# PCM- PART TEST-2 13th.pdf

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MCP- 13th Paper-2 Code-A TEST-3 .pdf
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### PCM- PART TEST-2 13th.pdf

2. ROUGHWORK bansal classes Page # 2 PART - A Select the correct alternative(s) (choose one or more than one) [4 × 18 = 72] Q.1 Standingwaves areproducedonastretchedstringof length Lwith fixed ends. When there is a node at a distance L/3 from one end, then (A)minimum andnext highernumberofnodes excludingtheends are2,5 respectively (B)minimumandnext highernumberofnodes excludingtheends are2, 4 respectively (C) frequencyproduced maybe V/(3L) (D) frequencyproducedmaybe 3V/(2L) [V=velocityofwaves inthestring] Q.2 Asoundwavefrom stationarysourceoffrequency'f'travelshorizontallyto theright towards avertical wall. It isreflected from avertical wall surfacemoving to theleft with aspeed v0. Thespeed ofsound in themediumisv. (A) The number of waves strikingthe wall surface per second is f v v v 0        (B) The wavelength of the reflectedwave is f v v 0  (C) The frequencyof the reflectedwave is f v v v v 0 0           (D)The numberofbeatsheardbya stationarylistenerplacedbetween source& thereflecting surfaceis f v v v 0 0         
3. ROUGHWORK bansal classes Page # 3 Q.3 Aseriescircuitconsistsofthreeidenticallampsconnectedtoabatteryas shown. When switchS is closed. (A)theintensityofbulbAincreases 1.25times ofits initial value (B)theintensityofbulbBincreases 2.25times ofits initial value (C) theintensityofbulb Cremains constant (D)the intensityofbulbAdecreases 25 . 1 1 timesofitsinitial value Q.4 P–V graph for an ideal gas undergoing polytropic process PVN = constant is shownhere. Then N is (A) 1 (B) 2 (C) 1.5 (D) none of these Q.5 Inthecircuitshown,theamountofcharge that will flowthroughsectionAB of the connectingwire to the batterywhen the switch S is closed is: (A) zero (B) 5 C (C) 10 C (D) 20 C Q.6 CapacitorC isinitiallyuncharged. X isjoined toYfora longtime, during which H1 heat is produced in resistance R. X is now joined to Z for a long time,duringwhich H2 heatis producedin R.Then : (A) H1 = H2 (B) H1 = 2H2 (C)Energysuppliedbycell duringchargingequals 2H2 (D)Energysuppliedbycell duringcharging equals H1 + H2
4. ROUGHWORK bansal classes Page # 4 Q.7 Forthefollowingcellreaction 2Hg(I) + 2Ag+ (aq) 2Ag(s) + Hg2 +2 (aq) is given that 0 Ag / Ag E  = 0.80 V, , [Ag+] = 10–3M ; 0 Hg / Hg 2 2 E  = 0.785V, ,   2 2 Hg = 10–1M (A) The forwardreaction is spontaneous (B) The backward reaction is spontaneous (C) Ecell = 1.585 V (D) Ecell = 3.170 V Q.8 Aspirin decomposes slowlyat room temperature byreacting with water in the atmosphere to produce acetic acidand salicyclic acid + H2O  AcOH + Considerthefollowinginitialconcentrationandinitial ratedataforthisreaction. [Aspirin], M [H2O], M Initial rate, Ms–1 0.0100 0.0200 2.4 × 10–13 0.0100 0.0800 9.6 × 10–13 0.0300 0.0200 7.2 × 10–13 0.0200 0.0300 7.2 × 10–13 Which ofthefollowingis thecorrect rate lawforthis reaction? (A) Rate= K[aspirin] (B) Rate = K[aspirin] [H2O] (C) Rate = K[H2O] (D) Rate = K[aspirin]2 [H2O] Q.9 Select the incorrect statement(s): (A) In  3 4 PO ion, the P–O bond order is 1.33. (B) Covalent bond can be formed by overlapping of py and pz orbitals (C) Bond angle in H2 O is lesser than bond angle in OCl2 molecule. (D) SeF4 and CH4 have same shape.
