12th IIT 24th Dec Test Paper-1 Solution

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1 th IIT 4th Dec Test Paper- Solution Subject-PHYSICS Part : SECTIN-A (MULTIPLE CHICE NE R MRE THAN NE CRRECT ANSWER) Q Two capacitors of capacitance C and C are charged to a potential difference of V and V respectively and are connected to an inductor of inductance L as shown in the figure. Initially key k is open. Now key k is closed and current in the circuit starts increasing. When current in the circuit is maximum (Given that C V C V ) charge on both the capacitors is same induced emf in the inductor is zero potential difference across both the capacitors is same electrostatic potential energy stored in both the capacitors is same (b, c) VL L di di As i is maximum 0 dt dt VL 0 Potential difference across two capacitors is zero Potential difference across two capacitors is equal & in opposite direction. As capacitance of capacitors is different & V is same, a & d are wrong. Q The magnetic field perpendicular to the plane of conducting ring of radius r changes at the rate Emf induced in the ring is r Emf induced in the ring is r the potential difference between diametrically opposite points on the ring is half of induced emf At positions of ring magnitude of electric field is r (a) A db db r r dt dt As it is not given that magnetic field is symmetrical to ring c & d option are not correct. 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78 db. Then dt

2 th IIT 4th Dec Test Paper- Solution Q Two non-conducting solid spheres of radii R and R, having uniform volume charge densities and respectively, touch each other. The net electric field at a distance R from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio Q4 4 5 can be 4 5 (b, d) A particle of mass m is acted upon by a force F F0 cos t. The distance travelled by the particle when (initial velocity of particle is zero) F 0 is 4 F0 m F 0 is It stops first time is 8 F0 m 6 F0 m It stops second time is 6 F0 m (a, d) a F0 cos t m v dv 0 t cos t dt 0 dv a dt F0 dx v sin ( / t ) dt m ( / ) x 0 At, F0 m dx F0 m t 0 sin ( / t ) dt x 4 F0 m cos 0 t t F 0 t 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

4 th IIT 4th Dec Test Paper- Solution It stops first time at t It stops IInd time at t 4 Q5 A puck is moving in a circle of radius r0 with a constant speed V0 on a level frictionless table.

3 4 th IIT 4th Dec Test Paper- Solution It stops first time at t It stops IInd time at t 4 Q5 A puck is moving in a circle of radius r0 with a constant speed V0 on a level frictionless table. A string is attached to the puck, which holds it in the circle; the string passes through a frictionless hole and is attached on the other end to a hanging object of mass M. The puck is now made to move with a speed v = v0, but still in circle. The mass of the hanging object is left unchanged. The acceleration a of the puck and the radius r of the circle are now given by 9 a0 r ' r ' r0 9 r0 (a, d) a = T mg a = a0 v r v 0 9 v 0 r0 r' a= Q6 a ' a ' a0 r = 9r0 Two blocks attached to a spring are given initial speeds as shown. Mass of kg is found to have moved 40 cm, when spring restores its normal length for the first time. Find time period of oscillation of spring ( 0) Timer Spring constant Timer period = 4/5 period = /5 Spring constant 5/ N/M 50 / N/M (a, c) After every T/ spring comes in natural length. In given case VC Q7 8 5 m/ s T 0. 4 T 4 5 ne mole of an ideal gas is taken through the cyclic process shown in the V - T diagram, where V volume and T absolute temperature of gas. Which of the following statements is/are correct Heat is given out by the gas in the complete cycle 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

4 5 th IIT 4th Dec Test Paper- Solution Heat is absorbed by the gas in the complete cycle The magnitude of the work by the gas in one cycle is RT0 ln The magnitude of the work done by the gas is V0 T0 (b, c) n PV diagram process is clockwise, hence heat is absorbed in complete cycle w w AD wcb R T0 Log RT0 Log R T0 Log Q8 Suppose the potential energy between an electron and a proton at a distance r is given by Ke/r. Application of Bohr s theory to hydrogen atom in this cases shows that: Q9 Energy in the nth orbit is proportional to n6 Energy is proportional to m- (m = mass of electron) Energy in the nth orbit is proportional to n- Energy is proportional to m (m = mass of electron) (a, b) Which of the following is/are conservative force(s)? F r r F 5 rˆ r F ( xiˆ yˆj ) F (x y ) (a, b, c) Since, W F. d r Clearly, for forces a and b the integration does not require any information of the path taken For WC ( xiˆ yˆj ) (x y ). (dx iˆ dy ˆj ) x dx y dy (x y ) Taking x y t, we get x dx y dy dt dt dt / dt WC / / t t xdx ydy 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78 [ yi xj ] (x y )

