Let S be the touching $$2x + y = 4$$ at $$(1,2)$$ and bisecting the circumference of $$x^2+y^2 = 3$$ then

equation of common chord of both the circles is y = x

equation of common chord of both the circles is y = -x

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

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

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

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

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

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

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

$$9\left( \alpha +\beta +\gamma \right) =60$$

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

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

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

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,

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

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

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

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

MCQ Questions for Class 8 Maths Introduction To Graphs Quiz 6

The number of points with integral co-ordinates that are interior to the circle

x^{2} + y^{2} = 16

$x^{2} + y^{2} = 16$ is

0%
$43$
0%
$45$
0%
$47$
0%
$49$

The federal government in the United States has the authority to protect species whose populations have reached dangerously low levels. The figure above represents the expected populations of a certain endangered species before and after a proposed law aimed at protecting the animal is passes. Based on the graph, which of the following statements is true?

0%
The proposed law is expected to accelerate the decline in population.
0%
The proposed law is expected to stop and reverse the decline in population.
0%
The proposed law is expected to have no effect on the decline in population.
0%
The proposed law is expected to slow, but not stop or reverse, the decline in population.

Explanation

The federal government in the United States has the authority to protect species whose populations have reached dangerously low levels. Based on the given graph, we can say that the proposed law is expected to slow, but not stop or reverse the decline in population.

Hence, option

D

$D$ is correct.

The possible range of values in which area of quadrilateral which straight line cuts off from the given triangle lie in

0%
$(4, 5)$
0%
$\left (\dfrac {5}{2}, \dfrac {7}{2}\right )$
0%
$\left (4, \dfrac {9}{2}\right )$
0%
$(3, 4)$

The possible range of values in which area of quadrilateral which straight line cuts off from the given triangle lie in:

0%
$(4,5)$
0%
$\left( \cfrac { 5 }{ 2 } ,\cfrac { 7 }{ 2 } \right)$
0%
$\left( 4,\cfrac { 9 }{ 2 } \right)$
0%
$(3,4)$

The chart below represents the average amount of rain falling each month in the town of Tegulpa. During which month of the year does the most rain fall?

0%
January
0%
April
0%
August
0%
December

Let S be the touching

2 x + y = 4

$2x + y = 4$ at

(1, 2)

$(1,2)$ and bisecting the circumference of

x^{2} + y^{2} = 3

$x^2+y^2 = 3$ then

0%
centre of S is $(1, -1)$
0%
centre of S is $(-1, 1)$
0%
equation of common chord of both the circles is y = x
0%
equation of common chord of both the circles is y = -x

The maximum number of points with rational co-ordinates on a circle whose centre is

(\sqrt{3}, 0)

$(\sqrt {3}, 0)$ is

0%
One
0%
Two
0%
Four
0%
Infinite

If PQ is a chord of Parabola

x^{2} = 4 y

$x^{2} = 4y$ which subtends right angle at vertex. Then locus of centroid of triangle PSQ (S is locus) is a parabola whose

0%
vertex is (0,3)
0%
length of LR is 4/3
0%
axis is x = 0
0%
tangent at the vertex is x = 3

Origin is shifted to

(\frac{9}{2}, p)

$\displaystyle \left( \frac{9}{2}, p \right)$ . If the new equation of the locus

y^{2} + 2 x - 8 y + 7 = 0

$y^2 + 2x - 8y + 7 = 0$ does not contain a term in Y, then p =

0%
2
0%
4
0%
8
0%
12

A = (a t^{2}, 2 a t); B (\frac{a}{r^{2}}, \frac{- 2 a}{t})

$A = (at^{2}, 2at); B \left (\dfrac {a}{r^{2}}, \dfrac {-2a}{t}\right )$ and

S (a, 0)

$S(a, 0)$ then

1 / S A + 1 / S B =

$1/SA + 1/ SB =$

0%
$a$
0%
$1/a$
0%
$3/a$
0%
$2a/3$

{(x - 2)}^{2} + {(y + 3)}^{2} = 16

${ \left( x-2 \right) }^{ 2 }+{ \left( y+3 \right) }^{ 2 }=16$ touching the ellipse

\frac{{(x - 2)}^{2}}{p^{2}} + \frac{{(y + 3)}^{2}}{q^{2}} = 1

$\dfrac { { \left( x-2 \right) }^{ 2 } }{ { p }^{ 2 } } +\dfrac { { \left( y+3 \right) }^{ 2 } }{ { q }^{ 2 } } =1$ from inside. If

(2, - 6)

