Solution:

0488

Explanation
A) Its a 4 digit number. --- 0488

B) Its first digit is of no use --- 0 at the start is of no use.

C) Its third and fourth digit is the mirror image of each other. --- 8 is the only digit which is a mirror image of itself.

D) The second digit is half the third. --- 4 is half of the digit 8.

Solution:

28745

Explanation

New Number = (Last Number +1 ) * 9
and Then New Number = (Last Number - 1 ) * 8 and so on.

i.e
1
(1+1) * 9 = 18
(18-1) * 8 = 136
(136+1) * 7 = 959
(959-1) * 6 = 5748
(5748+1) * 5 = 28745
(28745-1) * 4 = 114976
(114976+1) * 3 = 344931

Solution:

The solution is:
547809 + 087549 + 780954 = 1416312

Solution:

    35997
+ 284508
========
    320505
========

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:

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:

168
12 14
6 2 7
3 2 1 7

Explanation:
If we multiply two numbers below, we will get the number above it.
like. 3*2 of the last row =>6 of the third row.

Solution:

34293

Solution:

3.4142788e+29

The biggest number using four 2s will be:
22^22