$Hence, it is non-conservative Q0 The plot between refractive index of a medium µ and wavelength of the light λ for a material medium may be best represented by a b c d (a) SECTIN-D Integer Answer$

5 6 th IIT 4th Dec Test Paper- Solution Which is solvable Hence, a, b, and c, are conservative forces But d requires some more information on path. Hence, it is non-conservative Q0 The plot between refractive index of a medium µ and wavelength of the light λ for a material medium may be best represented by a b c d (a) SECTIN-D Integer Answer Type This section Contains 8 questions. The answer to each of the questions is a single digit integer, ranging from 0 to The appropriate bubbles below the respective question numbers in the MR have to be darkened. Q In the circuit shown what is the maximum number of switches that must be closed to turn on all the lights (4) Switch //4/5 should be on Q A cannon of mass 0 0 kg is rigidly to the earth so it can recoil only by a negligible amount. The cannon fires a 0 kg shell horizontally with an initial velocity of 550 m/s. Suppose the cannon is then unbolted from the earth, and no external force hinders its recoil. the velocity (in m/s) of a shell fired horizontal by this loose cannon is 0 N then value of N is (50) VR will be same in both cases by momentum conservation VB 500 Q Three conducting concentric shells of radius.5 cm/.5 cm/4.5 cm are given charges - 5 c, + 0 c & +0 c respectively. What is interaction energy of rd shell (outer most) with other two (0) Interaction energy = qv 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

7 th IIT 4th Dec Test Paper- Solution q q V K R R Q4 9 0 9 5 0 6 = 0 J 4.5 0 Interaction energy 0 5 The magnetic field of a cylindrical magnet that has a pole face radius.

At a radial distance of cm from the axis, find the amplitude of the electric field (in units of 0 mn/c) induced by the magnetic field variation. () Ed A db dt As B 7 (0.) sin ( t ) ; E r (0.

6 7 th IIT 4th Dec Test Paper- Solution q q V K R R Q = 0 J Interaction energy 0 5 The magnetic field of a cylindrical magnet that has a pole face radius.8 cm can be varied sinusoidally between the minimum value 6.8 T and the maximum value 7. T at a frequency of 50 / Hz. Cross section of the magnetic field created by the magnet is shown in fig. At a radial distance of cm from the axis, find the amplitude of the electric field (in units of 0 mn/c) induced by the magnetic field variation. () Ed A db dt As B 7 (0.) sin ( t ) ; E r (0.) cos ( t ) Magnitude of the amplitude Q5 E ( r ) r (0.) cos ( t ) r (0.) 0 mn/c A planet moves around the sun in an elliptical orbit such that its KE is K and K when it is nearest to the sun and farthest from the sun respectively. It is given that K = 9K. Find the ratio of largest distance (r) to the smallest distance (r) between planet and the sun Q6 () In the figure shown all the surfaces are frictionless, and mass of the block is m 00 g. The block and the wedge are held initially at rest. Now the wedge is given a horizontal acceleration of 0 ms by applying a force on the wedge, so that the block does not slip on the wedge. Then find the work done in joules by the normal force in ground frame on the block in s. 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

7 8 th IIT 4th Dec Test Paper- Solution Q7 (5) A current carrying ring has moment of inertia Kg m about an axis passing through its centre and perpendicular to its plane. The centre of the ring is at the origin. The ring has magnetic moment M iˆ 4 ˆj A m. A magnetic field B 4iˆ ˆj T is switched on at t 0. Find the maximum angular velocity of the ring (in rad sec ) (5) U I mb cos = 0 [m & B are ) U F U Q8 I Iw A radioactive element decays by -emission. A detector records n beta particles in s and in next s it records 0.75n beta particles. Find mean life in second correct to nearest whole number. Given ln = 0.69, ln =.0986 (7) 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

8 9 th IIT 4th Dec Test Paper- Solution SECTIN-E (CLUMN MATCHIMG TYPE) Q. Column A (p) Body is a block lying on a rough inclined Column B plane. Angle angle of repose. A is Force exerted by A on body can be equal to it s weight in magnitude inclined surface (q) Body is a ball falling in liquid with terminal velocity. A is liquid If density of body is somehow increased without changing r, it s acceleration/constant state of motion velocity) or (constant equilibrium position will be disturbed (r) Body is a spherical ball rolling purely on inclined plane; inclined at an angle equal Work done by the force exerted by A on the body is zero to angle of repose. The inclined surface is 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

