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PAPER CODE : A Class : XII & XIII INSTRUCTIONS 1. The question paper contain 7 pages and 2-parts. Part-B contains 6 questions of "Match the Column" type and Part-C contains 18. All questions are compulsory. Please ensure that the Question Paper you have received contains all the QUESTIONS and Pages. If you found some mistake like missing questions or pages then contact immediately to the Invigilator. PART-B (i) Q.1 to Q.6 are "Match the Column" type which may have one or more than one matching options and carry 8 marks for each question. 2 marks will be awarded for each correct match within a question. ThereisNEGATIVE marking. 0.5 Marks will be deducted for each wrong match. Marks will be awarded only if all the correct alternatives are selected. PART-C (ii) Q.1 to Q.17 are "Subjective" questions. There is NO NEGATIVE marking. Marks will be awarded only if all the correct bubbles are filled in your OMR sheet. PART-D (iii) Q.1 to Q.2 are "Subjective" questions. There is NO NEGATIVE marking. Marks will be awarded only if all the correct bubbles are filled in your OMR sheet. 2. Indicate the correct answer for each question by filling appropriate bubble(s) in your answer sheet. 3. Use only HB pencil for darkening the bubble(s). 4. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed. 5. The answer(s) of the questions must be marked by shading the circles against the question by dark HB pencil only. P Q R S leading zero(s) if required after (A) rounding the result to 2 decimal places. (B) e.g. 86 should be filled as 0086.00 (C) . . (D) . . . . . . . . USEFUL DATA: Atomic Mass: Al = 27, Mg = 24, Cu = 63.5, Mn = 55, Cl = 35.5, O = 16, H = 1, P = 31, Ag = 108, N = 14, Li = 7, I = 127, Cr = 52, K=39, S = 32, Na = 23, C = 12, Br = 80, Fe = 56, Ca = 40, Zn = 65.4, Ba = 137, Co = 59, Hg = 200, Pb = 207, He = 4, F=19. Radius of nucleus =10–14 m; h = 6.626 ×10–34 Js; me = 9.1 ×10–31 kg, R = 109637 cm–1. Take g = 10 m/s2 where ever required. PART-B MATCH THE COLUMN [2 × 8 = 16] There is NEGATIVE marking. 0.5 Marks will be deducted for each wrong match. INSTRUCTIONS: Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries of column-II. One or more than one entries of column-I mayhave the matching with the same entries of column-II and one entryof column-I mayhave one or more than one matching with entries of column-II. Q.1 On a capacitor of capacitance C0 following steps are performed in the order as given in column I. (a) Capacitor is charged by connecting it across a battery of EMF V0. (b) Dielectric of dielectric constant k and thickness d is inserted (c) Capacitor is disconnected from battery (d) Separation between plates is doubled Column I Column II (Steps performed) Final value of Quantity (Symbols have usual meaning) (A) (a) (d) (c) (b) (P) Q = (B) (d) (a) (c) (b) (Q) Q

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- PAPER CODE : A Class : XII & XIII Time : 3 hour Max. Marks : 210 INSTRUCTIONS PART-B For example if Correct match for (A) is P, Q; for (B) is P, R; for (C) is P and for (D) is S then the correct method for filling the bubble is P Q R S (A) (B) (C) (D) PART-C Ensure that all columns (4 before decimal and 2 after decimal) are filled. Answer having blank column will be treated as incorrect. Insert leadingzero(s)ifrequiredafter rounding the result to 2 decimal places. e.g. 86 should be filled as 0086.00 . . . . . . . . . . PART-D Ensure that all columns {1 before decimal and 2 after decimal with proper sign (+) or (–)} arefilledand columns after 'E'usedfor fillingpower of 10 with proper sign (+) or (–). Answer having blank column will be treated as incorrect. e.g. – 4.19 × 1027 should be filled as – 4.19 E + 27 P A P E R - USEFULDATA: Atomic Mass:Al = 27, Mg = 24, Cu = 63.5, Mn = 55, Cl = 35.5, O = 16, H = 1, P = 31, Ag = 108, N = 14, Li = 7, I = 127, Cr = 52, K=39, S = 32, Na = 23, C = 12, Br = 80, Fe = 56, Ca = 40, Zn = 65.4, Ba = 137, Co = 59, Hg = 200, Pb = 207, He = 4, F=19. Radius of nucleus =10–14 m; h = 6.626 ×10–34 Js; me = 9.1 ×10–31 kg, R = 109637 cm–1. Take g = 10 m/s2 where ever required. 1. The question paper contain 7 pages and 2-parts. Part-B contains 6 questions of "Match the Column" type and Part-C contains 18. All questions are compulsory. Please ensure that the Question Paper you have received contains all the QUESTIONS and Pages. If you found some mistake like missing questions or pages then contact immediately to the Invigilator. PART-B (i) Q.1 to Q.6 are "Match the Column" type which may have one or more than one matching options and carry 8 marks for each question. 2 marks will be awarded for each correct match within a question. ThereisNEGATIVE marking. 0.5 Marks will be deducted for each wrong match. Marks will be awarded onlyif all the correct alternatives are selected. PART-C (ii) Q.1 to Q.17 are "Subjective" questions. There is NO NEGATIVE marking. Marks will be awarded onlyifall the correct bubbles are filled in your OMR sheet. PART-D (iii) Q.1 to Q.2 are "Subjective" questions. There is NO NEGATIVE marking. Marks will be awarded only if all the correct bubbles are filled in your OMR sheet. 2. Indicate the correct answer for each question by filling appropriate bubble(s) in your answer sheet. 3. Use only HB pencil for darkening the bubble(s). 4. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed. 5. The answer(s) of the questions must be marked by shading the circles against the question by dark HB pencil only.