5. ROUGHWORK bansal classes Page # 5 Q.10 Which of the following statement (s) is/are incorrect : (A) Ni(CO)4 and [Ni(CN)4 ]2– both are d sp2 hybridised (B) The splitting energyof K3 [VF6 ] is greater than that of K3 [V(CN)6 ] (C) Paramagnetic behaviour increases in the order [V(H2 O)6 ]3+ < [Ni(H2 O)6 ]3+ < [Co(H2 O)6 ]3+ (D) [Ti(H2 O)6 ]3+ is a colourless species. Q.11 ) A ( 12 9H C      4 KMnO ) B ( 4 6 8 O H C     Fe / Br2 C8 H5 BrO4 (Only one product) A is  (A) (B) (C) (D) Q.12 2 ZnCl HCl HCHO        A KCN . alc . aq     B PhCHO ) ii ( Na O H C ) i ( 5 2        C   D 2 2 CO ) ii ( H / O H ) i (         E   HBr F (A) Compound D is (B) Compound Ais (C) Compound F is (D) Compound F is
6. ROUGHWORK bansal classes Page # 6 Q.13 You are given an unlimited supplyof each of the digits 1, 2, 3 or 4. Using only these four digits, you constructn digitnumbers. Such n digitnumbers will be calledLE GITIMATE if itcontains the digit 1 either aneven number times ornot at all. Numberof n digitlegitimate numbers are (A) 2n + 1 (B) 2n + 1 + 2 (C) 2n + 2 + 4 (D) 2n – 1(2n + 1) Q.14 Whichofthefollowingstatements arecorrect? (A) Number of words that can be formed with 6 onlyof the letters of the word "CENTRIFUGAL" if each word must contain all the vowels is 3 · 7! (B) There are 15 balls of which some are white and the rest black. If the number of ways in which the balls can bearranged in a row, is maximum than the number of white balls must be equal to 7 or 8. Assume balls of the same colour to be alike. (C)Thereare12things, 4alikeofonekind, 5alikeofanotherkindandtherestarealldifferent. Thetotal number ofcombinations is 240. (D) Number of selections that can be made of 6 letters from the word "COMMITTEE" is 35. Q.15 Given three points P1, P2 and P3 with position vectors k̂ ĵ î 2 r1     ; ĵ 3 î r2    and k̂ 3 ĵ î r3     respectively.Equation ofalineorthogonalto theplanecontainingthesepoints and passingthrough the centroid P0 of the triangle P1P2P3, is (A)   k̂ 2 j ˆ 3 î 4 3 1 r     + ) k̂ 2 j ˆ 3 î 14 (    (B) k̂ 3 2 j ˆ î 3 4 r     + ) k̂ 2 j ˆ 3 î 14 (    (C) k̂ 2 j ˆ 3 î 4 r     + ) k̂ 2 j ˆ 3 î 14 (    (D)   k̂ 2 ĵ 3 î 4 3 1 r     + ) k̂ 2 j ˆ 3 î 10 (   
7. ROUGHWORK bansal classes Page # 7 Q.16 Evaluate           3 0 2 1 2 dx x 1 x 2 ·sin x 1 1 = (A) 72 7 2  (B) 16 2  (C) 9 2  (D) none Q.17 Which of the followingis always true about a function f(x) on theinterval [a, b] = {x |a < x <b|}? (A) If f (x) > 0 on [a, b], then    b a b a dx ) x ( dx ) x ( 2 f f (B) If f (x) is increasing on [a, b] then f 2(x) is increasing on [a, b] (C) If f (x) attains a minimum at c where a < c < b, then f ' (c) = 0 (D) none Q.18 Let      dx e 2 x =  and f (t) =      dx e 2 x t , (t > 0) (A) f (x) is equal to x  (B)f(x)is monotonicdecreasing (C) if area bounded by y = f (x), x = 2, x = 16 and y = c is minimum then c = 3  (D) equation of normal to curve y = f (x) at x =  is y – 1 = 2(x – )
