Which of the following sets of numbers is a pythagorean triple? i begg of 77, 35, 112 70, 35, 78 75, 36, 83 77, 36, 85

One way to find the answer is to add the squares of the smaller numbers, and see that the sum equals the square of the largest number.
Example:
77^2+35^2=5929+1225=7154
112^2=12544
So the first triplet is not Pythagorean.
Repeat for the other triplets to find the answer.

Another way is to first eliminate the impossible (triplet=(a,b,c), a<c, b<c)
- if a+b>=c, then triplet is not Pythagorean
  77+34=112, ==> (77,34,112) is not Pythagorean
- check the last digits.  if the last digit of the sum of the squares of the last digits of the smaller number is not equal to the last digit of the square of the largest number, the triplet is not Pythagorean
 Example: For (70,35,78),
         0^2+5^2=0+25 last digit is 5.
         8^2=64         last digit is 4   4 &ne; 5 => triplet is not pythagorean.
   (75,36,83) :  5^2+6^2=25+36=61 => last digit is 1  3^2=9
    1 &ne; 9,    so (75,36,83) is not Pythatorean.

Since we have eliminated the first three triplets, we have no choice but to check the squares of the last triplet:
77^2=5929
36^2=1296
   Sum=5929+1296=7225
85^2=7225 = 77^2+36^2 => (77,36,85) is a Pythagorean triplet

Whose mistake? can you give more details to what the question is asking?

You have to give us options