Permutations and Combinations Test 53

Result

Permutations and Combinations Test 53

Score
-
out of -
Rank
-
out of -

TIME Taken - -

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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 $$ (\sqrt{2x}+\sqrt{3y}^{2} -36(\sqrt{3x}-\sqrt{2y})^{2}=0$$ 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 4
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 5
1 / -0

A triangle has two of its vertices at (0, 1) and (2, 2) in the cartesioan plane. Its third vertex lies on the x-axis. If the area of the triangle is 2 square units then the sum of the possible abscissae of the third vertex, is -

A
-4

B
0

C
5

D
6

Solution
Question 6
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 7
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 8
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 9
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 10
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