. (D). (B). (). (). (D). (A) 7. () 8. (B) 9. (B). (). (A). (D). (B). (). (B) NAAYANA I I T / T A A D E Y XIS-I-IIT-SA (..7) o m m o n c t i c e T e s t 9 XI-I SA Dte:..7 ANSWE YSIS EISTY ATEATIS. (B). (). (D). (B) 7. (A). (A) 7. (D). () 8. (A). (A) 8. (A). (D) 9. (A). () 9. (). (D). (A). (A). (A). (A). (D). (B). (A). (B). (A) 7. (D). (D) 7. (). (D) 8. (). (A) 8. (A). (D) 9. (B). (A) 9. (). (B). (). (D) 7. (B). (A). (). (B) 7. (D) 7. (D). (A) 7. (A) 7. (A) 8. (B). (A) 8. (D) 7. () 9. (). (B) 9. (D) 7. (A). (). (B). (A) 7. (B) (int & Solution) AT A : YSIS 7. (B) 77. (A) 78. (B) 79. (D) 8. () 8. (B) 8. () 8. (D) 8. (B) 8. (A) 8. (D) 87. (B) 88. (B) 89. () 9. ().. (D) ; E net Gm G m m, is distnce fom m ; ;. d d d m Gm G nd d d ; V m d G = m d.: (B) ; At distnce. o Gm m. = m, m. d G m. d m, G m m E 8Gm NAAYANA IIT/T AADEY ()
G G : () ; At cente, V c, on sufce V s ; V c Vs mgh mg : () ; U, h gien ; U h e ge e. (D) ; g g m. (A) ; / T / T ; T T 8T 8 T 7. () ; otentil eneg is two times the mechnicl eneg. 8. (B) ; m e mgh h 9. (B) ; otentil t cente = m o m / e m o ds gh 8 h G g gh o ; Soling, we get 8 h XIS-I-IIT-SA (..7) h G = / otentil eneg = G Gm ; Binding eneg = Gm 8 G m e o e. () ; W EA E = A A V A ; V A J / kg. (A) ; U i U f ee, m educed mss = m m Gm G m ; m d d. (D) ; Using consetion of eneg Gm Gm mv h..(i) G V h (ii) Gm G V e. (iii) ; Soling (i), (ii), (iii) V Ve NAAYANA IIT/T AADEY () V
. (B) ; Semimjo is Now, T / / T / T XIS-I-IIT-SA (..7) G g G. () ; g ; o h. (B) ; Sufce e of Q is fou times. Theefoe, dius of Q is two times. Volume is eight times. Theefoe, mss of Q is lso eight times. So, let nd Then, 8 nd Q Q Now, mss of is o. Theefoe, dius of is Q 9 / 9. Now, escpe G elocit fom the sufce of plnet is gien b ( = dius of tht plnet) G 8 G G 9 9 Q / Fom hee, we cn see tht Q ; nd. (B) ; In cicul obit of stellite of potentil eneg = kinetic eneg m m Just to escpe fom the gittionl pull, its totl mechnicl eneg should be zeo. Theefoe, its kinetic eneg should be m 7. (A) W U U U U U mv V (s m = ) f i Q otentil t point will be obtined b integtion s gien below. Let d be the mss of smll ing s shown in figue. d d d 7 dv G. d G 7. d G G = ; W 7 7 8. (A) As it looses some eneg, it will be ttcted towd the eth nd distnce deceses nd due to wok done b git its intection eneg deceses nd kinetic eneg inceses hence option (A) is coect. 9. V dv k dv d (A) ; We know tht g d d d V In V V. T T (A) ; Fom eple s thid lw T k ; T T. (D); Gm B eneg consetion we use Gm m ke G Whee e k NAAYANA IIT/T AADEY ()
. (A) Since T T T T nd T kmh nd So, speed of S with espect to S is kmh. (D). (D) ; As fom eple s lw we he km kmh nd. When the e closet. XIS-I-IIT-SA (..7) 8 T nd T T G Gm G. (B) ; Obitl elocit ; ence, E T T. (A) Wok done will be zeo when displcement is pependicul to the field. The field mkes n ngle tn with positie -is. While the line tn with positie -is. 9 mkes n ngle in kmph i.e., the line is pependicul to g 7. (D) In figue shown s we know t ll points in the plne of bse of hemispheicl shell gittionl field is noml to bse hence the sufce is equipotentil. 8. (B) If time peiod of stellites e T nd T we use T / nd T / B B eple s thid lw T B ; T ; B ; B 9 T B T 9 T / T 9. () The potentil, kinetic nd totl eneg of stellite ies inesel with the obit dius of the stellite nd the eltion we know is TE / E E hence option () is coect.. () As the septed pt hs sme speed s tht of stellite, it will continue to moe in the sme obit. NAAYANA IIT/T AADEY ()
