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Physics
A large heavy box is sliding without friction down a smooth plane of inclination . From a point P on the bottom of the box, a particle is projected inside the box. The initial speed of the particle with respect to the box is u, and the direction of projection makes an angle with the bottom as shown in figure. Find the distance along the bottom of the box between the point of projection P and the point Q where the particle lands. (Assume that the particle does not hit any other surface of the box. Neglect air resistance.) If the horizontal displacement of the particle as seen by an observer on the ground is zero, find the speed of the box with respect to the ground at the instant when particle was projected.
Chemistry
(Subjective Type) In the Arrhenius equation for a certain reaction, the value of A and E_a (activation energy) are 4 x 10¹³ sec^-1and 98.6 kJmol^-1 respectively. If the reaction is of first order, at what temperature will its half-life period be ten minutes? IIT 1990)
Mathematics
Let be the roots of the quadratic equation ax² + bx + c = 0 and . If are in G.P. Then, (IIT 2005)

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