Permutations and Combinations Test 23

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Permutations and Combinations Test 23

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Weekly Quiz Competition

Question 1
1 / -0

Image

A
70

B
75

C
65

D
80

Solution

Suppose, the apple is $$x$$ and the pear is $$y$$
Given in the question,

$$2x+y=230 $$ eq—1

And,
$$y-x=5$$ eq—2

So, from —2
$$y= 5+x$$ eq—3

Putting eq—3 in eq—1

$$2x+5+x=230$$

$$3x+5=230$$

$$3x=225$$

$$x=\dfrac{225}{3}$$

$$x=75$$

Now from eq—3

$$y=5+75$$

$$y=80$$

So the value of a pear is $$80$$

Hence Option D is the correct answer.
Question 2
1 / -0

How is 'vegetables are red flowers' written in this code ?

A
Pec silk mit hee

B
silk peehee be

C
il silk mit hee

D
none

Solution

Type Direct coding (Jumbled fashion)
S.no. code sentence
1. il be pee roses are blue
2. silk hee red flowers
3. pee mit hee Flowers are Vegetables
common word in sentences 1 & 3 $$ \displaystyle \rightarrow $$ 'are' and code $$ \displaystyle \rightarrow $$ 'pee'
common word in sentences 2 & 3 $$ \displaystyle \rightarrow $$ flowers and code $$ \displaystyle \rightarrow $$ 'hee'
Therefore
Codes words
pee are
hee flowers
silk red
niit vegetables
il roses/ blue
be blue./ rose
nit silk hee pee
Question 3
1 / -0

In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number .If the first number is -5, how many of the numbers in the sequence are positive?

A
None

B
One

C
Two

D
Three

E
Four

Solution
Question 4
1 / -0

The area of triangle with vertices $$A(5,\,0),\,B(8,\,0)$$ and $$C(9,\,5)$$ is

A
$$7\dfrac{1}{4}$$

B
$$7\dfrac{1}{2}$$

C
$$\dfrac{15}{4}$$

D
None of the above

Solution

Area of triangle $$=\dfrac{1}{2}\begin{bmatrix}x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\end{bmatrix}$$
$$A=\dfrac{1}{2}\begin{bmatrix}5(0-5)+8(5-0)+9(0-0)\end{bmatrix}$$
$$A=\dfrac{1}{2}\begin{bmatrix}-25+40\end{bmatrix}=\dfrac{15}{2}$$ square units.
So, option B is correct.
Question 5
1 / -0

A researcher plans to identify each participant in a $$174$$ certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are $$12$$ participants,and each participant is to receive a different code?

A
$$4$$

B
$$5$$

C
$$6$$

D
$$7$$

E
$$8$$

Solution

The number of single letter code possible are $$n$$ and no of distinct codes $$={^n{C}_{2}}$$
So, $${^n{C}_{2}}+n\ge 12$$
$$\dfrac{n(n-1)}{2}+n\ge 12$$
$$n(n+1)\ge 24$$
$$n$$ min $$=5$$ as least number is asked.
Hence the answer is $$5.$$
Question 6
1 / -0

$$\triangle OPQ$$ is formed by the coordinates $$P(0,\,5),\, Q(8,\,0)$$ and origin $$O$$. The area of $$\triangle OPQ$$ is ____ square units.

A
$$20$$ sq. units

B
$$10$$ sq. units

C
$$30$$ sq. units

D
None of the above

Solution

We know that the area of the triangle whose vertices are $$\displaystyle (x_{1},y_{1}),(x_{2},y_{2}),$$ and $$(x_{3},y_{3})$$ is $$\cfrac{1}{2}\left | x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1}) +x_{3}(y_{1}-y_{2})\right |$$
Area of $$\triangle OPQ $$
$$=\dfrac 12 \left[ 1(0) - 1(0) +1(-40)\right]$$
$$=\dfrac 12 \times 40 = 20$$ sq. units
Question 7
1 / -0

The area of triangle with vertices $$A(0,\,9),\,B(0,\,4)$$ and $$C(-5,\,-9)$$ is

A
$$\dfrac{25}{2}$$ sq. units

B
$$\dfrac{23}{2}$$ sq. units

C
$$\dfrac{19}{2}$$ sq. units

D
None of the above

Solution

Area of triangle $$=\dfrac{1}{2}\begin{bmatrix}x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\end{bmatrix}$$
$$=\dfrac{1}{2}\begin{bmatrix}0(4+9)+0(-9-9)+(-5)(9-4)\end{bmatrix}$$
$$=\dfrac{1}{2}\begin{bmatrix}-5\times5\end{bmatrix}$$
$$=-\dfrac{25}{2}$$
The area cannot be negative.
$$\therefore$$ It must be $$\dfrac{25}{2}$$ sq. units
So, option A is correct.
Question 8
1 / -0

Complete the pattern: $$3, 5, 8, 13,$$ ___

A
21

B
22

C
23

D
24

Solution

The next number is $$21$$.
We get the next number by adding the previous two numbers.
Question 9
1 / -0

Find the next number of the series.
$$7, 10, 8, 11, 9, 12,....$$

A
9

B
10

C
8

D
7

Solution

The next number is $$10$$.
The first $$2$$ numbers difference is $$3$$.
The second $$2$$ numbers difference is $$2$$.
So, this is simple alternating addition of $$ 3$$ and subtraction of $$2$$.
Question 10
1 / -0

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A
15

B
6

C
28

D
56

E
64

Solution

Matches played between 8 teams =$$ 7+6+5+4+3+2+1 = 21$$
In these 8 matches, 4 winners will emerge.
So, total number of matches between these 4 winners = $$ 3+2+1= 6$$
Two winners will emerge from these 4 winners who will play the final match.
so, total matches played in the tournament = $$21 + 6+1 = 28$$ (option C)

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Re-Attempt Weekly Quiz Competition

Permutations and Combinations Test 23

Result

Permutations and Combinations Test 23

Score

-

Rank

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SHARING IS CARING

Question 1

70

75

65

80

Solution

Question 2

Pec silk mit hee

silk peehee be

il silk mit hee

none

Solution

Question 3

None

One

Two

Three

Four

Solution

Question 4

$$7\dfrac{1}{4}$$

$$7\dfrac{1}{2}$$

$$\dfrac{15}{4}$$

None of the above

Solution

Question 5

$$4$$

$$5$$

$$6$$

$$7$$

$$8$$

Solution

Question 6

$$20$$ sq. units

$$10$$ sq. units

$$30$$ sq. units

None of the above

Solution

Question 7

$$\dfrac{25}{2}$$ sq. units

$$\dfrac{23}{2}$$ sq. units

$$\dfrac{19}{2}$$ sq. units

None of the above

Solution

Question 8

21

22

23

24

Solution

Question 9

9

10

8

7

Solution

Question 10

15

6

28

56

64

Solution

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