ANSWERS, HINTS & SOLUTIONS HALF COURSE TEST VII (Main)

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1 AIITS-HT-VII-PM-JEE(Mai)-Sol./7 I JEE Advaced 06, FIITJEE Studets bag 6 i Top 00 AIR, 7 i Top 00 AIR, 8 i Top 00 AIR. Studets fom Log Tem lassoom/ Itegated School Pogam & Studets fom All Pogams have qualified i JEE Advaced, 06 FIITJEE ALL INDIA INTEGRATED TEST SERIES ANSWERS, HINTS & SOLUTIONS HALF OURSE TEST VII (Mai) JEE(Mai)-07 Q. No. PHYSIS HEMISTRY MATHEMATIS. A A. A B B. B B. B. A B 6. A A 7. A B B 8. A A 9. D A D 0. D B B. B B A. B B D. A A. D B. D D 6. D B 7. B A 8. B D D 9. A B 0. B A. B A. A A B. B B. A D. 6. A A B 7. A D B 8. D B D 9. D B 0. D A D FIITJEE Ltd., FIITJEE House, 9-A, Kalu Saai, Savapiya Viha, New Delhi -006, Ph , 6699, Fa 69

2 AIITS-HT-VII-PM-JEE(Mai)-Sol./7 Physics PART I SETION A. oside a abitay momet whe the wedge has tavelled a distace ito egio II. The aea of the top suface iside the egio II = a sec Foce o it = a sec P = a sec [P =] ompoet of the foce opposite velocity = a sec. si = a ta. If it futhe moves by d the the wok doe = a ta d v 0 = b mv 0 ata d 0 abh M h. S A = v 0 t Agt S B = v 0 t Bgt S A S B = L t = L g B A. Fist law of motio.. Fo vetical oscillatio time peiod T = m k... () Fo the tasvese oscillatio peiod of simple pedulum T = But T = T k = mg g GMm. mv 0 v = gr R 6. Tesio i the stig T = mg F B = vg vg = vg Balacig toque kr/ = TR = T/k = vg/k 7. mg T ma () m a T () g mg Fom () ad (), a & T mg FIITJEE Ltd., FIITJEE House, 9-A, Kalu Saai, Savapiya Viha, New Delhi -006, Ph , 6699, Fa 69

3 AIITS-HT-VII-PM-JEE(Mai)-Sol./7 9. Let V ad V y be compoets of velocity. At cotact poit A ad B, the velocity alog omal should be same. o o o ucos60 V cos0 V cos 60. () v u y 60 o V u v V V y u 60 o 0 o V y. Now dowwad foce o the ight block is moe. T T mg mg. I = I 0 + M(O) = I 0 + M(OB + B ) = I B + M(B). = RT M d =. dt = RT M 0 0 T T R L 0 T 0 dt 0 L M A T 0 d L B T L L t ( T T ) L 0 M R. Fom cosevatio of agula mometum mr R cos tat 0 R = R T R T = T. oceptual, toque of pseudo foce. 9 0 RT RT M M y y P(,t) F t FIITJEE Ltd., FIITJEE House, 9-A, Kalu Saai, Savapiya Viha, New Delhi -006, Ph , 6699, Fa 69

4 AIITS-HT-VII-PM-JEE(Mai)-Sol./7 hemisty PART II SETION A. Ode of Pk a value is IV > III > II > I. 8. Requied cis diol. 9. Thee ae thee steeocete. = 8. Due to +ve chage o N.. Bomiatio at cabo.. ad ae aomatgic due to ( + ) ule. 9. l, OOH, NO ae electo with dawig goup. 0. The itemediate cabocatio become atiaomatic.. Due to p - p backbodig.. Ode of stability A > B > D >. 0. l has o vacat p ad d-obital. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Saai, Savapiya Viha, New Delhi -006, Ph , 6699, Fa 69

