2IIT1516MT5PC2MS1 PHYSICS, CHEMISTRY AND MATHEMATICS ClassII IIT-JEE Achiever 2015-2016 Centres Solutions to Test 05MainSSRVM- E, N, CMR, Sadhana Date 01-08-2015 PART I: PHYSICS Multiple choice questions with one correct alternative1.A steady beamof o-particles (q =2e) travelling with constant kinetic energy 20 MeV carries a current 0.25 A. If the beamis directed perpendicular to a plane surface, how many o-particles strike the surface in 2 sec.? (A) 1.5 1012(B) 1.5 1019(C) 1.5 108(D) 1.5 106

Ans (A)61219q it 0.25 10 2q 2ne, n , n 1.5 102e 2e 2 1.6 10 = = = = = 2.The terminal potential difference of a cell when short circuited is(A) E(B) E2(C) zero (D) E3 Ans (C)E EI , V E .r 0r r= = =3.AprotonentersinamagneticfieldofstrengthB(Tesla)withspeedv,paralleltothedirectionof magnetic lines of force. The force on the proton is(A) evB(B) zero(C) (D) evB2 Ans (B) Fm =Bqv sin u, u =0Fm =04.Proton and o-particle enter with same velocity at 90 in a uniformmagnetic field. Ratio of radius of their paths will be(A) 1 : 2(B) 2 : 1(C) 4 : 1(D) 1 : 4Ans (A) p ppm v 4m vr or rB e B 2eo = = pr1r 2o=5.A circular loop of mass mand radius r in a horizontal (XY plane) table as shown in figure. A uniformmagnetic field B is applied parallel to x-axis. The current I in the loop, so that its one edge just lifts fromthe table, is:(A) 2mgr B t(B) mgrB t (C) mg2 rB t(D) rBmgt Ans (B) The normal to the plane of coil makes 90 angle with the field direction.Therefore the torque on the coilr O I X Y 2IIT1516MT5PC2MS2 t =Bi A =Bi. tr2

Since only one edge lifts fromthe table, the torque required is mgr2=

2mgr mgBi r or i2 2 rBt = =t 6.A strong magnetic field is applied on a stationary electron, then(A) the electron moves in the direction of the field(B) the electron moves in an opposite direction(C) the electron remains stationary (D) the electron starts spinning Ans (C)No magnetic force acts on the stationary charged particle.7.Following figure (1) and (2) represent lines of force. Which of the following is correct statement?(A) Figure (1) represents magnetic lines of force(B) Figure (2) represents magnetic lines of force (C) Figure (1) represents electric lines of force (D) Both figure (1) and figure (2) represent magnetic lines of forceAns (A) In figure (1) the lines of force are closed curves, while in figure (2) the lines of force are open curves. Magnetic lines of force are closed curves while electric lines of force are open curves. Hence figure (1) represents magnetic lines of force.8.A long vertical wire in which a current is flowing produces a neutral point with the earths magnetic field at a distance of 5 cms from the wire. If the horizontal component of the earths magnetic induction is 0.18 gauss, then the current in the wire, is(A) 0.45 ampere (B) 4.5 ampere(C) 0.9 ampere(D) 0.036 ampere Ans (B)74 02i 2 10 2 iB . or 0.18 104 r 5 10 = =t i =4.5 A9.In a region of space the magnetic field B i 0.3j = , area A i 6j 3k = + is placed in this uniformfield. The magnetic flux | linked with this area is(A) 0.8 unit (B) 0.1 unit (C) 0.18 unit (D) +0.8 unitAns (A) B.A (i 0.3j).(i 6j 3k) | = = + | =1 1.8 =0.8 unit10. Acharge(q) passing through a uniformelectricfield(E) and uniformmagnetic field(B) remains undeflected. Which of the following variations would still let the charge to remain undeflected? (A) signs of q andB are changed (B) signs of q andE are changed(C) signs ofB and E are changed (D) all of theseAns (D) Weknowthatwhenacharge(q)passesthroughuniformelectricfield(E),thenitissubjectedto electrostatic force equal toqE. Similarly, when a charge (q) passes through uniformmagnetic field(B), thenitissubjectedtomagneticforceequaltoq(v B) ,wealsoknowthatthechargewillremain undeflected, if these two forces are equal and opposite.Therefore for charge to remain undeflected, the signs of q andB are changed.2IIT1516MT5PC2MS3 11. A length of wire carries a steady current. It is bent first to forma circular plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is(A) 1th4 the first value (B) remains same(C) four times its first value (D) 1th2 its first value Ans (C)L =2tr (for one loop) 01L i 2r ,B2 2L t= =t For two loop, 2 2tr' =L02 1L 2 ir , B 4B4 2r ' = = =' t 12. An electron is revolving in a circular orbit of radius r in a hydrogen atom. The angular momentumof the electron is L. The magnetic dipole moment associated with it is(A) eLm(B) eL2m (C) mLe(D) 2mLe Ans (B) 13. An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric filed along +X direction and a magnetic field along the +Z direction, then(A) positive ions deflect towards +Y direction and negative ions towards Y direction (B) positive ions deflect towards Y direction and negative ions towards +Y direction (C) all ions deflect towards +Y direction (D) all ions deflect towards Y direction Ans (D)14. Current flows through a cylindrical conductor of variable crossection carrying a current I as shown in the figure. Then(A) BP =BQ =BR (B) BP BR (D) BP =BP 0, then the maximumvalue of f(x) is equal to(A) 2e1(B) e 21 (C) e1(D) none of theseAns (A) By data, f(x) =x2 e2xx 2 2 x 2e x 2 xe 2 ) x ( f = ' 1 x or 0 x 0 ) x 1 ( e x 2 0 ) x ( fx 2= = = = ' Also 2x 2x 2xf (x) 2e (1 x) 4xe (1 x) 2xe '' = At x =0, 0 2 ) x ( f > = ' 'Also0e2e . 2 0 0 ) 1 ( f220(D)ab cd