# PCM PART TEST-3 12th.pdf

29 Mar 2023

### PCM PART TEST-3 12th.pdf

• 2. ROUGHWORK PART - A Select the correct alternative(s) (choose one or more than one) [4 × 18 = 72] Q.1 Consider the two concentric conducting loops placed in same plane. There exists auniform magneticfieldforregion0 <r<r1, withthedirection alongthe axisofloopsherefieldisincreasingattherate dt dB .IftheresistancesR1&R2 are in the ratio1 : 2, and current in these resistance are I1 & I2 then (A) I1 = I2  0 (B) I1 = I2 = 0 (C) I1 = –I2  0 (D) I2 = 2I1  0 (Theresistances R1 & R2 liealongcommondiameter) Q.2 Aconductingwireframeis placedinamagneticfield, whichis directed into thepaper.The magnetic field is increasing at a constant rate.The directions of induced currents in wiresAB and CD are (A)Ato B and C to D (B) B toAand C to D (C) Ato B and D to C (D) B to Aand D to C Q.3 AmetalbarABcanslideon twoparallellongthickmetallicrails separatedbya distance l. A resistance R and an inductance L are connected to the rails as shown in thefigure.Alongstraight wirecarryinga constant current I0 is placed intheplaneoftherailsandperpendicularto themas shown.The barABis held at rest atadistancex0 fromthelongwire.Att =0, itis madetoslideon therails awayfrom the wire. Find a relation among i, di/dt and d/dt, where i is the current in the circuit and is the flux of the magnetic fielddue to the long wire through thecircuit. (A) dt d + L dt di – iR = 0 (B) 0 iR dt di L dt d     (C) 0 iR dt di L dt d     (D) none of these
• 3. ROUGHWORK Q.4 Asoundwavefrom stationarysourceoffrequency'f'travelshorizontallyto theright towards avertical wall.It isreflectedfrom avertical wallsurfacemovingtotheleft withaspeed 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          Q.5 Figureshowsahorizontalmagneticfieldwhichisuniformabovethedottedline and is zero belowit.Averylong, rectangular, conductingloop of width lmass m, resistanceR is placed partlyaboveand partlybelow the dottedlinewith the lower edgeparallel to it. Thevelocitywith which theloop be pushed downward sothat itmaycontinuetofallwithout anyacceleration (A) 2 2 B mgR l (B) R B mg 2 (C) mgR B 2 2 l (D) mg B 2 2 l Q.6 Apoint sourceoflight is 60cm from a screen and is kept at thefocus of aconcavemiror which reflects lightonthescreen.Thefocallengthofthemirroris20cm.Theratioofaverageintensitiesoftheillumination on the screenwhen the mirror is present and when the mirroris removed is: (A) 36 : 1 (B) 37 : 1 (C) 49 : 1 (D) 10 : 1
• 4. ROUGHWORK Q.7 Considerahypothetical reversiblereaction 2 1 A A2(g) + 2 3 B2(g) AB AB3(g), H = –30kJ If the standard entropies of A2, B2 and AB3 are 80, 60 and 90JK–1 mol–1 respectively, the above reactionwillbeatequilibriumat (A) 450 K (B) 750 K (C) 250 K (D) 1500 K Q.8 The enthalpyof reaction at 273 K is –3.75 kJ. What will be the enthalpyof reaction at 373 K if Cp is assumed to be zero? (A) –3075 kJ (B) zero (C) –3.75 × 273 373 kJ (D) –3.75 kJ Q.9 Whichofthefollowingstatements is/arecorrect : (A) Pure silicon can be obtained byreduction of Na2 SiF6 with Na. (B)Wroughtironis thepurest form of iron. (C)Quenchingofwrought iron makes it soft whereas steel becomeshard on quenching. (D) In contact process of manufacture of sulphuric acid NO is used as a catalyst. Q.10 Whichofthe followingstatement(s)is/areincorrect : (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.
