Introduction to Graphs Test

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Introduction to Graphs Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

$${ \left( x-2 \right) }^{ 2 }+{ \left( y+3 \right) }^{ 2 }=16$$ touching the ellipse $$\dfrac { { \left( x-2 \right) }^{ 2 } }{ { p }^{ 2 } } +\dfrac { { \left( y+3 \right) }^{ 2 } }{ { q }^{ 2 } } =1$$ from inside. If $$\left( 2,-6 \right)$$ is one focus of the ellipse then $$\left( p,q \right)=$$

A
$$\left( 4,5 \right)$$

B
$$\left( 5,4 \right)$$

C
$$\left( 5,3 \right)$$

D
$$\left( 3,5 \right)$$
Question 2
1 / -0

If tangent at (1, 2) to the circle $$c_1$$ : $$x^2$$ + $$y^2$$ = 5 intersects the circle $$c_2$$ : $$x^2$$ + $$y^2$$ = 9 at A & B and tangents at A & B to the second circle meet at point C, then the co-ordinates of C is

A
(4, 5)

B
$$(\frac{9}{15}$$, $$\frac{18}{5})$$

C
(4, -5)

D
$$(\frac{9}{5}$$, $$\frac{18}{5})$$

Solution
Question 3
1 / -0

The vertices of a triangle are $$\left( pq,\cfrac { 1 }{ pq } \right) ,\left( qr,\cfrac { 1 }{ qr } \right) ,\left( rp,\cfrac { 1 }{ rp } \right) $$ where $$p,q,r$$ are roots of the equation $${ y }^{ 3 }-3{ y }^{ 2 }+6y+1=0$$. The coordinates of its centroid are

A
$$\left( 1,2 \right) $$

B
$$\left( 2,-1 \right) $$

C
$$\left( 1,-1 \right) $$

D
$$\left( 2,3 \right) $$
Question 4
1 / -0

Consider three lines y axis, y = $$2$$ and lx + my = 1 where (l, m) lies on $$y^2 = 4x$$. Locus of circum centre of triangle formed by given three lines is a parabola whose vertex is

A
$$(-2, \frac{3}{2})$$

B
$$(2, \frac{-3}{2})$$

C
$$(-2, \frac{-3}{2})$$

D
$$(2, \frac{-5}{2})$$

Solution
Question 5
1 / -0

Directions For Questions

Let $$A(0,6,8)$$ and $$B(15,20,0)$$ are two given points and $$P(\lambda,0,0)$$ is a point on x-axis such that $$PA=PB$$ is minimum

...view full instructions

If image of origin along plane mirror passing through $$P,A,B$$ is $$\left( \alpha ,\beta ,\gamma \right) $$ then

A
$$9\left( \alpha +\beta \right) $$

B
$$9\left( \beta +\gamma \right) =20$$

C
$$9\left( \gamma +\alpha \right) =20$$

D
$$9\left( \alpha +\beta +\gamma \right) =60$$
Question 6
1 / -0

One of the end-points of a circle having centre at origin is $$A(3,-2)$$, then the other end-point of the diameter has the coordinates

A
$$(-3,2)$$

B
$$\left( \cfrac { 3 }{ 2 } ,1 \right) $$

C
$$\left( \cfrac { 7 }{ 2 } ,-1 \right) $$

D
None of these
Question 7
1 / -0

If $$\left( -2,-1 \right) ,\left( 1,0 \right) ,\left( x,3 \right) ,\left( l,y \right) $$ form a parallelogram the $$\left( x,y \right) =$$\left[ \right] $$

A
$$\left( 4,2 \right) $$

B
$$\left( 2,4 \right) $$

C
$$\left( -2,-4 \right) $$

D
$$\left(- 4,-2 \right) $$

Solution
Question 8
1 / -0

The intercept cut off by a line from y-axis is twice that of the intercept cut off from the x-axis. If line passes through (1,2), then the equation of the line is

A
2x+y=4

B
2x+2y-6=0

C
2x-y=4

D
2x+2y+2=0

Solution
Question 9
1 / -0

If the line segment joining the point $$P(x_1, y_1)$$ and $$Q (x_2, y_2)$$ subtends an angle $$\alpha$$ at the origin $$O$$. Then which of the following is true,

A
$$\text{OP}\cdot \text{OQ}\cdot \sec\alpha = x_1 x_2 + y_1y_2 $$

B
$$\text{OP}\cdot \text{OQ}\cdot \tan\alpha = x_1 x_2 + y_1y_2 $$

C
$$\text{OP}\cdot \text{OQ}\cdot \cos \alpha = x_1 x_2 + y_1y_2 $$

D
$$\text{OP}\cdot \text{OQ}\cdot \sin\alpha = x_1 x_2 + y_1y_2 $$

Solution
Question 10
1 / -0

If $$\left( { x }_{ 1 },{ y }_{ 1 } \right) ,\left( { x }_{ 2 },{ y }_{ 2 } \right) ,\left( { x }_{ 3 },{ y }_{ 3 } \right) $$ are the vertices of an equilateral triangle such that $$\\ \left( { x }_{ 1 }-2 \right) ^{ 2 }+\left( { y }_{ 1 }-3 \right) ^{ 2 }=\left( { x }_{ 2 }-2 \right) ^{ 2 }+\left( { y }_{ 2 }-3 \right) ^{ 2 }=\left( { x }_{ 3 }-2 \right) ^{ 2 }+\left( y_{ 3 }-3 \right) ^{ 2 }$$ then $${ x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 }+2\left( { y }_{ 1 }+{ y }_{ 2 }+{ y }_{ 3 } \right) =\\ $$

A
18

B
24

C
6

D
8

Solution