XIS-I-IIT-SA (..7). S S S S S S. p nge to between to AT B : EISTY t the equilence point =. p.. AgBO S Ag q BO.. q Ag is pecipitted b S ; V nt n V T 78. tm L 7..8 L tm mol 9 S q S q Ag S s Ag Ag S. mol in 8 So, ml Ag 7.8 mol in ml Ag BO Ag 7.8. S. ; p In p p In In log In i.e., In In. p In log 9. In log ; In ; So, % ioniztion In In So, it is equilence point. p colou chnge stts fom So, () is incoect 9. Zn S 8. 8. SZnS So, ppt fomed 9 u S 8. 8. S us So, ppt fomed. 7. p, po ; O 9. O B O B B S 8 B O N, N, N... Totl olume = ( + + ) + = L N V N V NV N mi V mi mol In p nd complete t p In NAAYANA IIT/T AADEY ()
N mi.. Volume stength =.. 9. 9. Degee of hdness of wte = ppm i.e., g of wte contins O g. mol of O mol of gso. mol of. mol of. mol of gso g of gso i.e., g of wte contins g of gso g mg of gso g equied.g NO. O g equied. g NO. O XIS-I-IIT-SA (..7). = mol No. O 8 mol of NO mol of O gm O ; ppm =. uso. O is epesented s u O SO. O Onl one molecule, which is pesent outside the coodintion sphee is hdogen bonded. The othe wte molecules e bonded to u b coodinte bond.. O n onge coloued solution, on cidifiction with dil. SO is oidized b O to blue peoide of chomium, O which is unstble. O SO SO O O O O O O 7 O O O SO O O SO O 7 O. Two O bonds in lie in diffeent plnes.. Zn NO NZnO. Line, O Line N midl, 7. Wte is colouless, tsteless nd neutl, so cn t be detected b smelling, tsting o dding phenolphthlein. On dding, pinch of nhdous uso (white) to wte, hdted uso is fomed which is blue in colou. uso uso. O white blue 8. O O O O NO O O NO NOl O Ol NO O O O O 9. Tue peoide he O-O- bond o gies O with dilute cids. bo does not gie O with dil. cids. NAAYANA IIT/T AADEY ()
XIS-I-IIT-SA (..7). Let the simultneous solubilities of AgSN nd AgB be nd, espectiel, in mol L-. AgSNs Ag q SN q AgBs Ag q B q At equilibium : Ag ; SN ; B Accoding to electicl chnge neutlit eqution. Totl positie chnge = Totl negtie chge Note tht : Ag B SN [This is n Electicl chge neutlit eqution] spagb sp AgSN Ag Ag spagb spagsn Ag Ag B Also SN.. (i) sp AgB sp AgSN. Using equtions (i) nd (ii), we get, 8. (ii) 7 ;. 7. A B A B S S (Let, S is solubilit) S S 8 b using hit nd til method, not lid, not lid, lid. Solubilit of slt of W A is gien b the fomul. / / S S = - In In Acid fom Bse fom st cse 8% ellow % ed nd cse % ellow 8% ed st cse p p log 8 p p log nd cse p p log p p log log. Tittion of W B / S A 8. S. NAAYANA IIT/T AADEY (7)
XIS-I-IIT-SA (..7). The p fom hs lowe eneg, nd t bsolute zeo the gs contins % of the p fom. As the tempetue ised, some of the p fom chnges into the otho fom. At highe tempetue the gs contins bout 7% O 7. O ects with IO in the following mnne 8. 7 O IO O O IO Oidtion stte of I ies fom +7 to +, i.e., deceses, Thus IO gets educed hence, O is educing gent with N O N O O N O O Oidtion stte of N ies fom - to +. ee oidtion numbe inceses, hence O is cting s n oidizing gent. 8 : S ; S X S X : S S. ; S X : S 7S.7 ; S Ode of solubilit is X X X 9. Alkli metl slts e usull moe soluble thn the slts of tnsition metls. Also us is less 9 soluble thn ZnS becuse of d configution of u. Theefoe, solubilit ode is N S ZnS us. Fo pecipittion of occu, S QS 9 QS. S ence, pecipitte will be fomed in this cse, In ll othe cse Q nd no pecipittion will occu. S S AT : ATEATIS. (B) ; ee E, A,, T, Q, U,, imum numbe of pemuttions = coefficient of = coefficient of = coefficient of 8 =.. in 8 in in!!!.9.8.7 8.7.... = 9....... () ; 97. (D) ; Let n n. If, b, c e in A ; then b c i.e., sum of two numbes is een. ee, m is odd nd m is een numbe. Sum of two numbes is een, then both numbes e een o odd. equied numbe of ws =. (D) ;! 8 9. (A) One possible ngements is m m m m m m m = NAAYANA IIT/T AADEY (8) n n