$\left( 2,-6 \right)$ is one focus of the ellipse then

(p, q) =

$\left( p,q \right)=$

0%
$\left( 4,5 \right)$
0%
$\left( 5,4 \right)$
0%
$\left( 5,3 \right)$
0%
$\left( 3,5 \right)$

If tangent at (1, 2) to the circle

c_{1}

$c_1$ :

x^{2}

$x^2$ +

y^{2}

$y^2$ = 5 intersects the circle

c_{2}

$c_2$ :

x^{2}

$x^2$ +

y^{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

0%
(4, 5)
0%
$(\frac{9}{15}$ , $\frac{18}{5})$
0%
(4, -5)
0%
$(\frac{9}{5}$ , $\frac{18}{5})$

From a point on the line 4x - 3y = 6 tangents are drawn to the circle

x^{2} + y^{2} - 6 x - 4 y + 4 = 0

$x^{2} + y^{2} - 6x - 4y + 4 = 0$ which make an angle of

t a n^{- 1} \frac{24}{7}

$tan^{-1} \dfrac{24}{7}$ between them, then the coordinates of all such points are

0%
(-2, 0), (6, -6)
0%
(2, 0), (6, 6)
0%
(0, -2) and (6, 6)
0%
None of these

The vertices of a triangle are

(p q, \frac{1}{p q}), (q r, \frac{1}{q r}), (r p, \frac{1}{r p})

$\left( pq,\cfrac { 1 }{ pq } \right) ,\left( qr,\cfrac { 1 }{ qr } \right) ,\left( rp,\cfrac { 1 }{ rp } \right)$ where

p, q, r

$p,q,r$ are roots of the equation

y^{3} - 3 y^{2} + 6 y + 1 = 0

${ y }^{ 3 }-3{ y }^{ 2 }+6y+1=0$ . The coordinates of its centroid are

0%
$\left( 1,2 \right)$
0%
$\left( 2,-1 \right)$
0%
$\left( 1,-1 \right)$
0%
$\left( 2,3 \right)$

Consider three lines y axis, y =

2

$2$ and lx + my = 1 where (l, m) lies on

y^{2} = 4 x

$y^2 = 4x$ . Locus of circum centre of triangle formed by given three lines is a parabola whose vertex is

0%
$(-2, \frac{3}{2})$
0%
$(2, \frac{-3}{2})$
0%
$(-2, \frac{-3}{2})$
0%
$(2, \frac{-5}{2})$

If image of origin along plane mirror passing through

P, A, B

$P,A,B$ is

(α, β, γ)

$\left( \alpha ,\beta ,\gamma \right)$ then

0%
$9\left( \alpha +\beta \right)$
0%
$9\left( \beta +\gamma \right) =20$
0%
$9\left( \gamma +\alpha \right) =20$
0%
$9\left( \alpha +\beta +\gamma \right) =60$

One of the end-points of a circle having centre at origin is

A (3, - 2)

$A(3,-2)$ , then the other end-point of the diameter has the coordinates

0%
$(-3,2)$
0%
$\left( \cfrac { 3 }{ 2 } ,1 \right)$
0%
$\left( \cfrac { 7 }{ 2 } ,-1 \right)$
0%
None of these

(- 2, - 1), (1, 0), (x, 3), (l, y)

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

(x, y) =

$\left( x,y \right) =$ \left[ \right] $$

0%
$\left( 4,2 \right)$
0%
$\left( 2,4 \right)$
0%
$\left( -2,-4 \right)$
0%
$\left(- 4,-2 \right)$

If the line segment joining the point

P (x_{1}, y_{1})

$P(x_1, y_1)$ and

Q (x_{2}, y_{2})

$Q (x_2, y_2)$ subtends an angle

α

$\alpha$ at the origin

O

$O$ . Then which of the following is true,

0%
$\text{OP}\cdot \text{OQ}\cdot \sec\alpha = x_1 x_2 + y_1y_2$
0%
$\text{OP}\cdot \text{OQ}\cdot \tan\alpha = x_1 x_2 + y_1y_2$
0%
$\text{OP}\cdot \text{OQ}\cdot \cos \alpha = x_1 x_2 + y_1y_2$
0%
$\text{OP}\cdot \text{OQ}\cdot \sin\alpha = x_1 x_2 + y_1y_2$

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

$\left( { x }_{ 1 },{ y }_{ 1 } \right) ,\left( { x }_{ 2 },{ y }_{ 2 } \right) ,\left( { x }_{ 3 },{ y }_{ 3 } \right)$ 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