9 0 th IIT 4th Dec Test Paper- Solution A. (s) Body is m hanging on an ideal pulley Mechanical energy of body is constant as time passes (e.) The kinetic energy of body is constant as time passes system. A is string m < m Q. p a, c, d, e; q b, e; r c, d; s b. Column I gives certain situations in which a straight metallic wire of resistance R is used and column II given some resulting effect. Match the statements in column I with the statement in Column II Column A (p) Column B A fully discharged capacitor and a battery A Constant current flows through the wire of constant Emf is connected to the end of the wire (q) The wire is rotate about one end of it s Thermal energy is generated in the wire A constant potential difference develops between the length with constant angular velocity in a uniform magnetic field perpendicular to the plane of motion (r) The wire is bent into a semi circular ring and placed in a constant electric field with ends of the wire it s diameter perpendicular to electric field (s) A A.C. current source is connected to the Charge of constant magnitude appear at the ends of end of the wire the wire p b; q c, d; r d; s b. 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

10 th IIT 4th Dec Test Paper- Solution Subject-CHEMISTRY Part : SECTIN-A (MULTIPLE CHICE NE R MRE THAN NE CRRECT ANSWER) Q Correct statement(s) for complex compound [CoBr (NCS) (H ) (NH ) ] (N ) Its ionization isomer is diamagnetic It has one pair of enantiomers In one of its optical isomers Br and NCS are at trans position It is less stable than [Co(en)]+ (a, b, c, d) (a) For its Ionization isomer [Co(N )(NCS)(H )(NH ) ] Br : P Δ 0 (b) nly cis form is optically active; hence number of enantiomeric pairs = (c) All trans forms are optically inactive and these forms are included in optical isomers (d) [Co (en) ] is more stable than the given complex because of chelation as well as ethylene diamine is stronger ligand than NH. Q Pair (s) of cations that can be separated by NH 4 H solution. Pb (aq), Cu (aq) Hg (aq), Ag (aq) Fe (aq), Mg (aq) Ni (aq), (a, b, d) 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78 Mn (aq)

11 th IIT 4th Dec Test Paper- Solution Q ctahedral complex which neither show ionization nor hydrate isomerism. [Fe (H ) 5 NH ]S 4 [Fe (H ) 5 Cl] S 4 [Co (NH ) S 4 ] Cl 4 [Fe (H )5 Cl] Cl (a, c, d) Complex A, C, D donot exhibit ionization isomerism because: In complex - (A): there is absence of anionic ligand. In complex - (B): S 4 is working as bidentate ligand while Cl acts as monodentate ligand. In complex - (C): same anion lies within coordination sphere and out side it. If simple anion outside coordination sphere is exchanged with water ligands in complexes A and D then resulting complexes become natural hence they donot exhibit hydrate isomerism. Q4 HA HE HD HB HC correct statement about is/are Compound can show geometrical isomer During prolonged treatment Most This acidic hydrogen atom is C 5H replace by 5D compound can show addition reaction (b, c, d) Q5 HC C CH CH CH H CH Identify correct statement about product Product Enol is Q6 show iodoform test more stable than keto Product show tollen test Enol show geometrical isomer (a, b, c, d) In which of the following reaction geometrical isomer will be formed as a product. H+ H HC Ph C H + NH - H CH HC C H HC H+ () KCN () H H 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

th IIT 4th Dec Test Paper- Solution Q7 (a, b, c) In which of reaction final product is aldehyde Q8 H Ph C Cl Pd-BaS4 R C N DIBAL-H H Q9 R C N + SnCl + HCl Et C Et (A) DIBAL-H H (a, b, c, d) Which of

12 th IIT 4th Dec Test Paper- Solution Q7 (a, b, c) In which of reaction final product is aldehyde Q8 H Ph C Cl Pd-BaS4 R C N DIBAL-H H Q9 R C N + SnCl + HCl Et C Et (A) DIBAL-H H (a, b, c, d) Which of the following compound when reacts hot KMn 4 from pthallic acid? (b) 500 ml.4 V H solution and 500 ml 44.8 V H solution mixed together. Which is/are correct statement about final H solution of density equal to.8 gm/ml. volume strength is %.6 V w/v of H is 0. Molarity is M mole fraction of H is (a, b, c, d) 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78 H (B)

13 4 th IIT 4th Dec Test Paper- Solution Q0 For given parallel reaction - ) K sec ( in B + C A K (in sec ) 4D + E Which of the following is/are correctly for % yield of mole in product mixture? %B 40k k k %D 80 k k k %C 60 k k k %E 0 k k k (a, b, c) SECTIN-D Integer Answer Type This section Contains 8 questions. The answer to each of the questions is a single digit integer, ranging from 0 to The appropriate bubbles below the respective question numbers in the MR have to be darkened. Q From the following given species, find out total number of species having partially filled HM (Highest ccupied Molecular rbital) of sigma character. N, N,, C, B, H, C, N, 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

