1 A satellite is revolving in a circular orbit at a height h from the Earth's surface (radius of earth R, h<<R). The minimum I lease in its orbital velocity required so that the satellite could escape from the earth's gravitational field, is close to (neglect the effect of the atmosphere.) A) $\sqrt{2gR}$ B) $\sqrt{gR}$ C) $\sqrt{gR}/2$ D) $\sqrt{gR}(\sqrt{2}-1)$
2 A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance $\frac{2}{3}$ A from the equilibrium position. The new amplitude of the motion is A) $\frac{A}{3}\sqrt{41}$ B) 3A C) $A\sqrt{3}$ D) $\frac{7}{3}A$
3 Two identical wires A and B, each of length l, carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side a. If BA and BB are the values of the magnetic field at the centers of the circle and square respectively. then the ratio $\frac{B_{A}}{B_{B}}$ is A) $\frac{\pi^{2}}{8}$ B) $\frac{\pi^{2}}{16\sqrt{2}}$ C) $\frac{\pi^{2}}{16}$ D) $\frac{\pi^{2}}{8\sqrt{2}}$
4 An arc lamp requires a direct current of 10A at 80 V to function. If it is connected to a 220V (rms) , 50Hz AC supply, the series inductor needed for it to work is close to A) 80H B) 0.08H C) 0.044 H D) 0.065 H
5 An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears A) 10 times taller B) 10 times nearer C) 20 times taller D) 20 times nearer
6 Half-lives of two radioactive elements A and b are 20 min and 40min respectively. Initially, the samples have an equal number of nuclei. After 80min. the ratio of decayed number of A and B nuclei will be A) 1:16 B) 4:1 C) 1:4 D) 5:4
7 If $f(x0 +2f(\frac{1}{x})=3x, x\neq 0$ and $S= [x\epsilon R:f(x)=f(-x)]:$ then S A) is an empty set B) contains exactly one element C) contains exactly two element D) contains more than two elements
8 If the number of terms in the expansion if $(1-\frac{2}{x}+\frac{4}{x^{2}}), x\neq 0, is 28$ . then the sum of the coefficients of all terms in this expansion is A) 64 B) 2187 C) 243 D) 729
9 If the line, $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane, lx+my-z=9, then $l^{2}+m^{2}$ is equal to A) 26 B) 18 C) 5 D) 2
10 Which of the following is an anionic detergent? A) (a) Sodium lauryl sulphate B) (b) Cetyltrimethyl ammonium bromide C) (c) Glyceryl oleate D) (d) Sodium stearale
11 The species in which the N-atom is in a state of sp hybridization is A) $NO_{2}^{-}$ B) $NO_{3}^{-}$ C) $NO_{2}$ D) $NO_{2}^{+}$
12 Decomposition of H2O2 follows a first-order reaction. In 50 min, the concentration of H2O2 - decreases from 0.5 to 0.25 in one such decomposition. When the concentration of H2O2 reaches 0.05 M, the rate of formation of O2 will be A) $6.93\times 10^{-4} mol $ $min^{-1}$ B) $2.66 L /min$at STP C) $1.34\times 10^{-2} mol$ $min^{-1}$ D) $6.93\times 10^{-2} mol $ $min^{-1}$
13 The hottest region of Bunsen flame shown in the figure given below is A) region 2 B) region 3 C) region 4 D) region 1
14 The equilibrium constant at 298 K for a reaction $A+B \rightleftharpoons C+D$ is 100. If the initial concentrations of all the four species were I M each, then the equilibrium concentration of D(in Mol L-1) will be A) 0.818 B) 1.818 C) 1.182 D) 0.182
15 Which one of the following statements about water is false? A) Water can act both as an acid and as a base B) There is extensive intramolecular hydrogen bonding in the condensed phase C) Ice formed by heavy water sinks in normal water D) Water is oxidized to oxygen during photosynthesis
