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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 2, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

Let m1m_1, m2m_2 be the slopes of two adjacent sides of a square of side a such that a2+11a+3(m12+m22)=220a^2+11a+3\left(m_1^2+m_2^2\right)=220. If one vertex of the square is (10(cos⁡α−sin⁡α), 10 (sin⁡α+cos⁡α))(10(\cos\alpha-\sin\alpha),\ 10\,(\sin\alpha+\cos\alpha)), where α∈(0,π2)\alpha\in\left(0,\frac{\pi}{2}\right) and the equation of one diagonal is (cos⁡α−sin⁡α) x+(sin⁡α+cos⁡α) y=10(\cos\alpha-\sin\alpha)\,x+(\sin\alpha+\cos\alpha)\,y=10, then 72 (sin⁡4α+cos⁡4α)+a2−3a+1372\,(\sin^4\alpha+\cos^4\alpha)+a^2-3a+13 is equal to :
  1. (1)119119
  2. (2)128128Official answer
  3. (3)145145
  4. (4)155155

Official answer

Option 2

NTA final key.

Chapter
Straight Lines
Topic
Straight Line Distance
Idea tested
Square Area from Vertex and Diagonal

Same idea in other shifts

Asked 2× in all
  1. 8 Apr 2025, Shift 2 · Q11Let aa be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle α\alpha with the positive…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 108 of the 174 JEE Main shifts held from 2017 to 2026.