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JEE Advanced 2022 Paper 1 Online
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Consider the ellipse

$$\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$$$Let$H(\alpha, 0), 0<\alpha<2$, be a point. A straight line drawn through$H$parallel to the$y$-axis crosses the ellipse and its auxiliary circle at points$E$and$F$respectively, in the first quadrant. The tangent to the ellipse at the point$E$intersects the positive$x$-axis at a point$G$. Suppose the straight line joining$F$and the origin makes an angle$\phi$with the positive$x$-axis. List-I List-II (I) If$\phi=\frac{\pi}{4}$, then the area of the triangle$F G H$is (P)$\frac{(\sqrt{3}-1)^{4}}{8}$(II) If$\phi=\frac{\pi}{3}$, then the area of the triangle$F G H$is (Q) 1 (III) If$\phi=\frac{\pi}{6}$, then the area of the triangle$F G H$is (R)$\frac{3}{4}$(IV) If$\phi=\frac{\pi}{12}$, then the area of the triangle$F G H$is (S)$\frac{1}{2 \sqrt{3}}$(T)$\frac{3 \sqrt{3}}{2}$The correct option is: A$(\mathrm{I}) \rightarrow(\mathrm{R}) ;(\mathrm{II}) \rightarrow(\mathrm{S}) ;(\mathrm{III}) \rightarrow(\mathrm{Q}) ;(\mathrm{IV}) \rightarrow(\mathrm{P})$B (I)$\rightarrow$(R); (II)$\rightarrow(\mathrm{T}) ;(\mathrm{III}) \rightarrow(\mathrm{S}) ;(\mathrm{IV}) \rightarrow(\mathrm{P})$C (I)$\rightarrow(\mathrm{Q}) ;(\mathrm{II}) \rightarrow(\mathrm{T}) ;(\mathrm{III}) \rightarrow(\mathrm{S}) ;(\mathrm{IV}) \rightarrow(\mathrm{P})$D (I)$\rightarrow$(Q); (II)$\rightarrow$(S); (III)$\rightarrow$(Q); (IV)$\rightarrow$(P) 2 JEE Advanced 2022 Paper 1 Online Numerical +3 -0 Two spherical stars$A$and$B$have densities$\rho_{A}$and$\rho_{B}$, respectively.$A$and$B$have the same radius, and their masses$M_{A}$and$M_{B}$are related by$M_{B}=2 M_{A}$. Due to an interaction process, star$A$loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains$\rho_{A}$. The entire mass lost by$A$is deposited as a thick spherical shell on$B$with the density of the shell being$\rho_{A}$. If$v_{A}$and$v_{B}$are the escape velocities from$A$and$B$after the interaction process, the ratio$\frac{v_{B}}{v_{A}}=\sqrt{\frac{10 n}{15^{1 / 3}}}$. The value of$n$is __________ . Your input ____ 3 JEE Advanced 2022 Paper 1 Online Numerical +3 -0 The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction${ }_{7}^{16} \mathrm{~N}+{ }_{2}^{4} \mathrm{He} \rightarrow{ }_{1}^{1} \mathrm{H}+{ }_{8}^{19} \mathrm{O}$in a laboratory frame is$n$(in$M e V$. Assume that${ }_{7}^{16} \mathrm{~N}$is at rest in the laboratory frame. The masses of${ }_{7}^{16} \mathrm{~N},{ }_{2}^{4} \mathrm{He},{ }_{1}^{1} \mathrm{H}$and${ }_{8}^{19} \mathrm{O}$can be taken to be$16.006 u, 4.003 u, 1.008 u$and$19.003 u$, respectively, where$1 u=930 \,\mathrm{MeVc}^{-2}$. The value of$n$is ________ . Your input ____ 4 JEE Advanced 2022 Paper 1 Online Numerical +3 -0 In the following circuit$C_{1}=12 \mu F, C_{2}=C_{3}=4 \mu F$and$C_{4}=C_{5}=2 \mu F$. The charge stored in$C_{3}$is ____________$\mu C\$.