8. ROUGHWORK bansal classes Page # 8 PART - B MATCH THE COLUMN [8 × 6 = 48] INSTRUCTIONS: Column-Iand column-IIcontainsfour entries each. Entries ofcolumn-Iareto bematchedwith some entriesofcolumn-II.Oneormorethanoneentriesofcolumn-Imayhavethematchingwiththesameentries ofcolumn-IIandoneentryofcolumn-Imayhaveoneormorethanonematchingwithentriesofcolumn-II. Q1. Athinunchargedsphericalconductingshellofradius'R'isshowninfigure. Two point charges +q and –2q are fixed at pointA(inside shell) & point B outsideshellasshown infigure ColumnI Column II (A) Electricpotential at 'O' (P) – R Kq (B) Electric potential at 'O' due to charge (Q) + R Kq induced on inner surface of shell (C) Electric fieldstrength at 'O' (R) can becalculated easily (D) Electricfield strength at 'O'due to (S) can not be calculated easily charge on outer surface of shell Q.2 ColumnI ColumnII (A)Wavesinsolids (P)Transverseonly (B)Electromagneticwaves (Q) Can betransverseorlongitudinal (C)Longitudinalwaves (R) Require amedium to propagate (D) Pressure waves (S) Must be elastic parameters dependent
9. ROUGHWORK bansal classes Page # 9 Q.3 ColumnI ColumnII (A)Dithionousacid (P) S–O–S bond is not present (B)Thiosulphuricacid (Q)All S atom in the molecule has oxidation state +3 (C) Caro's acid (R)Acidic strength of all Hatoms present in the molecule is different (D)Pyrosulphuricacid (S) at least one S atom has oxidation state +6 in molecule Q.4 Column I Column II (A) CH3 –CN + HCl +AlCl3 (P) (B) +AlCl3 (Q) (C) 3 2 3 CO Na . aq of presence in POCl PhNMeCHO          (R) (D)         H ) ii ( H O O H ) i ( 2 2 (S)
10. ROUGHWORK bansal classes Page # 10 Q.5. ColumnI ColumnII (A) P(m, n) (where m, n  N) is anypoint in the interior of (P) 20 the quadrilateral formed bythe pair of lines xy= 0 & 8x2 + 5y2 + 14xy – 48x – 30y + 40 = 0 the possible number of positions of the point P is (B) The graph of y = x + k intersect the graph of (x–3)2 + (y + 2)2 (Q) 4 = 50 in one or more points if and only if a < k < b then b–a is (C) If a  , b  and c  are threemutuallyperpendicular unit vectors and (R) 12 d  is unit vector which makes equal angle with c and b , a    then 2 d c b a        = p + q r where q, r and p are three consecutive natural numbers then find the value of p + q + r (D)Abscissa andordinates of n given points areinAPwith first term a (S) 9 and common difference 1 and 2 respectively. If algebraic sum of perpendiculars from these given points on a variable line which always passes through the point       11 , 2 13 is zero, then a + n =
11. ROUGHWORK bansal classes Page # 11 Q.6 ColumnI ColumnII (A) The value of         n 4 r 1 r 2 n n 4 r 3 r n Lim = q p (P) 2 in its lowest form where p + q = (B) No.ofintegral values of a forwhichthe cubic (Q) 0 f(x) = x3 + ax + 2 is non monotonic and has exactly one real root. (C) The radicalcentreof three circles is at the origin. (R) 1 The equations of two of the circles are x2 + y2 = 1 and x2 + y2 + 4x + 4y – 1 = 0. If the equation of third circle passes through the point (1, 1) and (–2, 1) is x2 + y2 + 2gx + 2fy + c = 0 then f – c = (D) If x2 + y2 + z2 – 2xyz = 1 , then the value of (S) 11 2 2 2 z 1 dz y 1 dy x 1 dx     
12. PART - C Q.1 Two ideal springs of force constant K1 and K2 and block A of mass m are arranged in thefigure. Thestringpassing over two massless pulleys P1 & P2 is massless&inextensible. Thenfindtheangularfrequency(in rad/s)ofnatural oscillation of blockA(here K1 = K2 = 8000 N–m, m = 0.2 kg) [5]
