ANSWERS, HINTS & SOLUTIONS PART TEST II

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1 AITS-PT-II-PM-Sol -JEE(Main)/8 FIITJEE JEE(Main)-8 ANSWES, INTS & SLUTINS PAT TEST II (Main) ALL INDIA TEST SEIES Q. No. PYSIS Q. No. EMISTY Q. No. MATEMATIS.. 6. A.. 6. A. D A. A D D 67. D D. 4. A A 7.. A 4. D A A A A A D A 8. A 48. D D. D 8. A A D A. 8. D D A D 9. D D FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

2 AITS-PT-II-PM-Sol-JEE(Main)/8 Physics PAT I T T T In the pocess, PT = constant PP V = constant PV = constant mola heat capacity, = v x Q = nt = (T T ) T QA T Q T. QA = npt =. In steady state Q dt ka t dx Q dt TA t dx T Q dx A TdT t T Q 4AT t (i) Similaly, / T Q dx A TdT t T Q (9T T ) A t Dividing (ii) by (i) 9T T 4T T T T T. Given PT = constant T T constant V V = kt 4 The coefficient of themal expansion is dv 4kT 4 VdT 4 kt T T T T + dt T (ii) x dx FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

3 AITS-PT-II-PM-Sol -JEE(Main)/8 4. Equilibium tempeatue of mixtue is. Total heat eleased by wate = mwsw = 4 = kcal eat taken by ice to incease its tempeatue fom to = 4. = 4 kcal mass of ice melted = 4 6 kg 8 8 wate content in the equilibium mixtue = + = 7 kg. Given = V + T T dv V V T V dt T dv dt nk V T n(kv) T kv e Ve T = constant 6. The net electic potential due to extenal chage inside the cavity and the induced chage on the suface of the cavity at any point outside the cavity is zeo. If V is the electic potential due to induced chage on the suface of cavity at point P. kq V a kq V a 7. dt 4 ms AT dt 4 dt S 4 T dt T / 4 dt S 4 T T T T / T t dt t S 8 9t T S T 7S t 9 T 8. The electic field due to P at the position of P is KP E foce of inte action between the dipoles is FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

4 AITS-PT-II-PM-Sol-JEE(Main)/8 4 de F P d kp P F = 4 9. dq ds T T ds ncp T dt T S 4 n n J/k. The electic flux though the ight end plane suface. q q 4 PS ( cos ) 4 q PS ence, the electic flux though the cuved suface of the cylinde is q S PS = q q 4q q S. k(q) kq k(q)q Ui a 4a a kq kq a 4a kq Ui 4a k(q) 9kQ Uf 4a 4a Total heat dissipated, = Ui Uf kq 9kQ 4a 4a 4kQ kq 4a a FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

5 AITS-PT-II-PM-Sol -JEE(Main)/8. q q 4 q 6q 9 q = 7 magnitude of chage flown though the battey is q = 7 = = V q q q 4 4 q = F = F q q = F. The electic potential of shell is zeo V = kq kq a 4a Q q A q q a Q + q 4a a 4. The cell will delive maximum powe to the netwok if eq = =. The equivalent cicuit just afte closing the switch S is eq = + = I A eq = V 6. Since the paticle exists the magnetic field egion with a velocity v (i ˆ j) ˆ m/s tan The angula displacement of the paticle in the magnetic field egion is Angula velocity, = q m m t q FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

6 AITS-PT-II-PM-Sol-JEE(Main)/ Since is constant in the egion The net magnetic foce expeienced by the conducting wie MN is F ILeff Whee, L ˆ eff 6i F I6i ˆ ( k) ˆ F 6I( ˆj) 8. The net magnetic moment of the loop is M I (i ˆ k) ˆ The net magnetic toque expeienced by the loop is M = I (i ˆ k) ˆ j ˆ I (kˆ ˆi) 9. The net magnetic field at the cente of the cicula ac is I I I I I 8 8 = I 8. When jd 4 when >, jd d at, at =, 8, > j = FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

7 7 AITS-PT-II-PM-Sol -JEE(Main)/8. The emf induced between the points A and D is ( v) eff a v sin4 v = a va a. When d E dt d kt E dt d k E, when When > d E d dt d E dt ktd k E, whee > at, E at =, E E E k k 6 E = kt E E. q v q ( v ) dv Now, m i dt mdv = idt v q m dv dq mv = q S q +q M N m, v mv q Fom (i) and (ii) mv v (ii) FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

8 AITS-PT-II-PM-Sol-JEE(Main)/8 8 v (m ) 4. E = d (kt ) dt k E, at = a ka E To keep the ing stationay qea = mga qka mg kqa mg min kqa mg E = kt a E E q, m. When the cuent though the inducto is maximum di VL L dt ence capacitos A and will be in paallel Now, using consevation of enegy max Li 4 Limax i 4 max L i max +/ / A +/ / di di 6. L L dt dt i i L di L di L i L i (i) i i i (ii) L i i L L L i i and i L L L L L i U LL L U L L LL i i FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

