Permutations and Combinations Test 54

Result

Permutations and Combinations Test 54

Score
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Weekly Quiz Competition

Question 1
1 / -0

If the sides of a triangle are $$\dfrac{x}{y}+\dfrac{y}{z} ; \dfrac{y}{z}+\dfrac{z}{x} ; \dfrac{z}{x}+\dfrac{x}{y}$$ then the area of the triangle is

A
$$xyz$$

B
$$1$$

C
$$\sqrt{\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}}$$

D
$$\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}$$

Solution
Question 2
1 / -0

two medians drawn from the acute angles of a right angled triangle interect at the angle $$\pi /6$$ if thelength the hypotenuse of the triangle is 3 units then the area of the triangle is

A
$$\sqrt { 3 } $$

B
3

C
$$\sqrt { 2 }$$

D
9

Solution
Question 3
1 / -0

If $$m_1$$ and $$m_2$$ are the roots of the equation $$x^2 +(\sqrt 3 +2) x + \sqrt 3 - 1 = 0 $$, then the area of the triangle formed by the lines $$y=m_1x,y=-m_2x$$ and $$y=1$$ is:

A
$$\dfrac{1}{2} \Bigg ( \dfrac{-\sqrt 3 + 2}{\sqrt 3 -1} \Bigg )$$

B
$$\dfrac{1}{2} \Bigg ( \dfrac{-\sqrt 3 + 2}{\sqrt 3 +1} \Bigg )$$

C
$$\dfrac{1}{2} \Bigg ( \dfrac{\sqrt 3 + 2}{\sqrt 3 -1} \Bigg )$$

D
$$\dfrac{1}{2} \Bigg ( \dfrac{\sqrt 3 + 2}{\sqrt 3 +1} \Bigg )$$
Question 4
1 / -0

The area inside the parabola $$5x^2 - y = 0 $$ but outside the parabola $$2x^2 - y + 9 = 0$$ is

A
$$12\sqrt{3}$$ sq.units

B
$$6\sqrt{3}$$ sq.units

C
$$8\sqrt{3}$$ sq.units

D
$$4\sqrt{3}$$ sq.units
Question 5
1 / -0

The centroid and two vertices of a triangles are (4,-8), (-9,7), (1,4) then the area of the triangle is

A
333 sq.units

B
166.5 sq.units

C
111 sq.units

D
55.5 sq.units
Question 6
1 / -0

In a conference hall 10 executive are to be seated on 10 chairs placed left to right. Executive $$E_1$$ wants to sit to the right of $$E_2$$ Also, $$E_4$$ wants to sit the left of $$E_1$$ and $$E_5$$ wants to sits to the left of ways $$E_4$$ Number of ways the executives can be seated on the 10 chairs, is

A
$$\dfrac{10!}{4!}$$

B
$$\dfrac{10!}{3}$$

C
$$10!$$

D
$$3 \times \dfrac{10!}{4!}$$
Question 7
1 / -0

Number of positive integers $$n ,$$ less than $$17 ,$$ for which $$n ! + ( n + 1 ) ! + ( n + 2 ) !$$ is an integral multiple of $$49$$ is

A
$$2$$

B
$$5$$

C
$$7$$

D
$$9$$

Solution
Question 8
1 / -0

What is the hundreds digits of ( 20 !-15!) ?

A
0

B
1

C
2

D
4

E
5

Solution
Question 9
1 / -0

Area of the triangle formed by co-ordinate axes and the line x + y = 5 is

A
$$\dfrac { 5 }{ 2 } $$

B
$4\dfrac { 25 }{ 2 } $$

C
$$\dfrac { 75 }{ 2 } $$

D
$$\dfrac { 125 }{ 2 } $$
Question 10
1 / -0

Let $$A(h,k),B(1,1)$$ and $$C(2,1)$$ be the vertices of a right- angled triangle with $$AC$$ as its hypotenuse. If the area of the triangle is 1, then the set of values which $$k$$ can take is given by

A
{1, 3}

B
{0, 2}

C
{-1, 3}

D
{-3, 2}

Solution