Relations and Functions Test

Result

Relations and Functions Test - 64

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Weekly Quiz Competition

Question 1
1 / -0

Let $$F(x)=f(x)+f (\cfrac1 x)$$, where $$f(x)=\int \cfrac {lnt}{i+t}dt$$ then $$F(e)=?$$

A
2

B
1/2

C
0

D
1

Solution
Question 2
1 / -0

Let $$R:N \to N$$ be defined by $$R = \{ (a,b):a,b \in N$$ and $$a = {b^2}\}$$ then, which of the following is true?

A
$$(a,a) \in R,\forall a \in N$$

B
$$(a,b) \in R, \Rightarrow (b,a) \in R$$

C
$$(a,b) \in R,(b,c) \in R \Rightarrow (a,c) \in R$$

D
None of the above

Solution
Question 3
1 / -0

If $$A=\left\{ x:{ x }^{ 2 }-3x+2=0 \right\} $$, and R is a universal relation on A, then R is

A
$${(1, 1), (2, 2)}$$

B
$${(1, 1)}$$

C
$$\{ \phi \} $$

D
None of these.

Solution
Question 4
1 / -0

If $$f(x)={ x }^{ n },$$ then the value of
$$f(1)-\dfrac { f'(1) }{ 1! } +\dfrac { f''(1) }{ 2! } -\dfrac { f'''(1) }{ 3! } +\dfrac { f''''(1) }{ 4! } \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad -...+\dfrac { (-{ 1) }^{ n }{ f }^{ n }(1) }{ n! } is$$

A
1

B
$${ 2 }^{ n }$$

C
$${ 2 }^{ n-1 }$$

D
0

Solution
Question 5
1 / -0

If the range of function $$f\left( x \right) =\dfrac { x-1 }{ p-{ x }^{ 2 }+1 } $$ does not contain any values belonging to the interval $$\left[ -1,\dfrac { -1 }{ 3 } \right] $$ then the true set of values of p, is:

A
$$(-\infty ,-1)$$

B
$$(\infty ,\dfrac { -1 }{ 4 } )$$

C
$$(0,\infty )$$

D
$$(\infty ,0)$$

Solution
Question 6
1 / -0

If $$f:R\rightarrow R,f(x)=2x+|x|$$, then $$f(x)+f(-x)$$ is

A
$$2|x|$$

B
$$-2|x|$$

C
$$2x$$

D
$$-2x$$

Solution
Question 7
1 / -0

Let 3f(x)-2f(1/x) = x, then f'(2)=

A
2/7

B
1/2

C
2

D
7/2
Question 8
1 / -0

If $$f(x)=\dfrac{4^x}{4^x+2}$$, then $$f(x)+f(1-x)$$ is equal to -

A
0

B
-1

C
1

D
4

Solution
Question 9
1 / -0

If $$6,8$$ and $$12$$ are $$l ^ { th }, m ^ { th }$$ and $$n ^ { th }$$ terms of an A.P and $$f(x)=nx^{ { 2 } }+2lx-2m,$$ then the equation $$f ( x ) = 0$$ has

A
a root between $$0$$ and $$1$$

B
both roots imaginary

C
both roots negative.

D
both roots greater than $$1.$$

Solution
Question 10
1 / -0

If $$f(x-1)={ x }^{ 2 }$$, then $$f(x+1)=$$

A
$${ x }^{ 2 }+2x+1$$

B
$${ x }^{ 2 }+4x+1$$

C
$${ x }^{ 2 }+4x+4$$

D
$${ x }^{ 2 }+2x+4$$

Solution