1 A point particle of mass m moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals µ. The particle is released from rest, from point P and it comes to rest at a point R. The energies lost by the ball, over the parts PQ and QR of the track, are equal to each other and no energy is lost when particle changes direction from PQ to QR. the values of the coefficient of friction µ and the distance x (=QR), are respectively close to A) 0.2 and 6.5 m B) 0.2 and 3.5 m C) 0.29 and 3.5m D) 0.29 and 6.5 m
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 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
4 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) $\sqrt{2}s$
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 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.
7 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
8 The system of linear equation $x+\lambda y-z=\alpha, hx-y-z=\alpha, x+y-\lambda z=0$ has a non-trivial solution for A) infinitely many values of ? B) exactly one values of ? C) exactly two values of ? D) xactly three vales of ?
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 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
11 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
12 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 $ $min^{-1}$
13 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 $[CoCl_4]^{2-}$
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) $[Co(NH_{3})_{3}Cl_{3}]$