1 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) $n=\frac{C-C_{V}}{C-C_{P}}$
2 A uniform string of length 20m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (Take , g=10 ms-2) A) $2\pi\sqrt{2}s$ B) 2 s C) $2\sqrt{2}s$ D) $\sqrt{2}s$
3 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 $b_{min}=\sqrt{4\lambda L}$
4 Choose the correct statement A) In amplitude modulation, the amplitude of the high-frequency carrier wave is made to vary in proportional to the amplitude of the audio signal. B) In amplitude modulation, the frequency of the high-frequency carrier wave is made to vary in proportion to the amplitude of the audio signal. C) In frequency modulation, the amplitude of the high-frequency carrier wave is made to vary in proportion to the amplitude of the audio signal. D) In frequency modulation, the amplitude of the high-frequency carrier wave is made to vary in proportion to the frequency of the audio signal.
5 In an experiment for determination of the refractive index of a glass of a prism by i-δ plot, ut was found that a ray incident at an angle 35° suffers a deviation of 40° and that it emerges at an angle 790, In that case, which of the following is closest to the maximum possible value of the refractive index? A) 1.5 B) 1.6 C) 1.7 D) 1.8
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 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
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
10 A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. lf e and mare charge and mass of an electron, respectively, then the value of h/λ, where λ is the wavelength associated with electron wave) is given by A) $2meV$ B) $\sqrt{meV}$ C) $\sqrt{2meV}$ D) meV
11 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
12 The heats of combustion of carbon and carbon monoxide are - 393.5 and - 283.5 kJ mol-1, respectively. The heat of formation (in kI) of carbon monoxide per mole is A) 676.5 B) -676.5 C) -110.5 D) 110.5
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
14 The concentration of fluoride, lead, nitrate, and iron in a water sample from an underground lake was found to be 1000 ppb, 40 ppb, 100 ppm, and 0.2 ppm, respectively. This water is unsuitable for drinking due to the high concentration of A) lead B) nitrate C) iron D) fluroide
15 The pair in which phosphorus atoms have a formal oxidation state of +3 is A) pyrophosphorous and hypophosphoric acids B) orthophosphorous and hypophosphoric acids C) pyrophosphorous and pyrophosphoric acids D) orthophosphorous and pyrophosphorous acids
