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Jee Main 2025 — Medium JEE math MCQ

If \( \sum_{r=1}^{15} \frac{1}{\sin\left(\frac{r}{2} + \frac{1}{2}\right) \sin\left(\frac{r}{2} + \frac{3}{2}\right)} \) = \( a\sqrt{3} + b \), \( a, b \in \mathbb{Z} \), then \( a^2 + b^2 \) is equal to
  1. A. 10
  2. B. 4
  3. C. 2
  4. D. 8

Solution

The correct option is **D**. (D. 8)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
If ∑r=1151sin⁡(r2+12)sin⁡(r2+32) \sum_{r=1}^{15} \frac{1}{\sin\left(\frac{r}{2} + \frac{1}{2}\right) \sin\left(\frac{r}{2} + \frac{3}{2}\right)} = a3+b a\sqrt{3} + b , a,b∈Z a, b \in \mathbb{Z} , then a2+b2 a^2 + b^2 is equal to
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