A) = 4 and n(B) = 6. Then the number of one - one functions from A to B is

A
120

B
360

C
24

D
none of these

Solution

$$n(A)=4$$
$$n(B)=6$$

$$\text { Number of one-one functions }(A \rightarrow B)$$

$$=6 c_{4} \times 4 !$$

$$=\frac{6 !}{2 ! 4 !} \times 4 !$$

$$=6 \times 5 \times 4 \times 3$$

$$=360$$
Question 4
1 / -0

The domain of the definition of the function $$y\left(x\right)$$ given by the equation $$2^ {x}+2^ {y}$$ is

A
$$0 < x \le 1$$

B
$$0\le x\le 1$$

C
$$-\infty < x \le 0$$

D
$$-\infty < x < 1$$
Question 5
1 / -0

The domain of$$f(x)={ log }_{ 2 }{ log }_{ 3 }{ log }_{ \frac { 4 }{ \pi } }^{ \left( tan^{ -1 }x \right) ^{ -1 } }$$ :-

A
$$(-1,1)$$

B
$$(0,1)$$

C
$$\left( \dfrac { 4 }{ \pi } \infty \right) $$

D
$$R$$

Solution
Question 6
1 / -0

The domain of the function: $$f\left( x \right) =x.\dfrac { 1+2{ \left( x+4 \right) }^{ -0.5 } }{ 2-{ \left( x+4 \right) }^{ 0.5 } } +{ \left( x+4 \right) }^{ 0.5 }+4{ \left( x+4 \right) }^{ -0.5 }$$

A
$$\left(-4,4\right)$$

B
$$R$$

C
$$R^ {+}$$

D
$$\left( -4,0 \right) \bigcup \left( 0,\infty \right) $$

Solution
Question 7
1 / -0

Domain of $$y=\sqrt{log_{2}(\frac{x}{x+3})}$$ is

A
$$(-\infty ,-3)$$

B
$$(-\infty ,-3)\cup (0,\infty )$$

C
$$(0,\infty )$$

D
$$(-\infty ,\infty)$$

Solution
Question 8
1 / -0

The domain & Range of the function $$f\left( x \right) =\dfrac { x }{ \left\{ x \right\} } $$

A
$$D_{f}=R-\left\{0\right\},D_{f}=R-\left\{-1,1\right\}$$

B
$$D_{f}=\left\{0,\infty\right\},D_{f}=R-\left\{0,1\right\}$$

C
$$D_{f}=\left\{-\infty,0\right\},D_{f}=R-\left\{1,2\right\}$$

D
$$None\ of\ these$$

Solution
Question 9
1 / -0

The domain of function $${ log }_{ 10 }{ log }_{ 10 }{ log }_{ 10 }{ log }_{ 10 }{ log }^{ x }_{ 10 }$$ is :-

A
$$\left( 10^{ 4 },\quad \infty \right) $$

B
$$\left( 10^{ 10 },\quad \infty \right) $$

C
$$(10^{ 10^{ 10 } },\infty )$$

D
$$(10^{ 100 },\infty )$$

Solution
Question 10
1 / -0

The function f:$$R\rightarrow R$$ defined by f(x)=x-[x],$$\forall x\epsilon R\quad is$$

A
one-one

B
onto

C
Both one-one and onto

D
neither one-one nor onto

Solution