• 5. ROUGHWORK Q.11          O H ) ii ( / NaHCO . aq ) i ( 3 3 A      2 2 CS / Br B       O H in Boiled 2 C Product 'C' is (A) (B) (C) (D) Q.12 CH2=CH–     Li H C H C CH | | O 3 — 2        O H by followed 2 A A ) equivalent 1 ( H O X — 2       B         3 2 ) OCHMe ( Al C (A) compound 'A' is 3 2 2 3 CH | OH CH CH CH CH    (B) compound 'C' is 3 2 2 CH CH CH CH CH | OH     (C) compound 'B' is 3 2 2 CH C CH CH CH || O     (D) compound 'B' is H CH | | O C CH CH CH 3 2 3   
• 6. ROUGHWORK Q.13 Let P & Q are two points denoting the complex number  &  respectively on the complex plane. Which ofthe followingequations canrepresent the equationsof thecircle passing through P & Q with least possible area? (A)             Z Z Arg = 2  (B) Re (Z – )     Z = 0 (C) 2 Z   + 2 Z   = 2    (D) Z Z +            2 Z +          2 Z +   +   = 0 Q.14 The equation to theorthogonal trajectories of the system of parabolas y= ax2 is (A) 2 2 y 2 x  = c (B) 2 y x 2 2  = c (C) 2 2 y 2 x  = c (D) 2 y x 2 2  = c Q.15 Considerthefollowingregionsintheplane: R1 = {(x, y) : 0  x  1 and 0  y  1} R2 = {(x, y) : x2 + y2  4/3} The area of the region R1  R2 can be expressed as 9 b 3 a   , where a and b are integers. Then the value of (a + b) equals (A) 2 (B) 3 (C) 4 (D) 5
• 7. ROUGHWORK Q.16 Imagine that you have two thumbtacks placed at two points,Aand B. If the ends of a fixed length of string are fastened to the thumbtacks and the string is drawn taut with a pencil, the path traced by the pencilwillbeanellipse.Thebest waytomaximisetheareasurroundedbytheellipsewithafixedlength ofstringoccurs when I thetwopointsAand Bhavethemaximum distance between them. II two pointsAand B coincide. III Aand B are placed vertically. IV The areais always same regardless of the location ofAand B. (A) I (B) II (C) III (D) IV Q.17 Consider the expansion, (a1 + a2 + a3 + ....... + ap)n where nN and n  p. The correct statements are (A) number of different terms in the expansion is, n +p  1C n (B) co-efficient ofany term in which none of the variables a1 , a2 , ...... , ap occur more than once is 'n' (C) co-efficient of anyterm in which none of the variables a1 , a2 , ...... , ap occur more than once is n! (D) Number of terms in which none of the variables a1 , a2 , ...... , ap occur more than once is       n p . Q.18 The probabilitythat apositivetwodigit numberselectedat random hasits tens digit at least three more thenitsunitdigitis (A) 14/45 (B) 7/45 (C) 36/45 (D) 1/6
• 8. ROUGHWORK 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. A rod abof length L = 1m & resistanceR = 1 ismovingwithconstantvelocity V= 1m/sbyapplyingexternal forcealongthe longconducting rails. The conducting rails are placed in the same plane of longcurrent carrying wire having current I= 1A. Neglect theresistance of rails ColumnI ColumnII (A) emf inducedinrod is (P) 2 0 2          2 2 n l (B)inducedcurrent in rod is (Q)   2 0 ln 2 (C) external horizontal force(F)applied (R)   4 0 ln 4 on the rod is (D) rate of work done byexternal agent is (S) 2 0 2 n 4         l 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 Q.3 Column I ColumnII (Compound) (DissolvesIn) (A)Ag2 O (P)Aqueous NH3 (B)Ag2 S (Q) KCN (C)AgCl (R) HNO3 (D)Ag2 CrO4 (S) Na2 S2 O3 Q.4 ColumnI ColumnII (A)        O H , O H 3 2 (P) (B)        O H ) iii ( CO ) ii ( Ether , Mg ) i ( 3 2 (Q) (C) +H2C=O+HCl+ZnCl2A (R) & C      3 ) OEt ( Al B Compound 'C' is (D) 4 CCl NBS     [X ]       COK ) CH ( 3 3 [Y] Z (S) 2 CH O C | | O   Compound 'Z' is
• 10. ROUGHWORK Q.5. Column–I Column–II (A) Thedifferentialequationofallparabolashaving (P) 1 theiraxisofsymmetrycoincidingwiththeaxisof x has its degree (B) Thedifferentialequationof all parabolaseachof (Q) 2 which has a latus rectum '4a' & whose axes are parallel to x-axis is of degree (C) Degree ofthe differential equation y= a   a x e 1   , (R) 3 a being the parameter is (D) The polynomial f (x) satisfies the condition f (x + 1) = (S) does not exist x2 + 4x. The area enclosed by y = f (x – 1) and the curve x2 + y = 0, is k 2 16 where k is
