Narayana IIT Academy

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1 INDIA Sc: LT-IIT-SPARK Dat: _P Max.Mars: 86 KEY SHEET PHYSIS A 5 D 6 7 A,B 8 B,D 9 A,B A,,D A,B, A,B B, A,B 5 A 6 D 7 8 A HEMISTRY 9 A B D B B 5 A,B,,D 6 A,,D 7 B,,D 8 A,B,,D 9 A,B, A,B, A,B,,D A,B, D D 5 D 6 A MATHS 7 A 8 B 9 A B A B, A,,D 5 A,B, 6 A, 7 A,B,,D 8 A,D 9 A,B,D 5 A,D 5 D 5 A 5 B 5 A

2 9--8_LT-IIT_JEE-Adv_6_P Ky&Sol s PHYSIS. If r is th saratio btw A ad B or B ad, th forc r uit lgth i i A, i i F FB, F i i r r r r r r larly, FB F FA. I loo : O B. dl = i i i i loo : O B. dl = i i loo : O B. dl = i i i O B. dl = i i loo : i i t r ii. dl cos r vy ta or v. F.. 5. x cos 6 I a a a a a 5 5 cos I a a a a a cos I a a a a a cos 6 I a a a a a 6. x 5d / 5d ad x d d x x x 5d d d 7. I cas I ad II, th iducd mf, Bv l I cas III ad IV, th iducd mf, Bvl 8. Us Lz s law to gt th aswr. 9. Accordig to th giv data, Th iducd mf across th rod, Bvl si r Th quivalt rsistac btw B ad D is = Bvl si currt, i r / r Also VA VB. As show i th giv figur i th qustio, I clos loo ABDA ir Lx.(i) I clos loo, ABGFDA Q Q ir ir Lx Q or ir Lx or lx Lx Q Or Lx..(ii) Now i clos loo ABGFEA, Q Q ir ir Q or ir Lx LT-IIT-SPARK Pag

3 Q Q. Th maximum currt i th iductor i R Ergy stord i th iductor U Li 9--8_LT-IIT_JEE-Adv_6_P Ky&Sol s L L R R Wh y is i ositio, this rgy will covrt ito hat rgy through rsistor.. For, I a a aa cos a I d For, x dsi d si ; 8 6 f Phas diffrc, x d 5 Now I a a aa cos a I. 6q q I (), th ottial of th caacitors ar: V L q V. As VL VR ad so thr is o blow of charg i btw th quatios. 6q q I (), V L q VR. As VR VL ad so charg will blow towards lft caacitor.. R A d d A V q q q q i R R A d d A 5,6. Accordig to th roblm, at oit Q, from grah V.7 V, V V 6V ad V 8V I ma A I 6 A B A Sic, V I R VE R V VE I Similarly, VBB IBRB VBE VBB VBE 6.7 RB 6 I B BE BB LT-IIT-SPARK Pag E

4 5 5 I urrt gai,. 6 I B R Voltag gai =.5 RB 5 Powr gai = Voltag gai ,8 Lt us cosidr th cass bfor ad aftr dcay Bfor dcay; If th utro was at rst. Hc. E m c, Aftr -dcay, Or Also E m c c E m c c m c c Now alyig cosrvatio of rgy, m c c m c c m c m c 96 Mv, m c 98 Mv ad m c.5mv 9--8_LT-IIT_JEE-Adv_6_P Ky&Sol s Sic, th rgy diffrc btw ad is small, c will b small, c m c, whil c may b gratr tha m c c mc m c c m c Th first ordr c m c m c 98 Mv 96 Mv Mv This givs th momtum of roto or utro. Th, E m c c Mv E m c c.5.6 Mv 9. Zic has lowr boilig oit. F HO NO 5 SO, F :, d,. 7 FSO F O SO SO. HEMISTRY KlO Hl Kl lo l H O.. molculs of hyl hydrazi is usd. uaird lctros,.87 B.M, s d. Wl 6.6 7/ W l 65.5 LT-IIT-SPARK Pag

