1 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) $\frac{9p_{0}V_{0}}{nR}$
2 Hysteresis loops for two magnetic materials A and B are as given below These materials are used to make magnets for electric generators, transformer core, and electromagnet core. Then, it is proper to use A) A for electric generators and transformers B) A for electromagnets and B for electric generators. C) A for transformers and B for electric generators D) B for electromagnets and transformers
3 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
4 A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement. it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet, if the main scale reading is 0.5mm and the 25th division coincides with the main scale line? A) 0.75mm B) 0.80mm C) 0.70 mm D) 0.50mm
5 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
6 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
7 $\lim_{n \rightarrow \infty}[\frac{(n+1)(n+2)...3n}{n^{2n}}]^{1/n}$ is equal to A) $\frac{18}{e^{4}}$ B) $\frac{27}{e^{2}}$ C) $\frac{9}{e^{2}}$ D) 3 log 3-2
8 If one of the diameters of the circle, given by the equation $x^{2}+y^{2}-4x+6y-12=0$, is a chord of a circle S, whose centre is at (-3,2), then the radius of S is A) $5\sqrt{2}$ B) $5\sqrt{3}$ C) 5 D) 10
9 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
10 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
11 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 $ $min^{-1}$
12 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 $[CoCl_4]^{2-}$
14 At 300 K and I atm, 15 mL of a gaseous hydrocarbon requires 375 mL air containing 20% O2 by volume for complete combustion. After combustion, the gases occupy 330 mL. Assuming that the water formed is in liquid form and the volumes were measured at the same temperature and pressure, the formula of the hydrocarbon is A) $C_{3}H_{8}$ B) $C_{4}H_{8}$ C) $C_{4}H_{10}$ D) None