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NDA 1 2025 Maths, question 33

Topic: Trigonometry

Passage · Q31 to Q33

Let p=sin⁡35∘p = \sin 35^{\circ}, q=sin⁡25∘q = \sin 25^{\circ} and r=sin⁡(−95∘)r = \sin\left( - 95^{\circ} \right).

Q33

What is (p2+q2+r2)\left( p^{2} + q^{2} + r^{2} \right) equal to?

  1. (a) 1/21/2
  2. (b) 1
  3. (c) 3/23/2Correct answer
  4. (d) 2

Solution.

Answer: (c) 3/23/2

  1. The identities above give p+q+r=0p + q + r = 0 and pq+qr+rp=−3/4pq + qr + rp = - 3/4.
  2. Expand the square: p2+q2+r2=(p+q+r)2−2(pq+qr+rp)=0−2(−3/4)=3/2p^{2} + q^{2} + r^{2} = (p + q + r)^{2} - 2(pq + qr + rp) = 0 - 2( - 3/4) = 3/2.