NARAYANA. XI-REG (Date: ) Physics Chemistry Mathematics

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1 CPT-5 / XI-REG / / Hits & Solutio CODE NARAYANA I I T / N E E T A C A D E M Y XI-REG XI-REG (Date: 0..07) Physics Chemistry Mathematics Page

2 CPT-5 / XI-REG / / Hits & Solutio Page Hits & Solutio PART A: PHYSICS K. F, F mr r 3. wghw mghm W 5. Relative desity of the body air Wair Wwater Where Wair 5N (weigh of the body i air) Ad Wwater N (weight of the body i water) 5N R. Dblock 5 5N N. loss of weight i liquid 5 3 R. D L loss of weight i water 5 3 GMm 6. Total eergy of the system is E a GMm Which is coserved. So, KE PE a At positio r, orbital eed of the satellite is V. GMm The, KE mv ad PE r So, GMm GMm mv V GM r a r a. Apt wt of st body Apt wt of d body 8 m g Fb 8 g m g Fb 36 g d bodies are i equilibrium apt wts are equal g d g 36 ; d ; d.8 g / cc. d 3. accordig to the law of coservatio of agular mometum, r r r r K r K. r

3 CPT-5 / XI-REG / / Hits & Solutio. F upthrust force V g a g a N 800 F T W ma 3.75 T 0 ; w Mass of block desity of block T.75N 5. Vdbg V dg VDg 6. The tesio o deser here is upwards ad o lighter here is dowwards. Vb g T Vb g F.B.D of heavier body Lighter T w F.B.D of lighter body F B T F Heavier F B T mg mg g T 6 liquid g i Vb g T Vb g g T liquid g ii Substract eqs. (ii) from (i), we get 6 T g T 0.5N 7. P0 P0 PQ P0 h g g h g g PQ P0 0 gh 8. W TE3 T. E R 9. ta r v cos t 0. W k. E K. E. mvr mvr () r a e r a() e GMm GMm mv mv (3) r r solve for v Page 3 R

4 CPT-5 / XI-REG / / Hits & Solutio R. g g R h 3. W mv K. E. da L 3 6. T R dt m 8. Gravitatioal potetial eergy at ay poit at a distace from the cetre of the earth is 9. Gravitatioal field is a coservative field. Therefore, work doe i takig a mass from oe poit to aother i this field depeds oly o its ed poits but idepedet of the path followed. 3. For precipitatio reactio: Q. I P K PART B: CHEMISTRY B QIP Ca F.50 K, precipitate will be formed 3. For precipitatio to occur K <Q a Q K 3. Catios of strog bases ad aios of strog acids do ot hydrolyse, rather they exists as hydrated ios i water. 35. Catios ad aios of weak acids ad weak bases gives correodig acids or bases by hydrolysis. 36. a NaCl cotais Na + catio of strog base NaOH ad Cl aio of strog base which do ot hydrolyse. 39. BaSO s Ba aq SO aq S At Eqm. Solubility K S S 5 5 S K M 0. For Zr PO S 3 3 K 7 K S Page

5 CPT-5 / XI-REG / / Hits & Solutio 3 /5 3 K.0 5 / Ni OH Ni OH. S. S S NaOH Na OH K Ni OH 5 S S S 3 S 0 M. For salt of weak acid ad strog base 3 ph 7 log C log K a 7 log 0. log gl AgCl 6. Molarity of K S Metals have low ioizatio eergy. Ioizatio eergy of H- atom is 3 kj mol while that of Li, it is 50kJ mol oly 8. H or Q is ot a isotopes of hydroge. 9. H e, p, o H e, p, 3 H e, p, 53. The very first method of removig hardess of water used : volume H O 0 LO at STP from L H O H O H O O 3 g.l. LO 3g H O LO g H O g H O. Stregth of HO gl 58. KO is superoxide K O. BaO is peroxide is Ba O MO ad NO are dioxides O M O M 59. s aq Page 5 MX M aq X s s 3 K s. s s 0 s or s 0 3 3

