Sequences and Series Test 49

Result

Sequences and Series Test 49

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Weekly Quiz Competition

Question 1
1 / -0

Let P and Q be points $$(4, 4)$$ and $$(9, 6)$$ of parabola $${y^2} = 4a\left( {x - b} \right)$$ If R be a point on the arc of the parabola between P and Q, such that the area of $$\Delta PRQ$$ is largest, then R is

A
$$\left( {\frac{1}{4},4} \right)$$

B
$$\left( {\frac{1}{4},1} \right)$$

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

D
$$\left( {2,2\sqrt 2 } \right)$$
Question 2
1 / -0

If $${ p }_{ 1 },{ p }_{ 2 },{ p }_{ 3 }$$ are the altitudes of a triangle from its vertices $$A,B,C$$ and $$\triangle $$, the area of the triangle $$ABC$$, then $$\frac { 1 }{ { p }_{ 1 } } +\frac { 1 }{ { p }_{ 2 } } +\frac { 1 }{ { p }_{ 3 } } $$ is equal to-

A
$$\frac { s }{ \triangle } $$

B
$$\frac { s-c }{ \triangle } $$

C
$$\frac { s-b }{ \triangle } $$

D
$$\frac { s-a }{ \triangle } $$
Question 3
1 / -0

The arrangement of the areas of the triangles formed by the following points in ascending order is
i) P(0,0), Q(4,0), R(0,3)
ii) P(0,0), Q(5,0), R(0,2)
iii) P(0,0), Q(0,5), R(6,0)
iv) p(3,0), Q(0,6), R(0,0)

A
i,ii,iii,iv

B
ii,i,iii,iv

C
ii,i,iv,iii

D
iv,iii,ii,i

Solution
Question 4
1 / -0

If the sides of a triangle are $$\dfrac{x}{y}+\dfrac{y}{z} ; \dfrac{y}{z}+\dfrac{z}{x} ; \dfrac{z}{x}+\dfrac{x}{y}$$ then the area of the triangle is

A
$$xyz$$

B
$$1$$

C
$$\sqrt{\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}}$$

D
$$\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}$$

Solution
Question 5
1 / -0

two medians drawn from the acute angles of a right angled triangle interect at the angle $$\pi /6$$ if thelength the hypotenuse of the triangle is 3 units then the area of the triangle is

A
$$\sqrt { 3 } $$

B
3

C
$$\sqrt { 2 }$$

D
9

Solution
Question 6
1 / -0

If $$m_1$$ and $$m_2$$ are the roots of the equation $$x^2 +(\sqrt 3 +2) x + \sqrt 3 - 1 = 0 $$, then the area of the triangle formed by the lines $$y=m_1x,y=-m_2x$$ and $$y=1$$ is:

A
$$\dfrac{1}{2} \Bigg ( \dfrac{-\sqrt 3 + 2}{\sqrt 3 -1} \Bigg )$$

B
$$\dfrac{1}{2} \Bigg ( \dfrac{-\sqrt 3 + 2}{\sqrt 3 +1} \Bigg )$$

C
$$\dfrac{1}{2} \Bigg ( \dfrac{\sqrt 3 + 2}{\sqrt 3 -1} \Bigg )$$

D
$$\dfrac{1}{2} \Bigg ( \dfrac{\sqrt 3 + 2}{\sqrt 3 +1} \Bigg )$$
Question 7
1 / -0

The average expenditure of Sharma for the January to June is Rs. 4200 and he spent Rs. 1200 in January and Rs.1500 in July. The average expenditure for the months of February to July is:

A
4250

B
6520

C
2320

D
9999
Question 8
1 / -0

If $$ (\sqrt{2x}+\sqrt{3y}^{2} -36(\sqrt{3x}-\sqrt{2y})^{2}=0$$ and $$\sqrt{2x}-\sqrt{3y}+4\sqrt{5}=0$$ represents an Issosceles traiangle with base angle $$tan^{-1}6$$ then its area is

A
4

B
8/3

C
$$8\sqrt{6}$$

D
9

Solution
Question 9
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
$$\dfrac { 125 }{ 2 } $$
Question 10
1 / -0

In a conference hall 10 executive are to be seated on 10 chairs placed left to right. Executive $$E_1$$ wants to sit to the right of $$E_2$$ Also, $$E_4$$ wants to sit the left of $$E_1$$ and $$E_5$$ wants to sits to the left of ways $$E_4$$ Number of ways the executives can be seated on the 10 chairs, is

A
$$\dfrac{10!}{4!}$$

B
$$\dfrac{10!}{3}$$

C
$$10!$$

D
$$3 \times \dfrac{10!}{4!}$$