NDA Mathematics Question (2025) — Solution

Step-by-step solution

Since p, 1, q are in AP, we have p + q = 2(1) = 2. Since p, 2, q are in GP, we have pq = 2^2 = 4. For p, 4, q to be in HP, the middle term must be the harmonic mean of p and q, which is given by 2pq p+q . Substituting the values of p+q and pq, we get 2(4) 2 = 4. Thus, p, 4, q are in HP. Statement I is correct. By the definition of harmonic progression, if p, 4, q are in HP, their reciprocals 1 p , 1 4 , 1 q must be in AP. Thus, Statement II is also correct. Both statements I and II are correct. Answer: Both I and II