Introduction to Graphs Test

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Introduction to Graphs Test - 19

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Weekly Quiz Competition

Question 1
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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?

A
The proposed law is expected to accelerate the decline in population.

B
The proposed law is expected to stop and reverse the decline in population.

C
The proposed law is expected to have no effect on the decline in population.

D
The proposed law is expected to slow, but not stop or reverse, the decline in population.

Solution

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 $$D$$ is correct.
Question 2
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The possible range of values in which area of quadrilateral which straight line cuts off from the given triangle lie in

A
$$(4, 5)$$

B
$$\left (\dfrac {5}{2}, \dfrac {7}{2}\right )$$

C
$$\left (4, \dfrac {9}{2}\right )$$

D
$$(3, 4)$$
Question 3
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Directions For Questions

The base of an isosceles triangle is equal to $$4$$, the base angle is equal to $${45}^{o}$$. A straight line cuts the extension of the base at a point $$M$$ at the angle $$\theta$$ and bisects the lateral side of the triangle which is nearest to $$M$$.

...view full instructions

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

A
$$(4,5)$$

B
$$\left( \cfrac { 5 }{ 2 } ,\cfrac { 7 }{ 2 } \right) $$

C
$$\left( 4,\cfrac { 9 }{ 2 } \right) $$

D
$$(3,4)$$
Question 4
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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?

A
January

B
April

C
August

D
December

Solution
Question 5
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Let S be the touching $$2x + y = 4$$ at $$(1,2)$$ and bisecting the circumference of $$x^2+y^2 = 3$$ then

A
centre of S is $$(1, -1)$$

B
centre of S is $$(-1, 1)$$

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

D
equation of common chord of both the circles is y = -x
Question 6
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The maximum number of points with rational co-ordinates on a circle whose centre is $$(\sqrt {3}, 0)$$ is

A
One

B
Two

C
Four

D
Infinite
Question 7
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If PQ is a chord of Parabola $$x^{2} = 4y$$ which subtends right angle at vertex. Then locus of centroid of triangle PSQ (S is locus) is a parabola whose

A
vertex is (0,3)

B
length of LR is 4/3

C
axis is x = 0

D
tangent at the vertex is x = 3
Question 8
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Origin is shifted to $$\displaystyle \left( \frac{9}{2}, p \right)$$. If the new equation of the locus $$y^2 + 2x - 8y + 7 = 0$$ does not contain a term in Y, then p =

A
2

B
4

C
8

D
12

Solution
Question 9
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If $$A = (at^{2}, 2at); B \left (\dfrac {a}{r^{2}}, \dfrac {-2a}{t}\right )$$ and $$S(a, 0)$$ then $$1/SA + 1/ SB =$$

A
$$a$$

B
$$1/a$$

C
$$3/a$$

D
$$2a/3$$

Solution
Question 10
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From a point on the line 4x - 3y = 6 tangents are drawn to the circle $$x^{2} + y^{2} - 6x - 4y + 4 = 0$$ which make an angle of $$tan^{-1} \dfrac{24}{7}$$ between them, then the coordinates of all such points are

A
(-2, 0), (6, -6)

B
(2, 0), (6, 6)

C
(0, -2) and (6, 6)

D
None of these