XIS-I-IIT-SA (..7) Thee sun ngements e possible. The othe possible ngement is Thee such ngements e possible. ence, the totl numbe of ws = 9 + =. Theefoe, the numbe of ws is 9 In this cse, the numbe of ws is. (B) Totl numbe of ws = 8 = 7 7. () Since, the student is llowed to select tmost n books out of n books. Theefoe, in ode to select tlest one book, he hs the choice to select one, two, thee. n books. Thus, if T is the totl numbe of ws of selecting tlest one book, then n n n T... (i) n n n n n Now, n... n n n n n n n... n n n n T n [ fom Eq. {i)] n n n 8. (A) ;!!!! 9. () ; A seen digit numbe using,, nd nd hing s the sum of digits cn be fomed eithe b using digits,,,,,, o,,,,,,. 7! 7! So, equied numbe of seen digit numbes = 77!!! 7. (B) ; 7 ; b ; c 7 7. (D) ; T T ; n n ; n 7 n n 7. (A) ; No. ws = oefficient of in... = oefficient of = oefficient of in... in = 7 7. ()! X-X-X-X-X. The fou digits,,, cn be nged t (-) plces in ws!!! The fie digits,, 8, 8, 8 cn be nged t (X) plces in ws!! Totl numbe of ngements = = ws. 7. (A) We know tht numbes diisible b if the sum of its digits is diisible b. se I : digit numbes fomed using the digits,,,, e! = numbes. se II : Tking,,,, if we mke digit numbe then I plce cn be filled in = ws ( cn not come t I plce) II plce cn be filled in = ws III plce cn be filled in = ws IV plce cn be filled in = ws V plce cn be filled with = ws totl numbes e =! = 9 Thus totl numbes diisible b e = + 9 = 7. (B) ; Sum of diisos.7.. NAAYANA IIT/T AADEY (9)
7. (B) All diffeent =.! simil + diff. = sme + diff. =!.!!.!.. XIS-I-IIT-SA (..7)! sme + sme + diff. =..!!! sme + sme =..!! Totl selects = 7 Totl ngements = 77. (A) Gien wod is ISSISSII ee, I = times, S = times, = times, = time I_I_I_I 8 7! 8 7! 8 equied numbe of wods = 7..!!!! 78. (B) No. of E s = ; No. of X s = ; No. of ;s =, No. of s = No. of S s = ; No. of I s =, No. of O s =, No. of N s = equied numbe is 8 7!!... 9!!! 79. (D) The desied numbe is the coefficient of in............... which is 8 89 9 8. () O B A D A D A diff :! diff + sme :..!! diff + diff :.!! sme + sme :!.! Totl ws : 8. (B) Numbe of digited numbes with, 7, 8 = 7 Numbe of digited numbes =! ; Totl = 9 NAAYANA IIT/T AADEY ()
XIS-I-IIT-SA (..7) 8. ()! Ode of lettes e A, L, L,, S. No of wods begin with A, begin with L =! =!!!, begin with ; begin with SA ; begin with SL! ; net wod is!! SALL = ; totl = 8 8. 88879 (D) ; equied numbe of ws = 9 7 8. (B) All the plces of the fou digit numbe cn be filled b ws becuse epetition of digits is llowed. Totl numbe of ws = = Totl numbe of ws = = 8. (A) ; Totl numbe of stight lines fomed = 7 8. (D) ; ;!.! 8 87. (B) I + N + F + T + E sme + diff sme + sme sme + diff ll diff Totl 88. (A) Thee e diffeent lettes. We he to select sques, tking one fom ech ow nd then nge in ech selection. () () ()........ 8 8 Totl numbe of selections of sques = + 8 + 8 + =. Fo ech selection of sques. Totl no. of ws =! 87 89. () ; Totl numbe of ws = 9. () Let the bll be,,,,, b, b, b, b, b Numbe of ws of selecting blls is one, Numbe of ws of selecting - blls fom diffeent blls is ; NAAYANA IIT/T AADEY ()