The document discusses solving a math problem from a civil engineering exam. It goes through the steps of solving the problem, which involves recognizing that only the cosine terms matter and do not alternate in sign, ruling out choices where the sign alternates. It also rules out choices where all integers do not occur in the denominator. By a process of elimination, the only choice left is choice C.

1. GATE-2016
MATHEMATICS
CIVIL ENGINEERING
PAPER II

2. PROBLEM

3. SOLUTION
AT x=0 sin0 IS O
IGNORE THIS
PART

4. SOLUTION
AT x=0 sin0 IS O
IGNORE THIS
PART
ONLY THE cos-
TERMS MATTER
AND THEY DO
NOT ALTERNATE
IN SIGN

5. SOLUTION
ONLY THE cos-
TERMS MATTER
AND THEY DO
NOT ALTERNATE
IN SIGN
RULE OUT
THESE
CHOICES B
AND D AS THE
SIGN
ALTERNATES

6. SOLUTION
ELIMINATE THIS
AS ALL THE
INTEGERS DO NOT
OCCUR IN THE
DENOMINATOR
RULE OUT
THESE
CHOICES B
AND D AS THE
SIGN
ALTERNATES

7. CHOICES A, C AND D
CAN BE RULED OUT
1) ELIMINATE B AND
D AS THE SIGNS
OF THE TERMS
ALTERNATE
2) ELIMINATE
CHOICE A AS ALL
THE INTEGERS
OCCUR IN THE
DENOMINATOR

8. BY ELIMINATION
WE HAVE TO
CHOOSE CHOICE C