5 AIITS-HT-VII-PM-JEE(Mai)-Sol./7 Mathematics PART III SETION A. Family of lie passes though focus hece latus ectum will make shotest itecept.. Sice. + < 0, so si cos + 0 si cos si Maimum value of si is 0.. Give equatio of lies y y 0 y y y 0 y y 0 y, y APO 7 Legth of chod of cotact AB si7 6 sicos0 si0cos = 6 6. O A P B. Let z = + iy E zz (z ) z (z 6i) z 6i = = zz z z 9 6z zi 6 Emi 0 whee = ad y = y (999)! 999! 999! 999! log log log log... +log 999 log log 999! 999! 999! 6. Numbe of ways of choosig fist couple is Numbe of ways of choosig secod couple is = ( )(() ) y 7 ( ) (y ) y + 7 = 0 ad ecceticity is. is a ellipse, whose focus is (, ), diecti FIITJEE Ltd., FIITJEE House, 9-A, Kalu Saai, Savapiya Viha, New Delhi -006, Ph , 6699, Fa 69

6 AIITS-HT-VII-PM-JEE(Mai)-Sol./7 6 Legth of fom focus to diecti is ( ) 7 a ae e a 0 a a So legth of majo ais is 0 8. Majo ais of hypebola bisects the asymptote equatio of othe asymptote = y equatio of hypebola (y )( y) + k = 0 it passes though (, ) equied equatio + y y + 0 = ta ta ta + ta + = ta + ta ta + ta ta + = (ta ta ) + (ta ta ) + =. 0. The maimum value of cos (cos ) is ad that of si (si) is si, both eists fo = /. Hece maimum value is + si. z. Sice diagoals ae pepedicula to each othe ag z z z z z = ik(z z ). =. H = d ta, ad H h = d ta 60 ta 60 h ta 60ta 60ta 60si h h ta si cos cos cos = cos si h d H = 60 m. ( ) 00 = 00 c 00 c c 00 lealy ca ot be of e fom t Let cete be (, ) ( ) = = = 6 + = Let cete be (, ) ( ) = + = + = 0 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Saai, Savapiya Viha, New Delhi -006, Ph , 6699, Fa 69

7 7 AIITS-HT-VII-PM-JEE(Mai)-Sol./7 6 8 Also let cete be (, ) ( + ) = = Radius of lage cicle is y y 6. tab, tab A B = B + B y y y tab y y y y cotb ; similaly y y cot y B B B y y cot B + cot = y. y 7. t = = ( )( ) = ( ) ( ) ( )( ) 0 t = 0 8. O solvig the biquadatic, we get si = which is eve possible sice + is geate tha ad is egative. 9. Sice a, b, c ae thee cosecutive positive iteges theefoe b = a + c b = (a + c) = (a c) + ac ( c a = ) b = ( ) + ac b = + ac Now = loge a loge c... ac ac loge a loge c... ac ac ac = log ac e ac log e loge ac loge ac ac = loge ac loge b loge b FIITJEE Ltd., FIITJEE House, 9-A, Kalu Saai, Savapiya Viha, New Delhi -006, Ph , 6699, Fa 69

8 AIITS-HT-VII-PM-JEE(Mai)-Sol./ Let S = = a. () 0 0 Let S = = = S = = a a Fom S = a = a. Poduct of slope of diagoals = PQRS is a hombus. y y. log 0 + log 0 y y 00. Now y + y 00.. (0) 00 = (00 + ) 00 = (00) + 00 (00) + = 0 [ ] =.. Sice a, a, a, a ae the oots of give equatio, we have + p + q + p + q = ( a ) ( a ) ( a ) ( a ) puttig = i, we get pi q + pi + q = (i a ) (i a ) (i a ) (i a ) takig modulus of both sides we get a a a = a. + = cos (a + b) ( ) + = cos (a +b) cos (a + b) = whe =, a + b =, etc. 6. Equatio () ( + a) = = a Equatio () ( + b) = = b lealy, b. So eactly oe oot commo meas b + = a o b = a + a b = o a b =. 7. z + is eal z + eal z is eal Let z =, R The + = Give equatio epesets eal cicle if si + cos > 0 si + cos > which is ot possible. 9. Take log 0 = t takig log of both sides t t + > log 0 = t t t 0 t > o t < 0 > 0 o <. t log0 log t 0. If y =, the takes values fom to ad z takes the values fom 0 to (i.e values). Thus fo each values of y ( y 9), ad z take ( ) values Hece the thee digits umbes of the fom yz = 0 9. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Saai, Savapiya Viha, New Delhi -006, Ph , 6699, Fa 69

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