iitjee 2006
iitjee 2006 iitjee 2006
Q.18 f(t) = Asin 2 ωt + Bcos 2 ωt + CsinωtcosωtThe above function represents SHM(a) for all values of A and B, with C ≠ 0(b) A = –B, C = 2B; with amplitude √2 B(c) A = B, C = 2B; amplitude |B|(d) A = B, C = 0 Ans. (b, c)Section III:Questions based on comprehensionswith one correct answer.PASSAGE - 1A tank has a cylindrical opening as shown ofdiameter 2r. A cylinder of diameter 4r and densityρ/3 is placed on the top of the opening as shown infigure. Liquid of density ρ is to be filled in the tank.Q.19 The graph between1 and stopping potentialλh 1h h 24rdisc(V) of three metal having work functions φ 1, φ 2and φ 3in an experiment of photo electric effectis plotted as shown in the figure which of thefollowing statement(s) is/are correct ?(λ represents wavelength of the incident ray.)vmetal 1 metal 2 metal 3θ0.001 0.002 0.0041 –1nmλ(a) Ratio of work functions φ 1: φ 2:φ 3= 1: 2 : 4(b) Ratio of work functions φ 1: φ 2: φ 3= 4:2 : 1(c) tan θ is directly proportional to hc/e, whereh is plank's constant and c is the speed oflight(d) the violet color can eject photoelectrons frommetal 2 & 3. Ans. (a, c)Q.20 A black body at temperature T is kept in a darkroom with surrounding temperature T 0. Sunrays are allowed to fall on the black body througha hole in the roof of the room while T and T 0aremaintained. Assuming that there is no changein the surrounding temperature of the room,select the correct statement(s).(a) The quantity of radiation absorbed by theblack body per unit time will increase(b) The quantity of radiation emitted by blackbody per unit time will increase(c) Black body radiates more energy per unittime in the visible spectrum(d) The reflected energy per unit time by theblack body remains same Ans. (d)CAREER POINT, 112, SHAKTI NAGAR , KOTA (RAJ) PH. 25004924Q.21 What is the height h 1of the liquid level for themass to be lifted.(a)(c)5hh 1 =42hh 1 =32r(b)(d)5hh 1 =35hh 1 =2Ans. (b)Q.22 The disc is kept pressed and water is loweredin the tank upto the height 'h 2' as shown, whatis the height h 2for the disc to be again lifted.(a)(c)h32h34h(b) 9(d) h Ans. (b)Q.23 Water is still lowered in the tank, what is theanother height h' 2, for the disc to be lifted ?hh(a) (b) 3 4h(c) 5(d) no height h' 2at which disc will be liftedAns. (d)PASSAGE-2Equations of two waves are given asy 1= A cos[0.5πx - 100 πt)y 2 = A cos[0.46πx - 92 πt)Q.24 How many maximum will a stationary observerhear ?(a) 4 (b) 5(c) 6 (d) 7Ans. (a)PAPER - IIT-JEE-2006
Q.25 Resultant wave is given as y R= y 1+ y 2at x = 0.How many times is the resultant y Rzero in 1sec.(a) 100 (b) 192(c) 46 (d) 96Ans. (d)Q.26 Maximum velocity of the wave having maximumintensity.(a) 200 m/s(c) 192 m/s(b) 180 m/s(d) 100 m/sAns. (a)PASSAGE-3The capacitor of capacitance C can be charged(with the help of resistance R) by a battery ofe.m.f. V while keeping switch S 2open. Thecapacitor can be connected to an inductor ofinductance L by closing switch S 2and openingS 1.VQ.29 If maximum charge stored on the capacitor inLC circuit is Q 0then for t ≥ 0.(a) the charge on the capacitor⎛ π 1Q = Q 0cos⎟ ⎞⎜ − t⎝ 2 LC ⎠2d Q(b) the charge on the capacitor is Q = –LCdt 2(c) the charge on the capacitor is⎛ π 1Q = Q 0cos⎟ ⎞⎜ + t⎝ 2 LC ⎠(d) the charge on the capacitor is21 d QQ = –2LC dtAns. (b)RLQ.27 Initially the capacitor was uncharged, Nowswitch S 1is closed and S 2is kept open. If timeconstant of the given circuit is τ then(a) After 1 time constant, charge on thecapacitor is CV/2(b) After time interval 2τ, charge on the capacitoris CV(1 – e –2 )(c) The work done by the voltage source will behalf of the heat dissipated, when thecapacitor is fully charged(d) After 2 time constant, charge on thecapacitor is CV(1 – e –1 )Ans. (b)Q.28 After the capacitor gets fully charged, S 1isopened, and S 2is closed so that the inductoris connected in series with the capacitor, then(a) at t = 0, energy stored in the circuit is purelyin the form of magnetic energy(b)direction of current is same for any time t(c) at t > 0, there is no exchange of energy takesplace between the inductor and capacitorC(d) maximum current in