UPSC NDA I 2022 Mathematics Solved Paper

Concept:For data arranged in an arithmetic progression, the median is the middle term, found using the formula for the $n$th term of an AP.Explanation:The marks of 51 students form an arithmetic progression with first term $a = 4$ and common difference $d = 3$.Since 51 is odd, the median is the $( \frac{51+1}{2} )$th term, which is the 26th term.The $n$th term of an AP is $a + (n-1)d$.Here, $n = 26$, so median $= 4 + (26-1) \times 3 = 4 + 25 \times 3 = 4 + 75 = 79$.Thus, the median mark is 79.Answer:$79$ (Option D).