please answer these question
Answers
Answer:
Correct Options are : -
13. ( A )
14. ( B )
15. ( D )
16. ( B )
Step-by-step explanation:
Question 13 : -
Given sequence : 77 , 85 , 149 , 365 , 877.
Solution : -
On observing the given equation, we get that the differences between the given terms are the cubes of consecutive even numbers from 2.
The above statement states that differences( 85 - 77 , 149 - 85 , 365 - 145 , 877 - 365 ) are the cubes of consecutive even numbers ( starting from 2 ) .
An activity to prove the statement : -
= > 85 - 77 = 8 = 2^3
= > 149 - 85 = 64 = 4^3
= > 365 - 149 = 216 = 6^3
= > 877 - 365 = 512 = 8^3
Now, let the question mark will be replaced by a, so the difference between a and 877 should be the cube of the even number after 8( that is 10 ).
Now,
= > a - 877 = 10^3
= > a - 877 = 1000
= > a = 1000 + 877
= > a = 1877
Therefore the question mark will be replaced by 1877.
Answer : Correct option is ( A ).
Question 14 : -
Given sequence : 4 , 28 , 64 , 172 , 496.
I think, this sequence should be : 16 , 28 , 64 , 172 , 496.
Solution : -
On observing the given sequence, we get that the factors of the difference between two consecutive numbers is being multiplied by 3.
The above above statement states that the factors of the difference of consecutive numbers( factors of 28 - 16 , factors of 64 - 28 , factors of 172 - 64 , factors of 496 - 172 ) are being multiplied by 3.
An activity to prove the statement : -
= > Factors of 28 - 16 = factors of 12
⇒ 2 x 2 x 3 = 2^2 x 3
= > Factors of 64 - 28 = factors of 36
⇒ 2 x 2 x 3 x 3 = 2^2 x 3 x 3
= > Factors of 172 - 64 = factors of 108
⇒ 2 x 2 x 3 x 3 x 3 = 2^2 x 3 x 3 x 3
= > Factors of 496 - 172 = factors of 324
⇒ 2 x 2 x 3 x 3 x 3 x 3 = 2^2 x 3 x 3 x 3 x 3
Now, let the question mark will be replaced by a, difference between the a and 496 should be 2^2 x 3 x 3 x 3 x 3 ( that it 324 x 3 = 972 ) .
Now,
= > a - 496 = 972
= > a = 972 + 496
= > a = 1468
Therefore the question mark will be replaced by 1468.
Answer : Correct option is ( B ).
Question 15 : -
Given that the P means x , S means - , Q means ÷ , J means +
Given sequence : 28 Q 4 P 8 J 6 S 10
Solution : -
As given in the question, P means x , S means - , Q means ÷ , J means + . Substitute the values.
Then,
= > 28 ÷ 4 × 8 + 6 - 10
According to BODMAS,
= > [ ( 28 ÷ 4 ) x 8 ] + 6 - 10
= > [ ( 7 x 8 ) + 6 - 10 ]
= > 56 + 6 - 10
= > 62 - 10
= > 52
Therefore, 52 is the result of the sequence.
Answer : Correct option is ( D ) .
Question 16 : -
The word "NATIONAL" is written as "JUBOKZMN"
Solution : -
The word given here is a word containing 8 alphabets,
According to the question,
Word "NATIONAL" is grouped into two equal parts. Parts are NATI( assume it as part 1 ) and ONAL( assume it as part 2 ). And the word formed after applying the code is JUBOKZMN, similarly, divide it in the same way, 1st part = JUBO and 2nd part = KZMN.
The alphabets of part 1 are written as the alphabet next to them in a reverse order. So, N ⇔ O , A ⇔ B , T ⇔ U , I ⇔ J , or NATI ⇔ JUBO.
An activity to prove the above statement : -
⇒ N is written as O, O is next to N.
⇒ A is written as B, B is next to A .
⇒ T is written as U, U is next to T.
⇒ I is written as J, J is next to I.
And, in part 2, formed words are the previous words to the given words. Like, O ⇔ N , N ⇔ M , A ⇔ Z , L ⇔ K, or ONAL ⇔ KZMN.
It is just opposite of activity 1 .
An activity to prove the above statement : -
⇒ O is written as N, O is next to N
⇒ N is written as M, N is next to M.
⇒ A is written as Z, A is next to Z.
⇒ L is written as K, L is next to K.
Therefore,
NATIONAL = JUBOKZMN
In the same code,
First divide ELECTION in two groups,
ELEC = 1st group
TION = 2nd group
Similarly, as we did to prove NATIONAL as JUBOKZMN,
In 1st group,
E ⇔ F
L ⇔ M
E ⇔ F
C ⇔ D
Hence, ELEC ⇔ DFMF
In 2nd group,
T ⇔ S
I ⇔ H
O ⇔ N
N ⇔ M
Hence, TION ⇔ MNHS
Therefore,
ELECTION ⇔ DFMFMNHS
So, in the same code ELECTION will be written as DFMFMNHS.
Answer : Correct option is ( B ).
refer to attachment
