Relations and Functions Test

Result

Relations and Functions Test - 54

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Weekly Quiz Competition

Question 1
1 / -0

$$p \Rightarrow \,q$$ can also be written as

A
$$p \Rightarrow \, \sim q$$

B
$$ \sim p \vee q$$

C
$$ \sim q \Rightarrow \, \sim p$$

D
None of these

Solution
Question 2
1 / -0

If $$R$$ is relation is "greater then or equal" from $$A=\left\{1,2,3,4\right\}$$ to $$B=\left\{4,5,6\right\}$$, then $$R^{-1}=$$

A
$$\left\{(4,4)\right\}$$

B
$$\phi$$

C
$$A\ x\ B$$

D
$$R$$

Solution
Question 3
1 / -0

The domain of the function $$f(x)=log_5\left(log_4{log_{4/\pi }(tan^{-1})^{-1}}\right)$$ is

A
R

B
[0,1]

C
(0,1]

D
(0,1)

Solution
Question 4
1 / -0

The number of ordered pairs (x, y) of natural numbers satisfy the equation $$x^2+y^2+2xy-2018x-2018y-2019^o=0$$ is?

A
$$0$$

B
$$1009$$

C
$$2018$$

D
$$2019$$

Solution
Question 5
1 / -0

Let $$p(x)=ax^{2}+bx \ ,q(x)=\ell x^{2}+mx+n$$ and consider a function $$f(x)=p(x)-q(x)$$. If $$f(x)=0$$ only for $$x=1$$ and $$f(2)=1$$ then, the value of $$f(3)$$ is:

A
$$4$$

B
$$\frac{4}{9}$$

C
$$9$$

D
Cannot be determined

Solution
Question 6
1 / -0

The number of dissimilar terms in the expansion of $$(a+b+c)^{n}$$ is

A
$$n+1$$

B
$$n$$

C
$$n+2$$

D
$$1+2+3+...+(n+1)$$

Solution
Question 7
1 / -0

If the relation $$R:A \to B$$ where $$A = \left\{ {1,2,3,4} \right\},B = \left\{ {1,3,5} \right\}$$ is defined by $$R = \left\{ {\left( {x,y} \right):x < y,x \in A,y \in B} \right\}$$ then $$Ro{R^{ - 1}} = $$

A
$$\left\{ {\left( {1,3} \right),\left( {1,5} \right),\left( {2,3} \right),\left( {2,5} \right),\left( {3,5} \right),\left( {4,5} \right)} \right\}$$

B
$$\left\{ {\left( {3,1} \right),\left( {5,1} \right),\left( {3,2} \right),\left( {5,2} \right),\left( {5,3} \right),\left( {5,4} \right)} \right\}$$

C
$$\left\{ {\left( {3,3} \right),\left( {3,5} \right),\left( {5,3} \right),\left( {5,5} \right)} \right\}$$

D
$$\left\{ {\left( {3,3} \right).\left( {3,4} \right),\left( {4,5} \right)} \right\}$$

Solution
Question 8
1 / -0

Let $$f\left( x \right) =\dfrac { C\quad tanx-{ c }^{ x }+ln(sicx\_ tanx)-x }{ Tan\quad x-x }$$
be a continuous function at x=0.
The value of f(0) equals ________.

A
1/2

B
2/3

C
3/2

D
2

Solution
Question 9
1 / -0

Let $$f ( x ) = a x ^ { 2 } + b x + c \text { with } f ( - 1 ) < 1 , f ( 1 ) > - 1 , f ( 3 ) < - 4$$ and $$a \neq 0$$ then

A
$$a > 0$$

B
$$a < 1$$

C
$$a < - \frac { 1 } { 8 }$$

D
none of these

Solution
Question 10
1 / -0

If $$ \int f(x) \, cos x \, dx = \dfrac{1}{2} f^2(x) + c$$ then f(x) is

A
x

B
sin x

C
cos x

D
1

Solution