1 A roller is made by joining together two corners at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see the figure), with its axis perpendicular to CD and its centre O at the centre of the line joining AB and CD (see the figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to A) turn left B) turn right C) go straight D) turn left and right alternately
2 An ideal gas undergoes a quasi-static reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure p and volume V is given by pVn = constant, then n is given by (here Cp and Cv are molar specific heat at constant pressure and constant volume respectively) A) $n=\frac{C_{p}}{C_{v}}$ B) $n=\frac{C-C_{p}}{C-C_{v}}$ C) $n=\frac{C_{p}-C}{C-C_{v}}$ D) $n=\frac{C-C_{V}}{C-C_{P}}$
3 A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charge on the 4 µF and 9 µF capacitors ) at a point distant 30m from it, would equal to A) 240 N/C B) 360 N/C C) 420 N/C D) 480 N/C
4 The temperature dependence of resistance of Cu and undoped Si in the temperature range 300-400 K, is best described by A) Linear increase for Cu, linear increase for Si B) linear increase for Cu, exponential increase for Si C) linear increase for Cu, exponential decrease for Si D) Linear decrease for Cu, linear decrease for Si
5 The box of a pinhole camera of length L has a hole of radius a. I t is assumed that when the hole is illuminated by a parallel beam of light of wavelength λ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say bmin) when A) $a=\frac{\lambda^{2}}{L}$ and $b_{min}=(\frac{2\lambda^{2}}{L})$ B) $a=\sqrt{\lambda L}$ and $b_{min}=(\frac{2\lambda^{2}}{L})$ C) $a=\sqrt{\lambda L}$ and $b_{min}=\sqrt{4\lambda L}$ D) $a=\frac{\lambda^{2}}{L}$ and $b_{min}=\sqrt{4\lambda L}$
6 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
7 If the sum of first ten terms of the series $(1\frac{3}{5})^{2}+(2\frac{2}{5})^{2}+(3\frac{1}{5})^{2}+4^{2}+(4\frac{4}{5})^{2}+ ... is \frac{16}{5}m,$, then m is equal to A) 102 B) 101 C) 100 D) 99
8 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
9 Which of the following statements about low density polythene is false? A) (a) It is a poor conductor of electricity B) (b) Its synthesis required dioxygen or a peroxide initiator as a catalyst C) (c) It is used in the manufacture of buckets, dustbins etc. D) (d) Its synthesis requires high pressure
10 18 g of glucose (C6H12O6) is added to 178.2 g water. The vapor pressure of water (in torr) for this aqueous solution A) 76.0 B) 752.4 C) 759 D) 7.6
11 The pair have the same magnetic moment is[ at no. Cr=24, Mn=25, Fe=26 and Co=27] A) $[Cr(H_2O)_6]^{2+}$ and $[Fe(H_2O)_6]^{2+}$ B) $[Mn(H_2O)_6]^{2+}$ and $[Cr(H_2O)_6]^{2+}$ C) $[CoCl_4]^{2-}$ and $[Fe(H_2O)_6]^{2+}$ D) $[Cr(H_2O)_6]^{2+}$ and $[CoCl_4]^{2-}$
12 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
13 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
15 In the Hofmann-bromamide degradation reaction, the number of moles of NaOH and Br2 used Per mole of amine produce are A) 4 moles of NaOH and 2 moles of $Br_{2}$ B) 2 moles of NaOH and 2 moles of $Br_{2}$ C) 4 moles of NaOH and 1 mole of $Br_{2}$ D) 1 mole of NaOH and 1 mole of $Br_{2}$
