Solution:

17

Explanation :
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647

Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623

Solution:

Eighth Batsman

== Over Number 1 ==
Ball 1 : Batsman-1 got out
Ball 2 : Batsman-3 got out (Note: batsman-2 is on non-striker end)
Ball 3 : Batsman-4 got out
Ball 4 : Batsman-5 got out
Ball 5 : Batsman-6 got out
Ball 6 : Batsman-7 got out

== Over Number 2 ==
Ball 7 : Batsman-2 got out (Note: batsman-2 which was on non-striker end will switch end with batsman-8 at the end of 1st over)
Ball 8 : Batsman-9 got out (Note: Batsman-8 is on non-striker end)
Ball 9 : Batsman-10 got out
Ball 10 : Batsman-11 got out

Solution:

Amin is the terrorist

Explanation:
The message is "tstimeirorwatchretehourhtsisecondsnidialma"

Step1 :
Rewrite the above message as
"ts time iror watch rete hour htsi seconds ni dial m"

Step2:
Now remove all words related to time like (time,watch,hour,seconds,dial) and combine them.
"tsirorretehtsinima"

Step3
Reverse the word.
"tsirorretehtsinima"

Step4.
Add spaces where necessary
"tsirorret eht si nima"

Step5:
Reverse again
"amin is the terrorist"

Solution:

522

Explanation:
1st Number = Number of alphabtes
2nd Number = Number of vowels
3rd Nummber = Number Of Circles

Lavesh = 6 alphabets + 2 vowels(a,e) + 2 circles(in 'a' and in 'e') = 622
Anmol = 5 alphabets + 2 vowels(a,0) + 2 circles(in 'a' and in 'e') = 522
Shruti = 6 alphabets + 2 vowels(u,i) + 0 circles = 620
Aakriti = 7 alphabets + 4 vowels(a,a,i,i) + 2 circles(in 'A' and in 'a') = 742
Hence,
Sonal = 5 alphabets + 2 vowels(a,o) + 2 circles(in 'a' and in 'o') = 522

Solution:

89

Solution:

"EUNOIA" is the shortest(length-6) word that comprises of all vowels.
But many dictionaries does no include this word.

So next comes many seven letter words that contain all vowels.
* SEQUOIA,
* EULOGIA,
* MIAOUED,
* ADOULIE,
* EUDOSIA,
* EUNOMIA
* EUTOPIA
* MOINEAU
* DOULEIA.

EUNOIA means "alertness of brain"

Solution:

You must chose the electric chair because there is no electricity in the house and thus you will survive.

Solution:

McLaughlin

Solution:

One for all or all for one.

Solution:

151 (131+20)

Explanation:
1st 7 prime numbers post 100 are
101 , 103 , 107 , 109 , 113 , 127 , 131
...Adding 20 to numbers
121 , 123 , 127 , 129 , 133 , 147 , 151