- PART-B MATCH THE COLUMN [2 × 8 = 16] There is NEGATIVE marking. 0.5 Marks will be deducted for each wrongmatch. INSTRUCTIONS: Column-Iand column-IIcontainsfour entries each. Entries ofcolumn-Iareto bematchedwith some entriesofcolumn-II.Oneormorethanoneentriesofcolumn-Imayhavethematchingwiththesameentries ofcolumn-IIandoneentryofcolumn-Imayhaveoneormorethanonematchingwithentriesofcolumn-II. Q.1 On a capacitorof capacitanceC0 followingsteps are performed in the order as given in column I. (a) Capacitor is charged byconnecting it across a batteryof EMF V0. (b) Dielectricofdielectricconstant k and thicknessd is inserted (c) Capacitor is disconnected from battery (d) Separation betweenplates is doubled ColumnI ColumnII (Steps performed) Final value of Quantity (Symbols have usual meaning) (A) (a) (d) (c) (b) (P) Q = 2 V C 0 0 (B) (d) (a) (c) (b) (Q) Q = 1 k V kC 0 0 (C) (b) (a) (c) (d) (R) C = 1 k kC0 (D) (a) (b) (d) (c) (S) V = k 2 ) 1 k ( V0 [Ans.(A) P, R, S; (B) P, R, S; (C) R; (D) Q, R] [Sol. Q C V (A) C0V0 C0 V0 2 V C 0 0 2 C0 V0 2 V C 0 0 2 C0 V0 2 V C 0 0 1 K KC0 K 2 ) 1 K ( V0 (B) 0 d 2 C0 0 V0 d 2 C0 d 2 C0 V0 V0 d 2 C0 d 2 C0 V0 2 V C 0 0 1 K KC0 K 2 ) 1 K ( V0
- (C) 0 d KA 0 0 KC0V0 KC0 V0 KC0V0 KC0 V0 KC0V0 1 K KC0 (K+1)V0 (D) C0V0 C0 V0 KC0V0 KC0 V0 1 K V KC 0 0 1 K KC0 V0 1 K V KC 0 0 1 K KC0 V0 ] Q.2 ColumnIhas someconductoraccrosswhich batteryis connected asshown.Variationofresisitivityis alsoindicated.WhichofthequantitiesincolumnIIremainconstantthroughout thevolumeofconductor. ColumnI ColumnII (A) (P)Magnitudeofelectricfield (B) (Q) Magnitudeofcurrent density (C) (R) Powerdissipated per unit volume (D) (S) Drift speed of free electron [Ans.Bonus]
- PART-C SUBJECTIVE ThereisNO NEGATIVE marking. Q.1 Findthekineticenergyofpulsetravelling inatautstring.Given T=10N&=0.1 kg/m.[Giveanswer inmillijoules]. [Ans. 0.15 mJ] [Sol. at giventimey=m1x 0 < x < 0.1 m = m2 x + C 0.1 m < x < 0.15 m m1 = 1 . 0 10 3 = 10–2 T V m2 = 05 . 0 10 3 = 2 × 10–2 dK = 2 1 dm 2 P V = 2 1 dx 2 x y V K d = 2 1 2 V 15 . 0 1 . 0 2 2 1 . 0 0 2 1 dx m dx m K 2 1 ) 5 . 0 ( m ) 1 . 0 ( m 2 2 2 1 T = K + U = ) 5 . 0 ( 10 4 ) 1 . 0 ( 10 T 2 1 4 4 = 2 10 [10–4] (0.3) = 0.15 mJ Ans. ] Q.2 A sampleofideal gas is taken through the cyclic process shown in the figure.The temperature of the gas at stateAis TA=200 K.At states B and C the temperature of the gas is the same. Whatisthegreatesttemperatureofthegasinkelvinsduringthecyclicprocess? [Sol. At B and C (TB = TC) B B B T V P = C C C T V P B A B T V P = C A C T V 3 P PB = 3PC for lineAC PV (straightlinethroughorigin) so A C P P = A C V V = A A V V 3
