Straight Lines Test 34

Result

Straight Lines Test 34

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Weekly Quiz Competition

Question 1
1 / -0

The inclination of the straight line passing through the point (3 , 6) and the mid-point of the line joining the points (4 , 5) and (2 , 9) is

A
$$\dfrac{\pi}{4}$$

B
$$\dfrac{\pi}{6}$$

C
$$\dfrac{\pi}{3}$$

D
$$\dfrac{3\pi}{4}$$

E
$$\dfrac{5\pi}{6}$$
Question 2
1 / -0

The inclination of the line $$x - y + 3 = 0$$ with the positive direction of $$x - axis$$ is

A
$${45^0}$$

B
$${135^0}$$

C
$$ - {45^0}$$

D
$$ - {135^0}$$

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

Let A(-4, 0) & B(4,0). Then the number of points C=(x,y) on the circle $${x^2} + {y^2} = 16$$ lying in first quadrant $$(x,y \geqslant 0)$$ such that the area of the triangle whose vertices are A,B,C is a integer is

A
14

B
15

C
16

D
None of these

Solution
Question 6
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 7
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 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

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 10
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
$$\left( {2,2\sqrt 2 } \right)$$