Differentiation & Applications · JEE Main previous year questions

2025 2 questions

1. Q122025 · 4 Apr 2025 · Shift 2

   Let the product of ${\omega }_1=(8+i)\sin \theta +(7+4i)\cos \theta$ and ${\omega }_2=(1+8i)\sin \theta +(4+7i)\cos \theta$ be $\alpha +i\beta$, $i=\sqrt{-1}$. Let p and q be the maximum and the minimum values of $\alpha +\beta$ respectively. Then $\mathrm{p}+\mathrm{q}$ is equal to :

   1. A.130
   2. B.150
   3. C.160
   4. D.140
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   Answer: A

2. Q252025 · 2 Apr 2025 · Shift 2· Numerical answer

   Let $\mathrm{A}(4,-2)$, $\mathrm{B}(1,1)$ and $\mathrm{C}(9,-3)$ be the vertices of a triangle ABC . Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and $AB$ of the triangle $ABC$ respectively, is ____.

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   Answer: 3