14 5 th IIT 4 th Dec Test Paper- Solution () & N H ions have partially field HM of -character N,,, N, B species have partially filled HM of -character Q C ion has fully filled HM of -character Consider thermal decomposition of following ammonium salts and calculate value of expression P Q (NH 4 ) Cr 7, NH 4 N, NH 4 N, NH 4 Cl, CH CNH 4, NH 4 Cl 4, (NH 4 ) S, (NH 4 ) C, (NH 4 ) C4 Where: P: Total number of ammonium salts which liberates basic NH gas on thermal decomposition. Q: Total number of ammonium salts which liberates neutral N gas on thermal decomposition. () If anionic part in ammonium salt is weakly oxidizing or non-oxidising in nature then it produces NH gas on thermal decomposition If anionic part in ammonium salt is strong oxidizing in nature, then it produces N gas on thermal decomposition Q Consider the following reaction and predict the number of d-electrons in t g set of d-orbitals in purple (6) complex. Na [Fe(CN) 5 N] Na S purple complex. Q4 Calculate the total number of compound evolve C gas on heating? 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

15 6 th IIT 4th Dec Test Paper- Solution (a) CH H (b) H (c) CH H CH (d) (e) HC CH CH (i) CH (h) CH (j) HC Q5 (f) H CH (g) CH (k) CH CH (5) x = Number of compounds which become aromatic after reaction with KH. (a) (b) (c) (d) (e) (f) (g) (h) () H+ Q6 H x = Number of alkene (Including stereoisomers) 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

16 7 th IIT 4th Dec Test Paper- Solution Q7 (5) Given H(g) + S(s) HS(g) G of ( H S, gas ) kcal If K p for this reaction is 0 x at 00 K calculate the value of x. Q8 (5) To 50 ml of water, x g of acetic acid is added. If.5 % of acetic acid is dissociated, the depression in freezing point comes out What will be the value of x? Given: K f (water) =.86 K kg mol and density of water is g ml () SECTIN-E (CLUMN MATCHIMG TYPE) Q. Consider the following experimental setup: (p) Column A Column B (Expression for ph) (Extent of titration) pk a log [ salt ] [ Acid ] No titration 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

17 8 th IIT 4th Dec Test Paper- Solution (q) (r) ( pk a log C ) 4 log[h ] (s) ( pk w pk a log C ) p b; q a; r d; s c Q. Titration < 00 % Titration = 00 % Titration > 00 % Column A (p) NCl + (q) KCN H H Column B NaH/H CH Racemic mixture Addition reaction Substitution reaction Coupling reaction (e.) Carbanion as an intermediate 0oC Cl (r) (s) H C EtH Ethanolysis CH NBS p c, d, e; q a, b; r a, c; s p, b 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

18 9 th IIT 4th Dec Test Paper- Solution Subject-Mathematics Part : SECTIN-A (MULTIPLE CHICE NE R MRE THAN NE CRRECT ANSWER) Q x A Function f (x ) satisfies f ( x) sin x f ' (t ) ( sin t sin t ) dt then f (x ) is 0 x sin x cos x cos x tan x sin x sin x. sec x( sin x ) (b, d) Differentiate both sides w.r.t. x f ' ( x ) cos x f ' ( x ) ( sin x sin x) ( sin x sin x ) f ' ( x) cos x cos x cos x f ' ( x) sin x sin x ( sin x) cos xdx Integrating f ( x) (Put sin x t ); ( sin x) Also f (0) 0, hence C sin x sin x f ( x) sin x sin x sin x Q dt C t sin x t If A and B are different matrices satisfying A B and A B B A, then which is incorrect det (A B ) may be zero det (A B) may be zero det (A B ) as well as det (A B) must be zero At least one of det (A B ) or det (A B) must be zero f ( x) (a, b, c) A B..() and A B B A..() () () gives, A A B B B A A (A B) B (A B) (A B ) (A B) 0 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

19 0 th IIT 4th Dec Test Paper- Solution det(a B ) (A B) 0 det(a B ). det (A B) 0 Q The value of 0 Q4 sin x cos x, when ever defined never lies between cos x sin x and and and and (c, d) If the line passing through (,, b) and (4,, ) is perpendicular to the vector iˆ ˆj kˆ and is parallel to the plane containing the vectors iˆ ckˆ and cˆj bkˆ then the ordered pair (b, c ) is, (, 6) (, 0), (c, d) 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

