Permutations and Combinations Test 2

Result

Permutations and Combinations Test 2

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Factorial of negative numbers is always greater than 1.

A
True

B
False

C
Either

D
Neither

Solution

Factorial : product of an integer with integer less than it.
Factorial can be interpolated using gamma function and gamma function and
gamma function is not defined for negative integer.
Factorial is not defined for negative integer
Question 2
1 / -0

Choose the correct option for the following.
$$n!=n(n-1)(n-2).....3.2.1$$

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

Factorial : the product of an integer and all integer less than that
$$\therefore n!=n\times (n-1)\times (n-2)............3\times 2\times 1$$

$$\therefore $$ The given statement
$$n!=n\times (n-1)\times (n-2)............3\times 2\times 1$$ is True
Question 3
1 / -0

Three boys and three girls are to be seated around a table in a circle. Among them the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. How many such arrangements are possible?

A
$$5$$

B
$$6$$

C
$$4$$

D
$$2$$

Solution

As boy $$X$$ does not need any girl neighbour so he will have $$2$$ boys sitting next to him.
The $$2$$ boys can be arranged in $$2!$$ ways.
Similarly $$Y$$ will be surrounded by $$2$$ girls and these $$2$$ girls can be arranged in $$2!$$ ways.
So number of arrangements $$=2!\times 2!=2\times 2=4$$
Hence, the answer is $$4$$.
Question 4
1 / -0

Area of a triangle formed by the points A(5, 2), B(4, 7) and C(7, -4) is _____.

A
2 sq. units

B
$$2\sqrt2$$ sq. units

C
4 sq. units

D
$$4\sqrt2$$ sq. units

Solution

Area of a triangle ABC = $$ \frac { 1 }{ 2 } \left|[ x_{ 1 }\left( y_{ 2 }-y_{ 3 }

\right) +x_{ 2 }\left( y_{ 3 }-y_{ 1 } \right) +x_{ 3 }\left( y_{ 1 }-y_{ 2 }

\right) \right]|$$
Substituting the given coordinates, we have
=$$ \frac { 1 }{ 2 } \left[ 5 \left(7+4) \right) -\left( 4+2\right) +7\left( 2-7) \right) \right]$$
$$ =\frac { 1 }{ 2 } \left( 5 ( 11) +4\times( -6)
+7\times( -5)\right)$$
$$ =\frac { 1 }{ 2 } \left[(55) - ( 24) - ( 35) \right]$$
$$ =\frac { 1 }{ 2 } \times |-4| = 2$$ square units.
Question 5
1 / -0

The figure below shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible direction of travel. What is the number of distinct paths from A to F?

A
9

B
10

C
11

D
8

Solution

(B) The maximum routes from A to F are listed below.

(1) ABDF (2) ACDF (3) ABF (4) ABEF

(5) ACDEF (6) ABCDEF (7) ABDEF (8) ABCDF
Question 6
1 / -0

Which letter will be the fifth from the right if the first and second, the third and fourth and so on are interchanged among each other in the word "COMPANIONATE"?

A
A

B
I

C
N

D
O

Solution

When we interchange the first and the second, third and the fourth, and so on letters in the word COMPANIONATE, the new word becomes OCPMNAOIANET.
Therefore, 5th letter from right is I
Answer is Option B
Question 7
1 / -0

The positions of the first and the fifth digits in the number 83256479 are interchanged. Similarly the positions of the second and the sixth digits are interchanged and so on. Which of the following will be the third to the right of the seventh digit from the right end after rearrangement?

A
3

B
4

C
7

D
8

Solution

In the given number 83256479, the first and the fifth digits are interchanged.The number becomes 63258479.
Then second and the sixth digit are interchanged. The number becomes 64258379.
The third and the seventh digit are interchanged. The number becomes 64758329.
The fourth and the eighth digit are interchanged. The number becomes 64798325.
The seventh digit from the right end after rearrangement is 4.The third digit to the right of 4 is 8.
Answer is Option D
Question 8
1 / -0

The spread sheet on the right contains 20 cells. A cell In a spread sheet can be identified fIrst by the column letter and then by the row number. For example,. the number 10 is found in cell C4. If the number in cell A3 =B4-3(E2 +D4) then which of the following must be the number in cell E2?

A
-21

B
-15

C
-4

D
-12

Solution

Its given
A3=B4-3(E2+D4)
Substituting the values from the grid
$$18=-6-3(E2+4)$$
$$24=-3(E2+4)$$
$$-8-4=E2$$
$$E2=-12$$
Answer is Option D
Question 9
1 / -0

In numbers from $$1 \ to\ 100$$ the digit "$$0$$" appears ____________times.

A
$$9$$

B
$$10$$

C
$$11$$

D
$$12$$

Solution

$$10, 20, 30, 40, 50, 60, 70, 80, 90, 100$$
Thus the digit $$0$$ appears $$11$$ times.
Question 10
1 / -0

The greatest number that can be formed by the digits $$7,0,9,8,6,3$$

A
$$9,87,360$$

B
$$9,87,063$$

C
$$9,87,630$$

D
$$9,87,603$$

Solution

The greatest number that can be formed by the digits $$7,0,9,8,6,3$$ is $$9 8 7 6 3 0$$
To achieve this arrange the given numbers in descending order.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Permutations and Combinations Test 2

Result

Permutations and Combinations Test 2

Score

-

Rank

-

SHARING IS CARING

Question 1

True

False

Either

Neither

Solution

Question 2

True

False

Ambiguous

Data insufficient

Solution

Question 3

$$5$$

$$6$$

$$4$$

$$2$$

Solution

Question 4

2 sq. units

$$2\sqrt2$$ sq. units

4 sq. units

$$4\sqrt2$$ sq. units

Solution

Question 5

9

10

11

8

Solution

Question 6

A

I

N

O

Solution

Question 7

3

4

7

8

Solution

Question 8

-21

-15

-4

-12

Solution

Question 9

$$9$$

$$10$$

$$11$$

$$12$$

Solution

Question 10

$$9,87,360$$

$$9,87,063$$

$$9,87,630$$

$$9,87,603$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.