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Saturday, 31 October

JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2026, Shift 2, Maths Q16

Question 16 of 75 in this shift, Maths question 16 of 25, Section A.

Two adjacent sides of a parallelogram PQRSPQRS are given by PQ⃗=j^+k^\vec{PQ} = \hat{j} + \hat{k} and PS⃗=i^−j^\vec{PS} = \hat{i} - \hat{j}. If the side PSPS is rotated about the point PP by an acute angle α\alpha in the plane of the parallelogram so that it becomes perpendicular to the side PQPQ, then sin⁡2(5α2)−sin⁡2(α2)\sin^2\left(\frac{5\alpha}{2}\right) - \sin^2\left(\frac{\alpha}{2}\right) is equal to:
  1. (1)12\frac{1}{2}
  2. (2)32\frac{\sqrt{3}}{2}Official answer
  3. (3)34\frac{\sqrt{3}}{4}
  4. (4)235\frac{2\sqrt{3}}{5}

Official answer

Option 2

NTA final key.

Chapter
Trigonometric Functions
Topic
Dot Product
Idea tested
Angle Between Vectors

Same idea in other shifts

Asked 6× in all
  1. 4 Apr 2024, Shift 1 · Q18Let a unit vector which makes an angle of 60∘60^\circ with 2i^+2j^−k^2\hat{i}+2\hat{j}-\hat{k} and an angle of 45∘45^\circ with i^−k^\hat{i}-\hat{k} be…HardSingle correct
  2. 4 Apr 2024, Shift 2 · Q17Let a⃗=i^+j^+k^, b⃗=2i^+4j^−5k^\vec a=\hat i+\hat j+\hat k,\ \vec b=2\hat i+4\hat j-5\hat k and c⃗=xi^+2j^+3k^, x∈R\vec c=x\hat i+2\hat j+3\hat k,\ x\in\mathbb{R}. If d⃗\vec d is…MediumSingle correct
  3. 4 Apr 2024, Shift 2 · Q18For λ>0\lambda>0, let θ\theta be the angle between the vectors a⃗=i^+λj^−3k^\vec a=\hat i+\lambda\hat j-3\hat k and b⃗=3i^−j^+2k^\vec b=3\hat i-\hat j+2\hat k.…EasySingle correct
  4. 25 Jul 2021, Shift 2 · Q88If (a⃗+3b⃗)\left(\vec{a}+3\vec{b}\right) is perpendicular to (7a⃗−5b⃗)\left(7\vec{a}-5\vec{b}\right) and (a⃗−4b⃗)\left(\vec{a}-4\vec{b}\right) is…MediumNumerical value
  5. 3 Sep 2020, Shift 2 · Q69Let a, b, c∈Rc \in \mathbf{R} be such that a2+b2+c2=1a^2 + b^2 + c^2 = 1. If…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.