1. A projectile is fired at an angle 60◦ with some velocity u. If the angle is changed infinitesimally, let the corresponding fractional changes in the range and the time of flight be x and y, respectively, Then y is (A) (B)
2 x 3 − 23 x
(C) 2x
(D) −2x 2. A ball is dropped down vertically from a tall building. After falling a height h it bounces elastically from a table inclined at an angle θ and hits a wall at a distance d from the point of earlier impact horizontally, then
h d θ
(A) θ = (1/2) sin−1 (2d/h) (B) θ = (1/2) tan−1 (d/h) (C) θ = (1/4) sin−1 (d/h) (D) θ = (1/2) tan−1 (2d/h) 3. A photon with an initial frequency 1011 Hz scatters off an electron at rest. Its final frequency is 0.9 × 1011 Hz. The speed of the scattered electron is close to (h = 6.63 × 10−34 Js, me = 9.1 × 10−31 kg) (A) 4 × 103 m s−1
(B) 3 × 102 m s−1
(C) 2 × 106 m s−1
(D) 30 m s−1
Space for rough work
ET-21
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SET-A