9 9 AITS-PT-II-PM-Sol -JEE(Main)/8 7. ms cuent though esisto is I(ms) A Aveage powe developed in the esisto is P I(ms) 6. W 4 8. uent though the potentiomete wie is 6 I 6 V ( ) 8 + = 9 = 4 9. Let the initial chage on the spheical conducto A is Q. kq V a kq = Va (i) When switch S is closed, the total chage Q will appea on the oute suface of shell. Final potential of the spheical conducto A is kq Va V V 6a 6a 6. Given pocess is VT = constant VP V = constant PV / = constant mola heat capacity V x = / eat supplied to the gas is Q = nt = Incease in intenal enegy of the gas is U = nvt = U The atio Q FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

10 AITS-PT-II-PM-Sol-JEE(Main)/8 hemisty PAT II. N N N N N. The caboxylic acid goup stabilizes the conjugate base and I of othe goups at closest distance. 4. Total chial centes = n = = 8. In all alkyl goups ae at equatoial positions so most stable. Most stable will have least heat of combustion. 7. Glyptal is made fom polymeization of ethylene glycol and pthalic acid. 8. N MeI excess N + Me N Me Moist Ag 9. NMe l l FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

11 AITS-PT-II-PM-Sol -JEE(Main)/8 4. D D D D D D D 44. All l l l h l x GI 4 I GI 4 I l FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

12 AITS-PT-II-PM-Sol-JEE(Main)/8 l l l h l y l Na Na. Me Me e d P N N 4 N N Me. N Mg Mg Elimination FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

13 AITS-PT-II-PM-Sol -JEE(Main)/8. l Alc. AgN Agl l l Na l xidation.. 6. l l l l + l l + l In cis fom attaction between both chloine leads to stability. Tollen's eagent white ppt. / Me Et LA / 7. (ii), (vi) will not give annizzao test. 8. ate of eaction depends upon migation aptitude. 6. Intemolecula aldol eaction. FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

14 AITS-PT-II-PM-Sol-JEE(Main)/8 4 Mathematics PAT III 6. tan tan = = p p q q tan ptan q p p q p q q q p q p p q q q q 6. f(x) = (x )(x cos )(x sin ) + + = + sin + cos = 6. x (x + ) = x 4 + x x 9x + 6 = (x + x 4)(x + x ) + = 64. x = cos, y = sin sin cos (cos sin ) = 4 cosec 4 4 sin sec cosec sec cosec a = b a + b = 66. ab x cos a b a b ab sin ab sin ab sin cos xsin a b a b abc a b 4 sin A sin A b I a 67. cos x = o sin x x x o x n infinite solution x 68. f x cosec x = cosec x cot x cot x 4 cot x cot x ; x n, n I FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

15 AITS-PT-II-PM-Sol -JEE(Main)/8 99 x n,,,..., Sum = 69. p =, a = 4 b = 4 p =, a = 4 c = 4 is isosceles A 4 4 s a = = s b, 7. 4 tan tan tan 4 4 n 4 tan tan n tan 4 4 tan tan 4 = tan tan A x cos x sin x sin x Max A 7. x A x 7. Lines intesect at, which is cente of equied cicle. Given cicle x + y 4x y = whose cente is,, Fo just sufficient cicle d = 9 9 k k = If acute angle = cos a a d a a d a cos d a a cos acos Similaly, d a cos asin and dd = a 4sin cos sin FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

16 AITS-PT-II-PM-Sol-JEE(Main)/ Let log tan x t t, t < t t t t + t = t, log tan x tan x x 6 7. sin sin A a tan tan coscos coscos coscos cos cos = k Locus of othocente is a line paallel to 76. a = SP = a a = 77. (, ) lies on y + x =. ence only one ational point 78. x y y x y = distance between (x, y) and (, ) The distance fom (x, y) to x y + = is x y x y x y e fo hypebola < 79. ab a b a b 4 a b a 4 fo a =, a = 6, b = 8 ab 4 8. D = + = + x x 9 = x + x + 9 x + x = x = A x D 8. cos sin 4 8. PA P A is a diamete FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

17 7 AITS-PT-II-PM-Sol -JEE(Main)/8 8. b tan a sec b tan e PA P PA P PA + P PT y y a x c =, = and 4( + ) = + = = Equation of tangent is x cos y sin S cos sin. It is minimum at thocente (h, k) = a at t tt, att t t whee t t k = a(t + t) k h a at t tt a a a ah = a + k 88. Sides of squaes will be pependicula tangents to the ellipse. So vetices of squae will lie on diamete cicle Diamete of cicle = a + a + = a a = ut a > and a > 4 a 89., A = º, = 7º a a 4 a a 9. a b 4 4 A FIITJEE Ltd., FIITJEE ouse, 9-A, Kalu Saai, Savapiya Viha, New Delhi -6, Ph 466, 66949, Fax 694

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