13. Q.2 A metal sphere of radius a is surrounded bya concentric metal spherical shell of radius b (b > a). The spacebetweenthespheresis filledwithmaterial whoseelectrical conductivityvaries withtheelectric field strength E according to the relation  = KE where K is constant. A potential difference V is maintained between inner sphere and outer shell. Then find thecurrent (in ampere) between the inner sphere &outer shell. [Here K = 7 × 10–2 ohm–1 volt–1, V = 20 volts, b = ea (e : exponential) &  = 22/7] [5]
14. Q.3 In the given figure, a string of linear mass density 3 × 10–2 kg/m and length L = 1 m, is stretched by a force F = (3 – kt) N, where k is a constant andtis time insec.At thetimet =0,apulseisgenerated at the end P of the string. Findthe value of k (in N/s) if thevalue of force becomes zero as the pulse reaches point Q. [5]
15. Q.4 3 moles of an ideal gas        2 R 7 CP at pressure PA and temperature T TA is isothermally expanded to twice its volume. It is then compressed at constant pressure to its original volume. Finallythe gas is compressedatconstant volume toitsoriginal pressurePA. Calculatethenetwork done(injoule)bygas (here TA = 4000K; ln2 = 0.693, R = 8.31 J/mole0K) [5]
16. Q.5 Anorganiccompoundgives substitutionaswellaseliminationaccordingtothefollowingreaction OH R    + whendextrorotatorysample,heatedwithexcessalkylalcoholthenangleofrotationobservedatfollowing intervals t(sec) 0 3  Angleofrotation(deg) 450 250 50 Calculate the angle of rotation after10 sec. (take log 2 = 0.3) [5]
17. Q.6 A 0.347 g of a metal (A) was dissolved in dil. HNO3 . This solution gave a red colouration to Bunsen flameandonevaporationgave0.747gofmetaloxide(B).(A)alsoreactedwith N2 formingacompound (C) and with H2 , it forms (D). On reacting 0.1590 g of (D) with H2 O, a gas (E) was evolved and a sparinglysolublecompound(F)formed,whichgaveastronglybasicsolutionandrequired200mlof0.1 M HCl to neutralise it. (D) when treated with Lewis acid (G), forms a well known powerful reducing agent (H). Deduce the molar mass of (H) if (G) dissolves in excess of NaOH but does not dissolve in excess of aqueous NH3 . [5]
18. Q.7 Hydrocarbon (A) of M.F. C8 H16 reacts with O3 /Ph3 Pyield twomoles of B(C4 H8 O). Bis oxidized to C andthentreatedwith PCl5 togive D.Don treatement with hydroxylaminegavea compound(E) which gives redcolouration to Ferric chloride solution. When (E) is treatedwith strong HCl it gave (F) with evolution of CO2 . (F)on treatment with HNO2 gavea compound which gave ayellow precipitate with NaOI. What is the molecular weight ofF (in gm). [5]
19. Q.8 At 270 C the emf ofthe cell Pb |PbCl2 ||AgCl |Agis 0.42Vand its temperature coefficient is p dT dE       = –4.2×10–4 V/K.Calculatethe modulus of heat offormation ofAgCl (s)in Kcal if theheat offormation of PbCl2 is –85.09 Kcal. (Use 1 cal = 4.2 J) [5]
20. Q.9 Number of eight digit numbers which can be formed using the digits 1, 3, 4, 5, 6, 7, 8, 9 (without repetition) if eachnumberhas to be divisibleby275 is [5]
21. Q.10 The least integral value of a for which the function f(x) = 3 x 3 a + (a + 2)x2 + (a – 1)x + 2 possess a negativepointofminimum. [5]
22. Q.11 Let c and b , a    bethreenon-coplanarunitvectorsequallyinclinedto oneanotherat anacuteangle.If c b b a        = c r b q a p      , then p2 + q2/cos + r2 is equal to. [5]
23. Q.12 Equation ofstraight linemeetingthe circle x2 + y2 = 9intwo points at equal distances of 5from a point (x1, y1) on the circumference ofthe circle is given byxx1 + yy1 + q p = 0.Where p + q = (no. q p is in its lowestform) [5]