Correct Option: E

Method 1 to solve this question.
Let p be the first odd number.
Then next odd number is p + 2.
According to question,
Sum of five consecutive odd numbers 175
⇒ p + p + 2 + p + 4 + p + 6 + p + 8 = 175
⇒ 5p + 20 = 175
⇒ p = (175 - 20)/5 = 31
According to question,
Sum of the second largest and square of smallest one = (31 + 6) + (31)²
Sum of the second largest and square of smallest one = 37 + 961 = 998

Method 2 to solve this question.
Let p be the even number.
Then next odd number is p + 1. so on p + 3 , p + 5................ P + 9
According to question,
Sum of five consecutive odd numbers 175
⇒ p + 1 + p + 3 + p + 5 + p + 7 + p + 9 = 175
⇒ 5p + 25 = 175
⇒ p = (175 - 25)/5
⇒ p = (150)/5
⇒ p = 30
First odd number = p + 1 = 30 + 1 = 31
According to question,
Sum of the second largest and square of smallest one = (30 + 7) + (30 + 1)²
Sum of the second largest and square of smallest one = 37 + 961 = 998