Solution - Career Point

13. [B] Point P lies on the arms CD and AF so inclusionat P due to them is zero.Magnetic induction at p due to currents in ABand BC is given byµB 1 = B 2 = 0 isin 45º4π(2a)µ= 0 i(Q distance of p from AB or BC is8 2πa2a)similarly due to DE and EFµB 3 = B 4 = 0 iµsin 45º = 0 i⊗4πa4 2πaNet induction = 2(B 1 – B 3 )µ= 2 0 i8 2π a– µ 0 i4 2π a= – 2µ0 i8πa14. [C] v = rω = r × T2πor T =NowT p = km pq α4m= k2q2π rv2πm =qB=kmqm α = 4m p and q α = 2qvmαand T α = kqPP= 2k⇒ T α = 2T p or15. [D] i = i 0 (1 – e –t/τ )v ⎛ −i = ⎜ t1 − eR ⎜⎝L / Rm Pq ααT p = 21Tα⎞ ⎛⎟ 12 ⎜=⎟ ⎜1−e6⎠⎝−t(Q i = 1A given)⇒ t = 0.97 × 10 –3 s , i.e. t ≈ 1ms−38.4×106⎞⎟⎟ = 1⎠16. [A] Optical distance between fish and the bird isDifferentiating w.r.t.ds dy µdy= +dt dt´dt4 dyi.e. 9 = 3 + 3 dtdx 3or = 6 × = 4.5 ms–1dt 417. [A]1 ⎛ µ g =f ⎟ ⎞ ⎛⎜−1⎝ µ⎜m ⎠ ⎝1R−1 R 21 ⎞⎟⎠1 ⎛ 1.5 ⎞ ⎛ 1 1 ⎞ 1= ⎜ −1 ⎟⎠ × ⎜ − ⎟ =f ⎝1.75⎝ − R R ⎠ 3.5Ri.e. f = 3.5 R.In the medium it behaves as a convergent lens.18. [D] Reflection of light from plane mirror givesadditional path difference of λ/2 between twowaves.3λ π∴ Total path difference = + = 2λ2 2which satisfy the condition of maxima.Resultant intensity ∝ (A 2 + A 2 ) [Q I ∝ Α 2 ]4Α 2 = 4Ι19. [B] Hereλλ21( λ( λ00− λ1)2=− λ ) 15.4 ( λ0− 3.5×10or3.7 ( λ0− 5.4×10or λ 0 = 11.8 × 10 –7 mBut ω =eV02−7−7))= 12−34hcλ = (6.6×10 )(3×10 )= 1.05−7−19(11.8×10 )(1.6 × 10 )20. [D] Let whole the energy of electrons be convertedin x-rays. eV = hvor eV = λhc−34hc (6.6×10 )(3×10 )or λ = = eV−193(1.0 × 10 )(40×10 )i.e. λ = 3.1 × 10 –11 m or λ = 0.31 Åβ⎯ −21. [A] Here 88 Ra 222 ⎯⎯→α 86R 218 ⎯→ 87Fr 218β⎯ −⎯⎯→α 85Al 214 ⎯→ 80Rn 214⎯⎯→α 82Pb 2064α deceys and 2β decays.22. [A] A 1 = 4, A 2 = 3 and θ = 2π = 90º∴ Resultant amplitude,2 2A1 2 + 1 2Α = + A 2A A cos90º==23. [C] Using d sin θ = nλsin θ = θ = Dλ∴224 + 3 = 25 = 5 unitdy = nλD−7nD or y = λd88⎯⎯→α 84PO 2102 21 A2A +1×2×(6×10 )i.e.= 1.2 × 10 –3 = 1.2 mm−31×10Distance between first minima on either side ofcentrar maxima ∆y = 2y = 2.4 mm24. [B] For constructive inteferenceI max = ( I ) 21 + I 2 = ( 2 I + I ) 2XtraEdge for IIT-JEE 111APRIL 2010