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Answers
ANSWER :
I) n = 3
II) 2^½
III) 5^2x
2)Given,
3
n−1
×9
n−1
3
n
×9
n+1
=
3
n−1
×3
2n−2
3
n
×3
2n+2
=
3
3n−3
3
3n+2
=3
3n+2−3n+3
=3
5
=243
3)1st idea : Go through the left numbers. (i.e = 3+ , 5+, 7+, 9+ & obviously 11+ but here it is given 10+ ). Here odd numbers in order except the last one. Let it be.
Same for right digits (+2, +4, +6,+8, Obviously +10 but here it is +9...Keep aside.
2nd idea: Look into the answers given.
*all are prime numbers.
* Our answer may not be the prime. Bcoz there it is given (10 +9) not (11+ 10 - as we expected).
* The answers all are 8th multiple differences.
(i.e) --> look into the answers given in right.
7-23 = 16
47-23 = 24
79-47 = 32
__ - 79 = ? (should be a multiple of 8? ) Actually nope.
Here the trick comes.
Do what we know first => preceding to 32 is 40 (8x5 =40). So __ - 79 = 40
--> 79+ 40 = 119.
So the answer is 119? Nope.
Note: As the reduced values given 10 +9 not as 11+ 10 according to our calculation. So its reduced 1 in both digits. So (79-1 +40-1 = 117)
So ultimately 10 +9 = 117.
4)As we know that
(a
m
)
n
=a
mn
125
(2x)
5
2(x+6)
×25
2x−7
=
(5
3
)
2x
5
2x+12
×(5
2
)
2x−7
=
5
6x
5
2x+12
×5
4x−14
=
5
6x
5
2x+12+4x−14
=
5
6x
5
6x−2
=5
6x−2−6x
=5
−2
=
5
2
1
=
25
1