Differentiation Test 49

Result

Differentiation Test 49

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Weekly Quiz Competition

Question 1
1 / -0

The area of the triangle formed by the straight line $$x+y=3$$ and the bisectors of the pair of straight lines $${ x }^{ 2 }-{ y }^{ 2 }+2y=1$$ is

A
1

B
2

C
3

D
6

Solution
Question 2
1 / -0

If the area of triangle formed by the points $$(2a, b) (a + b, 2b + a)$$ and $$(2b, 2a)$$ be $$\lambda$$, then the area of the triangle whose vertices are $$(a + b, a - b), (3b - a, b + 3a)$$ and $$(3a - b, 3b - a)$$ will be

A
$$\frac{3}{2}\lambda$$

B
$$3\lambda$$

C
$$4\lambda$$

D
none of these

Solution
Question 3
1 / -0

If the area of triangle formed by the points (2a , b) (a + b , 2b + a) and (2b , 2a) be $$\lambda$$ , then the area of the triangle whose vertices are (a + b , a b) , (3b a , b + 3a) and (3a b , 3b a) will be

A
$$\dfrac{3}{2}\lambda$$

B
$$3\lambda$$

C
$$4\lambda$$

D
none of these

Solution
Question 4
1 / -0

The area of the triangle formed by the lines $$x=0;y=0$$ and $$x\sin { { 18 }^{ 0 } } +y\cos { { 36 }^{ 0 } } +1=0$$ is

A
1

B
2

C
3

D
4

Solution
Question 5
1 / -0

The value of $$\int _{ 0 }^{ \left[ x \right] }{ \left( x-\left[ x \right] \right) dx\quad is\left( \left[ . \right] denotes\quad greatest\quad integer\quad function \right) } $$

A
$$\left[ x \right] $$

B
$$2\left[ x \right] $$

C
$$\dfrac { \left[ x \right] }{ 2 } $$

D
$$3\left[ x \right] $$

Solution
Question 6
1 / -0

$${\log _5}2,\,\,{\log _6}\,2,\,\,{\log _{12}}\,\,2\,\,$$ are in

A
A.P

B
G.P

C
H.P

D
none of these

Solution
Question 7
1 / -0

If $$f\left( x \right) = {\left| x \right|^{\left| {\sin x} \right|}}$$, then $${f'}\left( { - \dfrac{\pi }{4}} \right)$$ is equals

A
$${\left( {\dfrac{\pi }{4}} \right)^{1/\sqrt 2 }}\left( { - \dfrac{{\sqrt 2 }}{2}{\text{ln}}\dfrac{4}{\pi } - \dfrac{{2\sqrt 2 }}{\pi }} \right)$$

B
$${\left( {\dfrac{\pi }{4}} \right)^{1/\sqrt 2 }}\left( {\dfrac{{\sqrt 2 }}{2}{\text{ln}}\dfrac{4}{\pi } + \dfrac{{2\sqrt 2 }}{\pi }} \right)$$

C
$${\left( {\dfrac{\pi }{4}} \right)^{1/\sqrt 2 }}\left( {\dfrac{{\sqrt 2 }}{2}{\text{ln}}\dfrac{\pi }{4} + \dfrac{{2\sqrt 2 }}{\pi }} \right)$$

D
None of these.
Question 8
1 / -0

In $$\triangle ABC,A(1,2);B(5,5),\angle ACB={ 90 }^{ 0 }$$. If area of $$\triangle ABC$$ is to be 6.5 sq. units, then the possible number of points for C is

A
1

B
2

C
0

D
4
Question 9
1 / -0

A line forms a triangle of area $$54\sqrt { 3 } $$ sq-units with the coordinate axes. Then the equation of the line if the perpendicular drawn from the origin to the line makes an angle of $${ 60 }^{ \circ }$$ with the x-axis is

A
$$x-\sqrt { 3 } y=18$$

B
$$x+\sqrt { 3 } y=18$$

C
$$x+\sqrt { 3 } y=-18$$

D
None of these

Solution
Question 10
1 / -0

Area of the triangle formed by co-ordinate axes and the line x + y = 5 is

A
$$\dfrac { 5 }{ 2 } $$

B
$4\dfrac { 25 }{ 2 } $$

C
$$\dfrac { 75 }{ 2 } $$

D
$$\dfrac { 125 }{ 2 } $$