5 9--8_LT-IIT_JEE-Adv_6_P Ky&Sol s.55 g blachig owdr has % Lactos is mad u of glucos ad glactos. otais,-liag 6. Ptl is diamagtic. Othrs hav uaird lctros,.8 B.M 7. HO ad F ar wa fild ligads. 8. (A) t O 9 s d hybridizatio. 6 (B) tg g F d, HO WFL ()..6 O FSE (D) Homogous catalyst. 9. A,B, cotai sulfur. D dos ot hav sulfur.. Isolubl chlorids ad covalt chlorids do ot giv chromyl chlorid tst. al is solubl ad ioic.. (A) T i m, T T T b b b s i for (a), (b), (c), (d) (B) () (D) f f, f s T i m T T T irt P Ps 8 m i P. I D, Asiri dos ot cotais Pholic grou.. is isomr ca form a chlat but ot th tras o with thyl diami.. Mabc, both gomtrical ad otical isomrs (5 + ), Total = 6 isomrs. cll r O / r HOOH / H5OH E E E V r r 6 cll H., H M E E cll.6 log log 6 E cll H OOH r H O 7 6 H H OH r O H H ] [Othrs ar uity xct LT-IIT-SPARK Pag 5

6 V 6. HOOH..7 log H H OH H H OH H OOH ; _LT-IIT_JEE-Adv_6_P Ky&Sol s MATHS Rquird o.of ways = 8. Usig thr digits, 5 ad 7 with rtitio ach ositio of th umbr ca b filld i ways. So th ositio ca b filld i... ( tims) = ways. Accordig to th quatio 9 6 Last valu of Lt th ight vctors of st V b dividd ito two grous as follows Grou Grou i j i j i j i j i j i j i j i j 5. Total o.of o-colaar vctors chos from V. Accordig to quatio cm (, q) = r t s. For cm, (, q) to cotai r followig ar th ossibl owrs of r i ad q. (,); (,); (,). Out of ths all xct (, ) ca b itrchagd for ad q. Total o.of ways for, q to cotai diffrt owrs of r ar 5. Similarly diffrt owrs of t that ca b giv to ad q ar (,), (,), (,), (,), (,) out of which xct(,) all othrs ca b itrchagd for ad q. Total o.of ways for, q to cotais diffrt owrs of t ar 5 9 Similarly total o.of ways for, q to cotais diffrt owrs of s ar 5 So total o.of ordrd airs = has 59 5 ositiv divisors, icludig 8 8. Thr is a o to o corrsodc btw th ositiv divisors lss tha 8 ad thos largr tha 5 8. It follows that thr ar ositiv divisors lss tha. octual. octual. Th last digit i th roduct ' ' umbrs,, a will b or or 7 or 9 oly wh th last digit i ach of th x x x is or or 7 or 9. 5 P E E E =Th vt that th last digit i th umbr a is,,,,6,7,8,9 E 8 E E E 8 LT-IIT-SPARK Pag 6

7 9--8_LT-IIT_JEE-Adv_6_P Ky&Sol s 8 P E 5 5. S 5, T S If S T Th... O addig o both sid Now will b tru if or or S... 5 r r... r Tr r T S Tr r 6 a b a d r r r r r r r which is tru, S T Giv, S lim dx ta x x x 6 i.., S Similarly, T LT-IIT-SPARK Pag 7

8 9. x x x ; s dx dx dy dx dy y x y x dx 5. x y x y x 9--8_LT-IIT_JEE-Adv_6_P Ky&Sol s dx x ut x z dy y y 5. Each of th 7 lmts hav choic. Thy ar x P ad x Q or x P ad x Q or x P ad x Q For ach lmt thr ar thr of abov choics. Hc th umbr of ways of slctio P or Q is As i both sts thr lmts ar commo so, thr lmts ca b choos i 7 ways. Ad rst of th lmts ca b choos i ay of th abov thr ways i 7 85 ways. So, total umbr of ways 5. If umbr of zros i b 6 is, th w hav oly o such umbr. If zro i b 6 th such umbrs. If two zros i b 6 th such umbrs. b I such a umbr ithr last digit is or So, a a a m,,5... a7 a6 a5 m m m LT-IIT-SPARK Pag 8