${ x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 }+2\left( { y }_{ 1 }+{ y }_{ 2 }+{ y }_{ 3 } \right) =\\$

0%
18
0%
24
0%
6
0%
8

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

0%
2x+y=4
0%
2x+2y-6=0
0%
2x-y=4
0%
2x+2y+2=0

The vertices of a triangle are

$A\left({x}_{1},{x}_{1}\tan{\alpha}\right),B\left({x}_{2},{x}_{2}\tan{\beta}\right)$ and

$C\left({x}_{3},{x}_{3}\tan{\gamma}\right)$ . If the circumcentre of triangle

$ABC$ coincides with the origin and

$H(a,b)$ be the orthocentre, then

$\dfrac{a}{b}=$

0%
$\dfrac { { x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 } }{ { x }_{ 1 }\tan { \alpha } +{ x }_{ 2 }\tan { \beta } +{ x }_{ 3 }\tan { \gamma } }$
0%
$\dfrac { { x }_{ 1 }\cos { \alpha } +{ x }_{ 2 }\cos { \beta } +{ x }_{ 3 }\cos { \gamma } }{ { x }_{ 1 }\sin { \alpha } +{ x }_{ 2 }\sin { \beta } +{ x }_{ 3 }\sin { \gamma } }$
0%
$\dfrac { \tan { \alpha } +\tan { \beta } +\tan { \gamma } }{ \tan { \alpha } .\tan { \beta } .\tan { \gamma } }$
0%
$\dfrac { \cos { \alpha } +\cos { \beta } +\cos { \gamma } }{ \sin { \alpha } +\sin { \beta } +\sin { \gamma } }$

To which point the origin be shifted so that the new coordinates of

$( 7,2 )$ would be

$( - 1,3 ) =$

0%
$( - 8,1 )$
0%
$( 8 , - 1 )$
0%
$( 6,5 )$
0%
$( - 7,1 )$

In a diagram, a line is drawn through the points A(0,16) and B(8,0). Point p is shown in the first quadrant on the line through A and B . Points C and D are chosen on the X and Y axis respectively. so that PDOC is a rectangle.
Sum of the coordinates of the point p if PDOC is a square is

0%
$\dfrac { 32 }{ 3 }$
0%
$\dfrac { 16 }{ 3 }$
0%
16
0%
11

If the equal sides AB and AC each of whose length is 2a of a right angle isosceles triangle ABC be produced of P and Q so that BP.

$CQ = A{B^2},$ then the line PQ always passes through the fixed point

0%
(a,0)
0%
(a,a)
0%
(2a,2a)
0%
None of these

In the graph,

$P$ and

$Q$ are two vertices of quadrilateral

$P Q R S.$
Given that coordinates of

$R$ and

$S$ are

$( 4,2 )$ and

$( 1 , - 1 )$ respectively. the quadrilateral

$P Q R S$ is a

0%
rectangle
0%
square
0%
rhombus
0%
trapezium

$\left( a,\frac { 1 }{ a } \right) ,\left( b,\frac { 1 }{ b } \right) ,\left( c,\frac { 1 }{ c } \right) \quad \& \quad \left( d,\frac { 1 }{ d } \right)$ are four distinct points on a circle of radius 4 units, then abcd is equal to :

0%
4
0%
16
0%
1
0%
2

Suppose

$ABCD$ is a quadrilateral such that the coordinates of

$A, B$ and

$C$ are

$(1, 3), (-2, 6)$ and

$(5, -8)$ respectively. For what choices of coordinates of

$D$ will make

$ABCD$ a trapezium?

0%
$(3, -6)$
0%
$(6, -9)$
0%
$(0, 5)$
0%
$(3, -1)$

Let

$({x}_{0},{y}_{0})$ be solution of the following equations

$\displaystyle {2x}^{ln2}_{{3}^{lnx}}={(3y)}^{ln3}$

${3}^{lnx}={3}^{lny}$
then

${x}_{0}$ is

0%
$\displaystyle \frac{1}{6}$
0%
$\displaystyle \frac{1}{3}$
0%
$\displaystyle \frac{1}{2}$
0%
$6$

$A=\left ( t^{2},2t \right )B=\left ( \frac{1}{t^{2}},\frac{-2}{t} \right )$ S(1,0) then

$\frac{1}{SA}+\frac{1}{SB}=$

0%
1
0%
2
0%
3
0%
4

CBSE Questions for Class 8 Maths Introduction To Graphs Quiz 6 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Introduction To Graphs Quiz 6 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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