6 CPT-5 / XI-REG / / Hits & Solutio or, M X solid M X aq s 0 M M 0 M 60. aq K s s 56 s. Solubility product, 5 K K s /5 PART C: MATHEMATICS 6. Give that 5 P 3 P ! 5! 3.!!! ! 3.! =. P 5 P 3 3! 5.! 3! 3! ! 5 56! 5! r 6! 5 r 3! 56! ! 50 r! 5 r! r r r 0 0 K K PK K K 0. K. K! K K! K Page 6

7 CPT-5 / XI-REG / / Hits & Solutio Page 7 0 K! K! K sum=! d d d3... d 3! First arrage ay 3 cosoats at eve places i p3 ways. Now the ewly created four odd places ca be filled by the remaiig letters which icludes 3 vowels ad cosoats, which ca be doe i p ways. Hece the required umber of permutatio. p p There are total 9 places out of which are eve ad rest 5 place are odd. wome ca be arraged at eve places i! Ways ad 5 me ca be placed i remaiig 5 places i 5 p5 ways. Hece the required umber of permutatio. 5! P Total umber of arragemet =8!=030 Number of arragemet whe best ad worst papers are together = 7!! 0080 Numbers of arragemet i which best ad worst papers are ot together = = Ay 5 soldiers ca stad i oe row ad the remaiig 5 soldiers ca stad i other row. 0 5 Required umber of arragemets: p5 p5! A passeger from ay statio may purchase ticket for ayoe of the other 9 statios. Therefore total umber of differet tickets Whe L ad T are fixed as first ad last letters of the word, the we have oly 6 letters to be arraged. Hece required umber of permutatios 6! 7. 90!!! M, M, T, T, H, C, S A, A, E, I 7 Whe all the vowels are together the 7 8 8!! Required umber of permutatios =0960!!! 73. T,T,T N,N,.N,G,G.G,R,I,I,I There are total 3 letters of which 3 are T s, 3 are G s, 3 are I s. Also there are 6 eve places ad 7 odd places. 3Is (i.e vowels) ca be arrages i the 6 eve places i 6 P3 0 ways. 3! 0! Now, we are left with 0 places i which 0 letters ca be filled up i 3! 3! 3! 6800 The total umber of permutatios i which vowels occupy eve places= Number of umbers of digits i which repetitio allowed Number of umbers of digits i which repetitios is ot allowed Hece the required umbers of digits = Total umber of 3digit umbers i which there is at least oe digit is First letter ca be posted i letter boxes i ways. Simillarly secod letter ca be posted i letter boxes i ways ad so o. Hece a the 5 letters ca be posted i Total umber of arragemet =6!=70

8 CPT-5 / XI-REG / / Hits & Solutio Numbers of arragemet i which two ladies are together =5! 0 Number of arragemets i which two ladies are ever together =70 0= Assumig Sahara, Ambai ad Mahidra as a sigle persoality, the there are total (0 3)+=8 perso, which ca be arraged i 7! Ways. Therefore required umber of arragemets=7! A perso ca be chose out of 8 people i 8 ways to be seated betwee Musharraf ad Mamoha. Now cosider Musharraf, Mamoha ad the third perso,sittig betwee them as a sigle persoality, we ca arrage them i 7! Ways but Musharraf ad Mamoha ca also be arraged i ways. 8 7! 8! 80. Required umbers of permutatio = C x C x C x x 8. 8, x ; ax Now put x = a = C!!! C!!! / p / q 85. I C0 C... C9 C0 C... C C 0 C... C 0 C0 9 0 C0 x y, if p or q divide r the umber of to ratioal terms are k else L.C.M. {p, q} ad [.] is greatest iteger fuctio k = L.C.M. {5, 0} = 0 5 divides 5 umber of terms are 86. r = 3, = 0 umber of terms C C 03 3 = 3 mm mx x... x x... mm m 3m m 3, mm 3 6 m 5 m m 7m -m + = - m = x a x a C C x a... k, where k = Page 8

9 CPT-5 / XI-REG / / Hits & Solutio 3 3 x x x x 5 5 / / 5 x(x ) x C x(x ) Highest power is Put x = i formula give i hit, the C 3 C C 3 C I f, f ' : 0 f ', 0 f I f f ' C0 C C C 6 I + f + f = iteger f + f = iteger betwee 0, ad f + f = I I = (99) - = 97 0 f f ' Page 9