Introduction to Graphs Test

Result

Introduction to Graphs Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

To which point the origin be shifted so that the new coordinates of $$( 7,2 )$$ would be $$( - 1,3 ) =$$

A
$$( - 8,1 )$$

B
$$( 8 , - 1 )$$

C
$$( 6,5 )$$

D
$$( - 7,1 )$$

Solution
Question 2
1 / -0

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

A
$$\dfrac { 32 }{ 3 } $$

B
$$\dfrac { 16 }{ 3 } $$

C
16

D
11

Solution
Question 3
1 / -0

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

A
(a,0)

B
(a,a)

C
(2a,2a)

D
None of these

Solution
Question 4
1 / -0

The vertices of a triangle are $$A({x}_{1},{x}_{1}\tan{\alpha}),B({x}_{2},{x}_{2}\tan{\beta})$$ and $$C({x}_{3},{x}_{3}\tan{\gamma})$$. If the circumcentre of the triangle $$ABC$$ coincides with the origin and $$H(a,b)$$ be its orthocentre then $$\cfrac{a}{b}$$ is equal to

A
$$\dfrac{x_1+x_2+x_3}{x_1\tan\alpha+x_2\tan\beta+x_3\tan\gamma}$$

B
$$\dfrac{x_1+x_2+x_3}{x_1\cot\alpha+x_2\cot\beta+x_3\cot\gamma}$$

C
$$\dfrac{-x_1+x_2+x_3}{-x_1\tan\alpha+x_2\tan\beta+x_3\tan\gamma}$$

D
None of these

Solution
Question 5
1 / -0

To which point the origin be shifted so that the new coordinates of $$( 7,2 )$$ would be $$( - 1,3 ) =$$

A
$$( - 8,1 )$$

B
$$( 8,-1 )$$

C
$$( 6,5 )$$

D
$$( - 7,1 )$$

Solution
Question 6
1 / -0

The abscissae of two points $$A \text { and } B$$ are the roots of the equation $$x ^ { 2 } + 2 a x - b ^ { 2 } = 0$$ ,and their coordinates are the roots of the equation $$x ^ { 2 } + 2 p x - q ^ { 2 } = 0$$ .Then the radius of the circle with $$A B$$ as diameter is

A
$$\sqrt { a ^ { 2 } + p ^ { 2 } }$$

B
$$\sqrt { b ^ { 2 } + q ^ { 2 } }$$

C
$$\sqrt { a ^ { 2 } + b ^ { 2 } }$$

D
$$\sqrt { a ^ { 2 } + b ^ { 2 } + p ^ { 2 } + q ^ { 2 } }$$

Solution
Question 7
1 / -0

For all values of $$a and b$$ the line $$\left(a + 2b\right) x + \left(a b\right)y + \left(a + 5b\right) = 0$$ passes through the point

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

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

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

D
$$\left(1, -2\right)$$
Question 8
1 / -0

If the vertices of a triangle be (a, b-c), (b, c-a) and (c,a-b), then the centro of the triangles lies-

A
On y-axis

B
Onx-axis

C
At origin

D
None of these
Question 9
1 / -0

If the vertices of a triangle are $$(a,1),(b,3)$$ and $$(4,c)$$, then the centroid of the triangle will lie on x-axis, if:

A
$$c = -4$$

B
$$a+b+c = 0$$

C
$$a= -2$$

D
$$b= -4$$

Solution
Question 10
1 / -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 $$\dfrac{a}{b}=$$

A
$$\dfrac { { x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 } }{ { x }_{ 1 }\tan { \alpha } +{ x }_{ 2 }\tan { \beta } +{ x }_{ 3 }\tan { \gamma } }$$

B
$$\dfrac { { x }_{ 1 }\cos { \alpha } +{ x }_{ 2 }\cos { \beta } +{ x }_{ 3 }\cos { \gamma } }{ { x }_{ 1 }\sin { \alpha } +{ x }_{ 2 }\sin { \beta } +{ x }_{ 3 }\sin { \gamma } }$$

C
$$\dfrac { \tan { \alpha } +\tan { \beta } +\tan { \gamma } }{ \tan { \alpha } .\tan { \beta } .\tan { \gamma } }$$

D
$$\dfrac { \cos { \alpha } +\cos { \beta } +\cos { \gamma } }{ \sin { \alpha } +\sin { \beta } +\sin { \gamma } }$$