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 A pendulum clock loses 12 s a day if the temperature is 40° C and gains 4 s a day if the temperature is 20° C. The temperature at which the clock will show the correct time and the coefficient of linear expansion α of the metal of the pendulum shaft are, respectively A) $25^{o}C , \alpha =1.85 \times 10^{-5}/^{o}C$ B) $60^{o}C , \alpha =1.85 \times 10^{-4}/^{o}C$ C) $30^{o}C , \alpha =1.85 \times 10^{-3}/^{o}C$ D) $55^{o}C , \alpha =1.85 \times 10^{-2}/^{o}C$
3 n moles of an ideal gas undergoes a process A and B shown in the figure. The maximum temperature of the gas during the process will be A) $\frac{9}{4}\frac{p_{0}V_{0}}{nR}$ B) $\frac{3}{2}\frac{p_{0}V_{0}}{nR}$ C) $\frac{9}{2}\frac{p_{0}V_{0}}{nR}$ D) $\frac{9p_{0}V_{0}}{nR}$
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 Arrange the following electromagnetic radiations in the order of increasing energy A.Blue light B.Yellow light C.X-ray D. Radio wave A) D,B,A,C B) A,B,D,C C) C,A,B,D D) B,A,D,C
6 A value of θ for which $\frac{2+3i\sin\theta}{1-2i\sin\theta}$ is purely imaginary , is A) $\frac{\pi}{3}$ B) $\frac{\pi}{6}$ C) $\sin^{-1}(\frac{\sqrt{3}}{4})$ D) $\sin^{-1}(\frac{1}{\sqrt{3}})$
7 Let $p=\lim_{x \rightarrow 0}(1+\tan^{2}\sqrt{x})^{\frac{1}{2x}}$, then $\log p$ is equal to A) 2 B) 1 C) $\frac{1}{2}$ D) $\frac{1}{4}$
8 The area (in sq units) of the region ${(x,y):y^{2}\geq2x, and x^{2}+y^{2}\leq 4x, x\geq0, and y\geq 0}$ is A) $\pi-\frac{4}{3}$ B) $\pi-\frac{8}{3}$ C) $\pi-\frac{4\sqrt{2}}{3}$ D) $\frac{\pi}{2}-\frac{2\sqrt{2}}{3}$
9 If curve y=f(x) passes through the point (1,-1) and satisfies the differential equation y(1+xy)dx=xdy , then f(-1/2) is equal to A) $-\frac{2}{5}$ B) $-\frac{4}{5}$ C) $\frac{2}{5}$ D) $\frac{4}{5}$
10 Two sides of a rhombus are along the lines, x-y+1=0 and 7x-y-5=0. If its diagonals interset at (-1,-2) then which one of the following is a vertex of this rhombus? A) (-3,-9) B) (-3,-8) C) $(\frac{1}{3},-\frac{8}{3})$ D) $(-\frac{10}{3},-\frac{7}{3})$
11 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
12 2-chloro-2-rnethylpentane on reaction with sodium methoxide in methanol yields A) Both I and III B) Only III C) Both I and II D) All of these
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 complexes shows optical isomerism? A) $cis[Co(en)_{2}Cl_{2}]Cl$ B) $trans[Co(en)_{2}Cl_{2}]Cl$ C) $[Co(NH_{3})_{4}Cl_{2}]Cl$ D) $[Co(NH_{3})_{3}Cl_{3}]$