- PC = 3PA Thus PC = 3PA ; PB = 3PC = 9PA .....(I) VC= 3VA ; VB = VA TA = nR V P A A .....(II) fromAto B ; sochoric P T so TB > TA for C toA; both (P, V) so T Thus from BtoC (we couldhavemaximum temperature) P = aV + b P = A A V 2 P 6 + 12 PA P = – A A V V P 3 + 12 PA PV = nRT V P 12 V V P 3 A A A = nRT T for Tmax dV dT = 0 A A V P 6 V + 12PA = 0 V = 2VA P = 6PA T = nR ) V 2 ( P 6 A A = nR V P 12 A A Tmax = 12 TA = 2400 K ] Q.3fl TwoobjectsofequalvolumeV=1m3 anddifferent densities d1=500kg/m3and d2 = 1000 kg/m3 areglued to eachother so that theircontact surface is flat and has an areaA= 0.1 m2. When the objects are submerged in a certain liquid, theyfloatinstableequilibrium, thecontact surface beingparallelto thesurface oftheliquid(seethediagram). How deep (Hin meters) canthecontact surface be inthe liquid so that the objects are not torn apart? The maximum force that the glue can withstand is F=250 N. [Ans H =3m] [Sol. Atthe"critical"depthH,theequilibrium conditionforthecompound object suggests thatthedensityof theliquidisd=(d1 +d2)/2.Forthetopandthebottomobjecttakenseparately,theequilibriumconditions are,respectively: d1Vg + F – (dVg – dgAH) = 0 d2Vg – F – (dVg + dgAH) = 0 (For eachobject, the term inparentheses indicates the "effective" buoyancyforce.) Combining the last two equations yields the answer : H = [(d2–d1)Vg – 2F] / [(d1 + d2) gA] ]
- Q.4 An inclined plane is placed on a horizontal smooth surface. The plane is struckbyanelasticballwhosevelocityishorizontaljustbeforetheimpact. The ball bounces off the inclined plane and then lands on it again at the pointoffirstimpact.Findtheratioofthemassesoftheballandtheinclined plane. (Angle = 30°) [Sol. Thishappensof after collision both ball and inclined planehavesamehorizontal velocities say V2 say V1 beinitialvelocityofballVy beverticalvelocityofballaftercollision,m1 –mass ofball,m2 –mass of inclinedplane Conservationoflinearmomentuminhorizontaldirection 2 2 1 1 1 V ) m m ( V m ....(1) coffeicientofrestitution=1 1 = – sin V 0 )] cos V sin V ( sin V [ 1 y 2 2 sin V cos V 1 y ....(2) Componentofvelocityofballalongtheinclinedplaneremainsame sin V cos V cos V y 2 1 ....(3) Vy sin = (V1–V2) cos Vy cos = V1 sin (3) & (2) using tan2 = 1 2 1 V V V V2 = V1(1– tan2) ....(4) (m1 + m2) V2 = m1V1 ....(1) Divide m1 + m2 = 2 1 tan 1 m 2 1 m m = cot2 –1; cot2 30° –1 = 2 Ans. ] Q.5 A radioreceiveris set upon a mast in themiddle of acalm lake to track the radio signal froma satellite orbitingtheearth.As the satelliterises abovethehorizon,theintensityof thesignal varies periodically. Theintensityisat a maximum when thesatellite is 1 =0.01 radian abovethe horizon and then again at 2 = 0.03 radian above the horizon. What is the wavelength (in meters) of the satellite signal? The receiver is h = 4.0 m above the lake surface. [Ans.0.16 m] [Sol. PR = sin h ; QR = PR cos 2 = sin 2 cos h X = PR – RQ + 2 h X = sin h (1–cos2) + 2 h = 2 h sin + 2 h X 2 h + 2 h sin =
- Maximumtomaximum = 2 h (2–1) + 0 = 2 (4) [0.03 – 0.01] = 2 (4) (0.02) = 0.16 m ] Q.6 Initiallyswitch S was closed for long time. Switch is opened at t = 0. Find the current (in amperes) through battery at time RC ln2. Take V = 12 V, R = 4 ohm, C = 1.0 F. [Ans.1.5A] [Sol. ]

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