1 A student measures the time period of 100 oscillatons of a simple pendulum four times. The data set is the 90s, 91s, 92s and 95s. If the minimum division in the measuring clock is 1s, then the reported mean times should be A) $(92\pm2s)$ B) $(92\pm5s)$ C) $(92\pm1.8s)$ D) $(92\pm3s)$
2 A person trying to lose weight by burning fat lifts a mass of 10kg up to a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8 × 107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate (Take, g=9.8 ms-2) A) $2.45 \times 10^{-3}kg$ B) $6.45 \times 10^{-3}kg$ C) $9.89 \times 10^{-3}kg$ D) $12.89 \times 10^{-3}kg$
3 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) $n=\frac{C-C_{V}}{C-C_{P}}$
4 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 $b_{min}=\sqrt{4\lambda L}$
5 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
6 For a common emitter configuration if α and β have their usual meaning the incorrect relationship between α and β is A) $\frac{1}{\alpha}=\frac{1}{\beta}+1$ B) $\alpha =\frac{\beta}{1-\beta}$ C) $\alpha =\frac{\beta}{1+\beta}$ D) $\alpha =\frac{\beta^{2}}{1+\beta^{2}}$
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 A wire of length 2 units is cut into two parts which are bent respectively to form a square of side =x units and a circle of radius =r units. If the sum of the areas of the square and the circle so formed is minimum, then A) $2x=(\pi+4)r$ B) $(4-\pi)x+4)=\pi r$ C) x=2r D) 2x=r
9 $\lim_{n \rightarrow \infty}[\frac{(n+1)(n+2)...3n}{n^{2n}}]^{1/n}$ is equal to A) $\frac{18}{e^{4}}$ B) $\frac{27}{e^{2}}$ C) $\frac{9}{e^{2}}$ D) 3 log 3-2
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 The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is A) $\frac{4}{3}$ B) $\frac{4}{\sqrt{3}}$ C) $\frac{2}{\sqrt{3}}$ D) $\sqrt{3}$
12 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
13 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
14 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 $[CoCl_4]^{2-}$
