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Straight Lines and Pair of Straight Lines question

2022 · 29 Jul · Shift 2 · Q31
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Straight Lines and Pair of Straight Lines question

2022 · 29 Jul · Shift 2 · Q31

JEE MainMathematicsStraight Lines and Pair of Straight LinesMCQ+4 / −1
Let m1,m2m_{1}, m_{2}m1​,m2​ be the slopes of two adjacent sides of a square of side a such that a2+11a+3(m12+m22)=220a^{2}+11 a+3\left(m_{1}^{2}+m_{2}^{2}\right)=220a2+11a+3(m12​+m22​)=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))(10(cosα−sinα),10(sinα+cosα)), where α∈(0,π2)\alpha \in\left(0, \frac{\pi}{2}\right)α∈(0,2π​) 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(cosα−sinα)x+(sinα+cosα)y=10, then 72(sin⁡4α+cos⁡4α)+a2−3a+1372\left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+a^{2}-3 a+1372(sin4α+cos4α)+a2−3a+13 is equal to :
  1. A
    119
  2. B
    128
  3. C
    145
  4. D
    155
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