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Friday, 9 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 topic in other shifts

All Dot Product questions
  1. 2 Apr 2026, Shift 1 · Q14If a⃗\vec a and b⃗\vec b are two vectors such that ∣a⃗∣=2|\vec a|=2 and ∣b⃗∣=3|\vec b|=3, then the maximum value of…HardSingle correct
  2. 2 Apr 2025, Shift 1 · Q11If a⃗\vec{a} is a nonzero vector such that its projections on the vectors 2i^−j^+2k^2\hat{i}-\hat{j}+2\hat{k}, i^+2j^−2k^\hat{i}+2\hat{j}-2\hat{k} and…MediumSingle correct
  3. 7 Apr 2025, Shift 2 · Q15Let a⃗\vec{a} and b⃗\vec{b} be the vectors of the same magnitude such that…MediumSingle correct
  4. 8 Apr 2025, Shift 2 · Q14Let a⃗=i^+2j^+k^\vec{a} = \hat{i} + 2\hat{j} + \hat{k} and b⃗=2i^+j^−k^\vec{b} = 2\hat{i} + \hat{j} - \hat{k}. Let c^\hat{c} be a unit vector in the plane of…MediumSingle correct
  5. 8 Apr 2024, Shift 1 · Q18The set of all α\alpha, for which the vectors a⃗=αti^+6j^−3k^\vec{a}=\alpha t\hat{i}+6\hat{j}-3\hat{k} and…MediumSingle correct
  6. 29 Jan 2024, Shift 1 · Q18Let O be the origin and the position vectors of A and B be 2i^+2j^+k^2\hat{i}+2\hat{j}+\hat{k} and 2i^+4j^+4k^2\hat{i}+4\hat{j}+4\hat{k} respectively. If…MediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.