Permutations and Combinations Test 3

Result

Permutations and Combinations Test 3

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

The area of a triangle whose vertices are $$(a, c+a), (a, c) $$ and $$(-a, c-a) $$ are

A
$$\displaystyle a^{2}$$

B
$$\displaystyle b^{2}$$

C
$$\displaystyle c^{2}$$

D
$$\displaystyle a^{2}+c^{2}$$

Solution

Area of a triangle with vertices $$({ x }_{ 1 },{ y }_{ 1 })$$ ; $$({ x }_{ 2 },{ y

}_{ 2 })$$ and $$({ x }_{ 3 },{ y }_{ 3 })$$ is $$ \left| \frac { {

x }_{ 1 }({ y }_{ 2 }-{ y }_{ 3 })+{ x }_{ 2 }({ y }_{ 3 }-{ y }_{ 1 })+{ x }_{

3 }({ y }_{ 1 }-{ y }_{ 2 }) }{ 2 } \right| $$
Hence, area of the triangle with given vertices is $$ \left| \frac { { a }(c-c+a)+a(c-a-c-a)-a(c+a-c) }{ 2 } \right| = \left| \frac { { a }^{ 2 }-2{ a }^{ 2 }-{ a }^{ 2 } }{ 2 } \right| = { a }^{ 2 } $$
Question 2
1 / -0

In the series given below. count the number of 9s, each of which Is not immediately preceded by 5 but is immediately followed by either 2 or 3. How many such 9s are there?
1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8

A
One

B
Three

C
Five

D
Six

Solution

There are 3 such 9s that are not immediately preceded by 5 and immediately followed by 2 or 3 in the given series. They are marked in bold.
1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8
Answer is Option B
Question 3
1 / -0

Answer the question based on the set of numbers given.
738 429 156 273 894
What will be the difference between the first digit of the highest number as well as of the lowest number after the positions of the first two digits in each number are reversed?

A
4

B
5

C
6

D
7

Solution

In the given series 738 429 156 273 894 when the first two digits are reversed for every number, the number becomes 378 249 516 723 984. The highest and the lowest number of this series are 984 and 249 respectively.
The difference between the first digits of these two numbers are $$9-2=7$$
Answer is Option $$D$$
Question 4
1 / -0

3F, 6G, 11 I, 18 L, .....

A
21O

B
25N

C
27P

D
27Q

E
29P

Solution

+1, +2, +3, +4, in letters; +3, +5, +7, +9 in numbers
Question 5
1 / -0

How many combinations of two-digit numbers having 8 can be made from the following numbers?
8, 5, 2, 1, 7, 6

A
$$9$$

B
$$10$$

C
$$11$$

D
$$12$$

Solution

The possible two-digit number are
88, 85, 82, 81, 87, 86, 58, 28, 18, 78, 68
These are 11 in number
Question 6
1 / -0

CE, GI, KM, OQ, ....

A
TW

B
TV

C
SU

D
RT

E
UW

Solution

The letters of each term are alternate Also the last letter of each term and the first letter of the next term are alternate
Question 7
1 / -0

There are $$5$$ roads leading to a town from a village. The number of different ways in which a villager can go to the town and return back, is

A
$$25$$

B
$$20$$

C
$$10$$

D
$$5$$

Solution

Permutation : - A Permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

For example, Suppose we have a set of three letters :A, B and C..... each possible arrangement would be an example of permutation.

Here in this question, there are $$5$$roads leading to a town from a village.

He can go by $$5$$ ways and can return by $$4$$ ways

So the number of different ways in which a villager can go to the town and return back is $$5 \times 4 = 20$$
Question 8
1 / -0

JE, LH, OL, SQ, ....

A
WV

B
WX

C
VW

D
VX

E
XW

Solution

First letter: +2, +3, +4, +5,.... Second letter: +3, +4, +5, +6, ....
Question 9
1 / -0

BDF, CFI, DHL, ....

A
CJM

B
EIM

C
EJO

D
EMI

Solution

First, 2nd, 3rd letters are moving +1, +2, +3 steps
Question 10
1 / -0

How many numbers amongst the numbers 9 to 54 are there which are exactly divisible by 9 but not by 3?

A
8

B
6

C
5

D
Nil

Solution

Any number divisible by 9 is also divisible by 3

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Permutations and Combinations Test 3

Result

Permutations and Combinations Test 3

Score

-

Rank

-

SHARING IS CARING

Question 1

$$\displaystyle a^{2}$$

$$\displaystyle b^{2}$$

$$\displaystyle c^{2}$$

$$\displaystyle a^{2}+c^{2}$$

Solution

Question 2

One

Three

Five

Six

Solution

Question 3

4

5

6

7

Solution

Question 4

21O

25N

27P

27Q

29P

Solution

Question 5

$$9$$

$$10$$

$$11$$

$$12$$

Solution

Question 6

TW

TV

SU

RT

UW

Solution

Question 7

$$25$$

$$20$$

$$10$$

$$5$$

Solution

Question 8

WV

WX

VW

VX

XW

Solution

Question 9

CJM

EIM

EJO

EMI

Solution

Question 10

8

6

5

Nil

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.