the circuit is vLAns. (d)CS 1S 2PASSAGE - 4A number of designs have been developed formagnetic leviation. In one of the designselectrodynamic system (EDS) is used. This modelis conceptually simple because it depends only onthe attractive force between magnets andferromagnetic materials. In Japan the magneticlevitated trains run based on the EDS model whichuses Lenz's Law in the simplest form. The traincarries a magnet. As the magnet passes over ametal plate or coils of wire currents are induced inthe plates or coils that tend to oppose the originalchange this results in repulsive force which lifts thetrain. This model has a stabilizing feature that if thetrain drops the repulsion becomes stronger andpushes the train back up. If the train rises the foredecreases and the train drops down. In Maglev Trainthe dissipative forces against friction are absent. Thedisadvantage of this modal is that induced currentresults in drag force as well as lift force. This requiresmore power for propulsion The drag force is largerthan the lift force for small speed, but the drag forcemaximizes at some speed and then begins todecrease. The lift force continues to increase as thespeed increases. Thus it is advantageous to travelat high speed, but the significant drag force at lowspeed must be overcome as the train starts up.Q.30 What causes the train to lift up -(a) Electrostatic force(b) Time varying electric field(c) Magnetic force(d) Induced electric fieldAns. (c)CAREER POINT, 112, SHAKTI NAGAR , KOTA (RAJ) PH. 25004925PAPER - IIT-JEE-2006
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Q.18 f(t) = Asin 2 ωt + Bcos 2 ωt + CsinωtcosωtThe above function represents SHM(a) for all values of A and B, with C ≠ 0(b) A = –B, C = 2B; with amplitude √2 B(c) A = B, C = 2B; amplitude |B|(d) A = B, C = 0 Ans. (b, c)Section III:Questions based on comprehensionswith one correct answer.PASSAGE - 1A tank has a cylindrical opening as shown ofdiameter 2r. A cylinder of diameter 4r and densityρ/3 is placed on the top of the opening as shown infigure. Liquid of density ρ is to be filled in the tank.Q.19 The graph between1 and stopping potentialλh 1h h 24rdisc(V) of three metal having work functions φ 1, φ 2and φ 3in an experiment of photo electric effectis plotted as shown in the figure which of thefollowing statement(s) is/are correct ?(λ represents wavelength of the incident ray.)vmetal 1 metal 2 metal 3θ0.001 0.002 0.0041 –1nmλ(a) Ratio of work functions φ 1: φ 2:φ 3= 1: 2 : 4(b) Ratio of work functions φ 1: φ 2: φ 3= 4:2 : 1(c) tan θ is directly proportional to hc/e, whereh is plank's constant and c is the speed oflight(d) the violet color can eject photoelectrons frommetal 2 & 3. Ans. (a, c)Q.20 A black body at temperature T is kept in a darkroom with surrounding temperature T 0. Sunrays are allowed to fall on the black body througha hole in the roof of the room while T and T 0aremaintained. Assuming that there is no changein the surrounding temperature of the room,select the correct statement(s).(a) The quantity of radiation absorbed by theblack body per unit time will increase(b) The quantity of radiation emitted by blackbody per unit time will increase(c) Black body radiates more energy per unittime in the visible spectrum(d) The reflected energy per unit time by theblack body remains same Ans. (d)CAREER POINT, 112, SHAKTI NAGAR , KOTA (RAJ) PH. 25004924Q.21 What is the height h 1of the liquid level for themass to be lifted.(a)(c)5hh 1 =42hh 1 =32r(b)(d)5hh 1 =35hh 1 =2Ans. (b)Q.22 The disc is kept pressed and water is loweredin the tank upto the height 'h 2' as shown, whatis the height h 2for the disc to be again lifted.(a)(c)h32h34h(b) 9(d) h Ans. (b)Q.23 Water is still lowered in the tank, what is theanother height h' 2, for the disc to be lifted ?hh(a) (b) 3 4h(c) 5(d) no height h' 2at which disc will be liftedAns. (d)PASSAGE-2Equations of two waves are given asy 1= A cos[0.5πx - 100 πt)y 2 = A cos[0.46πx - 92 πt)Q.24 How many maximum will a stationary observerhear ?(a) 4 (b) 5(c) 6 (d) 7Ans. (a)PAPER - IIT-JEE-<strong>2006</strong>
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