Straight Lines Test 50

Result

Straight Lines Test 50

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Question 1
1 / -0

if the points A(z),B(-z) and C(z+1) are vertices of an equilateral triangle then ---- test question

A
area of triangle is $$\left( \sqrt { 3 } /4 \right) $$sq. units

B
Re(z)=1/2

C
perimeter of the triangle is 3 units

D
Re(z)=1/4

Solution
Question 2
1 / -0

Area of a triangle whose vertices are $$(a\cos \theta ,b\sin \theta ),(-a\sin \theta ,b\cos \theta)$$ and $$(-a\cos \theta ,-b\sin \theta )$$ is-

A
$$ab\sin \theta \cos \theta $$

B
$$a\cos \theta \sin \theta$$

C
$$\frac 12ab$$

D
ab

Solution
Question 3
1 / -0

Area of the triangle formed by the tangents at the points $$\left( {4,6} \right),\left( {10,8} \right)$$ and $$\left( {2,4} \right)$$ on the parabola $${y^2} - 2x = 8y - 20,$$is (in sq. units)

A
4

B
2

C
1

D
8

Solution
Question 4
1 / -0

The area of the triangle inscribed in the parabola $$y^2$$ = $$4x$$ , the ordinates of whose vertices are 1 , 2 and 4 is :

A
7/2

B
5/2

C
3/2

D
3/4
Question 5
1 / -0

If three lines $$x-3y=p,ax+2y=q$$ and $$ax+y=r$$ form a right angled triangle, then

A
$${ a }^{ 2 }-9a+18=0$$

B
$${ a }^{ 2 }-6a-12=0$$

C
$${ a }^{ 2 }-6a+9=0$$

D
$${ a }^{ 2 }-9a+12=0$$

Solution
Question 6
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 7
1 / -0

Area of a triangle whose vertices are $$ (a \cos \theta, b \sin \theta),(-a \sin \theta, b \cos \theta) $$ and$$ (-a \cos \theta,-b \sin \theta) $$ is $$ - $$

A
a b sin $$ \theta \cos \theta $$

B
$$ a \cos \theta \sin \theta $$

C
$$ \frac{1}{2} a b $$

D
$$ a b $$

Solution
Question 8
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 9
1 / -0

If $$P , Q$$ are two points on the line $$3 x + 4 y + 15 = 0$$ such that $$O P = O Q = 9$$ then the area of $$\Delta O P Q$$ is

A
6$$\sqrt { 2 }$$

B
9$$\sqrt { 2 }$$

C
12$$\sqrt { 2 }$$

D
18$$\sqrt { 2 }$$

Solution
Question 10
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