• 11. ROUGHWORK Q.6 Column–I Column–II (A) The name of the conic represented bythe (P) Ellipse equation px + qy = 1, where p, q  R, p, q > 0 is (B) Two parabola y2 = 4a (x – 1), and x2 = 4a(y – 2) (Q) Circle always touch each other. 1 and 2 being variable parameters. Then, their points of contact lie on a (C) If parabolaof latus-rectum l, touchesa fixed equal (R) parabola parabola, theaxes of the two curves beingparallel, thenthe locusofthevertex of themovingcurveis (D) From a point P tangents are drawnto the parabola (S) hyperbola y2 = 4ax. If the chord of contact of these tangents touches the rectangular hyperbola x2 – y2 = a2, then thelocus of P is
• 12. PART - C Q.1 InaLloydmirrorinterferenceexperiment asshown inthefigure,thesource(S) and the screen are separated by a distance of 1 m. At a certain position of source the fringewidthis 1/4mm andbymoving the sourceawayfrom the mirror alongthelineABby0.6 mm the fringe width changed to 1/6 mm. What is the wavelength (in Å) of light used? 
• 13. Q.2 Findthemagnitudeofmagneticfield(inT)atOofthecoordinatesystemifthe wirecarryingcurrent i =8A hasshapeshowninfigure.Theradiusofthecurve part is R = 10 cm, the linear parts of the wire verylong (here  = 3.14) 
• 14. Q.3 In the circuit E = 50.0 V, R = 250 and C = 0.50 F, the switch S is closed for a long time. After the switch is opened, the voltage across thecapacitor is measured . It is found that maximum potential difference across capacitor is 150 V. What is the inductance L of ideal inductor? (in Henery) 
• 15. Q.4 Findthevoltage(inKV)appliedtoanX-raytubewithNickel(Z=28)asatargetmaterial,ifwavelength difference between the K line & cut off wavelength of continuous X-rayspectrum is equal to 84 pm (here ionisation energyof H–atom 13.6 e.v & hc = 12420 ev Å) 
• 16. Q.5 One hunter is out on a day in early Spring when the air temperature is –100C and the atmospheric pressureis1atm.Duetotheintense physical activityofhunting,thehunter's averagebreathingrateover a six hour period is 15 breaths per minute and each breath has a volume of 0.62 Lat body temperature (370C). The air inhaled is warmedto bodytemperature onthe wayof thelungs. How much heat is lost in the process of breathing during this six hour period? The specific heat capacity of air at constant pressure is approximately30JK–1 mol–1. Notethat air maybetreated as an ideal gas.(Take R = 0.08 lit atm K–1) Report your answer in kJ. 
• 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 . 
• 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). 
• 19. Q.8 1342gram of1.0 molal sucrose(M.W. =342)solutionin wateriscooled to –3.00C.What weightofice (in gm) would be separated out at this temperature? Given that the amount of icethat separates out on cooling a solution containing50g of glycol (OH–CH2–CH2–OH) in 0.2 kg waterto –100C is 50 g. 
• 20. Q.9 Let Z = 18 + 26i where Z0 = x0 + iy0 (x0, y0  R) is the cube root of Z having least positive argument. Find the value of x0y0(x0 + y0). 
• 21. Q.10 A dieis weighted such that theprobabilityofrollingan n is proportional to n2 (n= 1, 2,3, 4, 5,6).The die is rolled twice, yielding the numbers a and b. The probability that a < b in lowest form is q p where p + q = 
• 22. Q.11 If the expression z5 – 32 canbe factorised intolinear and quadratic factors over real coefficients as (z5 – 32) = (z – 2)(z2 – pz + 4)(z2 – qz + 4) then find the value of (p2 + 2p). 
• 23. Q.12 A movable parabola touches the x and the y-axes at (1, 0) and (0, 1). The locus of the focus of the parabola is ax2–ax + ay2 – ay + 1 = 0 where a is.