Straight Lines Test 35

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Straight Lines Test 35

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Weekly Quiz Competition

Question 1
1 / -0

Area of the triangle formed by $${ (x }_{ 1 },{ y }_{ 1 })$$,$${ (x }_{ 2 },{ y }_{ 2 })$$,
$${ (3x }_{ 2 }-{ 2x }_{ 1 },{ 3y }_{ 2 }-{ 2y }_{ 1 })$$ is

A
0 sq.units

B
$${ { x }_{ 1 } }y_{ 1 } $$sq.units

C
3 sq.units

D
6 sq.units
Question 2
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
$$\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}$$
Question 3
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 4
1 / -0

The area of a triangle whose sides are $$ a , b $$ and $$ c $$ is

A
$$ \sqrt { ( s - a ) ( s - b ) ( s - c ) } $$ sq. units

B
$$ \sqrt { s ( s + a ) ( s + b ) ( s + c ) } $$ sq. units

C
$$ \sqrt { s ( s \times a ) ( s \times b ) ( s \times c ) } $$ sq. units

D
$$ \sqrt { s ( s - a ) ( s - b ) ( s - c ) } $$ sq. units
Question 5
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 6
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 7
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 8
1 / -0

The area inside the parabola $$5x^2 - y = 0 $$ but outside the parabola $$2x^2 - y + 9 = 0$$ is

A
$$12\sqrt{3}$$ sq.units

B
$$6\sqrt{3}$$ sq.units

C
$$8\sqrt{3}$$ sq.units

D
$$4\sqrt{3}$$ sq.units
Question 9
1 / -0

The centroid and two vertices of a triangles are (4,-8), (-9,7), (1,4) then the area of the triangle is

A
333 sq.units

B
166.5 sq.units

C
111 sq.units

D
55.5 sq.units
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
$$\dfrac { 125 }{ 2 } $$

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Re-Attempt Weekly Quiz Competition

Straight Lines Test 35

Result

Straight Lines Test 35

Score

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Rank

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SHARING IS CARING

Question 1

0 sq.units

$${ { x }_{ 1 } }y_{ 1 } $$sq.units

3 sq.units

6 sq.units

Question 2

$$xyz$$

$$1$$

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

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

Question 3

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

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

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

$$\frac { s-a }{ \triangle } $$

Question 4

$$ \sqrt { ( s - a ) ( s - b ) ( s - c ) } $$ sq. units

$$ \sqrt { s ( s + a ) ( s + b ) ( s + c ) } $$ sq. units

$$ \sqrt { s ( s \times a ) ( s \times b ) ( s \times c ) } $$ sq. units

$$ \sqrt { s ( s - a ) ( s - b ) ( s - c ) } $$ sq. units

Question 5

i,ii,iii,iv

ii,i,iii,iv

ii,i,iv,iii

iv,iii,ii,i

Solution

Question 6

$$\sqrt { 3 } $$

3

$$\sqrt { 2 }$$

9

Solution

Question 7

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

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

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

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

Question 8

$$12\sqrt{3}$$ sq.units

$$6\sqrt{3}$$ sq.units

$$8\sqrt{3}$$ sq.units

$$4\sqrt{3}$$ sq.units

Question 9

333 sq.units

166.5 sq.units

111 sq.units

55.5 sq.units

Question 10

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

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

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

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

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