Differentiation Test 9

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Differentiation Test 9

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Question 1
1 / -0

_ab_caa_bbcaa_b_caaa

A
abaab

B
cabab

C
bccaa

D
baaba

Solution

Pattern is aabbc/ aaabbc/ aaabbc/ aaa
Question 2
1 / -0

If the area of the triangle formed by $$ (-2,5), (x,-3) $$ and $$(3,2)$$ is $$14 $$ square units, then $$x=$$ ____.

A
1

B
2

C
-2

D
-1

Solution

Area of triangle having vertices $$(x_1,y_1), (x_2,y_2)$$ and $$(x_3,y_3)$$ is given by
$$ = \dfrac{1}{2} \times [ x_1 (y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) ] $$
$$\therefore \displaystyle Area=\frac{1}{2}\left [ -2\left ( -3-2 \right )+x\left ( 2-5 \right )+3\left ( 5+3 \right ) \right ]$$
$$\displaystyle =\frac{1}{2}\left [ 10-3x+24 \right ]=\frac{34-3x}{2}$$
$$\displaystyle \therefore \frac{34-3x}{2}=14$$ or x = 2
Question 3
1 / -0

ab _ bc _ c _ ba _ c

A
baac

B
aabb

C
caab

D
aaab

Solution

Pattern is abc/bca/cab/abc
Thus letters are written in a cyclic order
Question 4
1 / -0

If CAT is $$48$$, Z is $$52$$ Then what is TEA equal to ?

A
$$48$$

B
$$52$$

C
$$60$$

D
$$50$$

Solution

Alphanumeric coding type
Word Code value Final code
(alphabet series)
CAT C=3,A=1,T=20 24X2=48
3+1+20=24
Z 26 24X2=52
TEA T=20,E=5,A=1 26X2=52
20+5+1=26
Question 5
1 / -0

A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is:

A
85

B
80

C
75

D
70

Solution

Out of 16 men, there is a captain.
Number of captains in 1200 men = $$\displaystyle \\ 1200\div 16=75$$.
Question 6
1 / -0

Observe the following pattern for obtaining the sums then find the sum of numbers from 781 to 790?
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 = 255
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 = 555
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 = 1055
251 + 252 + 253 + 254 + 255 + 256 + 257
258 + 259 + 260 = 2555

A
7055

B
7855

C
7955

D
8155

Solution

781 + 782 + 783 + 784 + 785
786 + 787 + 788 + 789
+ 790 = 7855
Question 7
1 / -0

A, B, C and D are four 4-digit numbers each having the digit 9 only once and in the place shown None of the other digits are known
What can be said about A, B, C and D?

A
D is the smallest of the four numbers

B
B is larger than C

C
A is the largest of the 4 numbers

D
D is the largest of the 4 numbers

Solution

A is the largest of the 4
numbers because its place
value is 9000
Question 8
1 / -0

At the end of a business conference, the ten people present all shake hands with each other once. How many handshakes will there be altogether?

A
20

B
45

C
55

D
90

Solution

Total number of handshakes=10×92=45
Question 9
1 / -0

In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament?

A
36

B
30

C
15

D
12

Solution

First player can play 5 matches with other five players. Second player can play 4 matches with other four players and proceeding this way, the fifth player will play only one match with sixth player.
$$\displaystyle \therefore $$ Total number of matches played = 5 +4 + 3 + 2 + 1 = 15.
Short cut : Number of matches played by n players = $$\displaystyle \frac { n\left( n+1 \right) }{ 2 } $$
Question 10
1 / -0

Choose the correct statement(s):
$$A$$: Every sequence is a progression.
$$B$$: Every progression is a sequence.

A
Only $$A$$

B
Only $$B$$

C
Both $$A$$ and $$B$$

D
None

Solution

The difference between a progression and a sequence is that a progression has a specific rule to calculate its next term from its previous term, whereas a sequence can be based on a logical rule like 'a group of prime numbers'.
Thus, every progression is a sequence but every sequence is not a sequence.

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Differentiation Test 9

Result

Differentiation Test 9

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SHARING IS CARING

Question 1

abaab

cabab

bccaa

baaba

Solution

Question 2

1

2

-2

-1

Solution

Question 3

baac

aabb

caab

aaab

Solution

Question 4

$$48$$

$$52$$

$$60$$

$$50$$

Solution

Question 5

85

80

75

70

Solution

Question 6

7055

7855

7955

8155

Solution

Question 7

D is the smallest of the four numbers

B is larger than C

A is the largest of the 4 numbers

D is the largest of the 4 numbers

Solution

Question 8

20

45

55

90

Solution

Question 9

36

30

15

12

Solution

Question 10

Only $$A$$

Only $$B$$

Both $$A$$ and $$B$$

None

Solution

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