20 th IIT 4th Dec Test Paper- Solution Q5 A committee of three persons it to be randomly selected from a group of three men and two women and the chair person will be randomly selected from the committee. The probability that the committee will have exactly two women and one man, and that the chair person will be a woman, is p then p Q (a, b) A circle having centre (0, k ) with k 6 is tangent to the lines pair x y 0 and y 6. The radius of the circle is a b c, here a, b, c are lowest possible natural numbers then a, b are same a, c are same b, c are same a, b, c are not all equal Q7 (b, d) cos n x n The function defined as f ( x) Lim n x n xn if x 0 if 0 x. Which of the following does not hold if x good? Q8 Continuous at x 0 but discontinuous at x Continuous Continuous both at x and x 0 discontinuous at x but discontinuous at x 0 both at x and x 0 (a, b, c) The line which contains all points ( x, y, z ) which are of the form ( x, y, z ) (,, 5) (,, ) intersects the plane x y 4 z 6 at P and intersects the YZ plane at Q. If the distance PQ is a b where a, b are relatively prime and a then (a b) equals 95 7 (a) 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

21 th IIT 4th Dec Test Paper- Solution Q9 The number is an example of nine digit number which contains each of the digit to 9 exactly once. It also has the property that the digit to 5 occur in their natural order, while the digit to 6 do not. Number of such numbers are 68 Q (b) The equation x 50 5 x cos 8 x is satisfied by x cos 8 7 x cos 8 x cos 8 (a, b, c) 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

22 th IIT 4th Dec Test Paper- Solution SECTIN-B Integer Answer Type This section Contains 6 questions. The answer to each of the questions is a single digit integer, ranging from 0 to The appropriate bubbles below the respective question numbers in the MR have to be darkened. Q A line intersects the straight lines 5 x y 4 0 and x 4 y 4 0 at A and B respectively. If a point P (, 5) on the line AB is such that AP : PB : (internally), find the sum of the co-ordinates of point A. Q (6) If the tangent at P of the curve y x intersects the curve again at Q and the straight lines P, Q make angles, with the x axis where is the origin, then what is the value of tan. cot? () 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

23 4 th IIT 4th Dec Test Paper- Solution Q x 4t. f ' (t ). dt. 4 t The value of 800. f ' (4) is 00 then will be given that f ( x) Q4 (64) From a point P outside the circle x y r, tangents PA and PB are drawn. If, then 6 r ( PA) find the length of chord of the pair of tangents. Q5 (8) In a triangle of base 6, the ratio of the other two sides is /. The maximum value of altitude of the triangle is. (4) 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

24 5 th IIT 4th Dec Test Paper- Solution Q6 An ellipse is drawn with major and minor axes of lengths 0 and 8 respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. Find the radius of the circle. () Q7 If cos 4 y sin 4 y cos 4 x sin 4 x Then find the value of.. cos x sin x cos y sin y () 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

25 6 th IIT 4th Dec Test Paper- Solution Q8 x 4, in [a, b] then a b x Solution set of the in equation sin sin () SECTIN-C (CLUMN MATCHING TYPE) Q. Column A (p) The expression tan 55. tan 65. tan 75 Column B 0 simplifies to cot x Where x (0, 90) 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

26 7 th IIT 4th Dec Test Paper- Solution then x equals (q) abc 0, a b c 0 Suppose a a b b c c x Then and 9 the value x 6 x 7 equals (r) f : R R and satisfies f (), 8 5 f ' () 4. If ( x) f " ( x)dx 7, then f () has the value equal to (s) The intersection of the planes x y z 8 and x y 4 z 4 is the line L. The value of 'a ' for which the line L is perpendicular to the line through (a,, ) and (6,, ) is (p) - d; (q) - a; (r) - a; (d) b. 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

27 8 th IIT 4th Dec Test Paper- Solution Q. The greatest and least value of functions in column I on [0, 4] are respectively: Column A (p) The maximum value of Column B z when z 4 (where z is a complex number) satisfies the conditions z is z (q) If (5 6 ) n I f, where I and n are positive integers and f is a Positive fraction less than one, than value of ( f ) ( f ) is (r) If three positive real nos. a, b, c are in AP such that abc 4, than minimum value of b is (s) log.5... The value of (0.6) (p) - b; (q) - c; (r) - d; (d) - a. is 4 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

28 9 th IIT 4 th Dec Test Paper- Solution 0, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 78

12th IIT 14th May Test Paper-1 Solution

12th IIT 14th May Test Paper-1 Solution th IIT 4th May Test Paper- Solution Subject-PHYSICS Part : SECTIN-A (MULTIPLE CHICE NE R MRE THAN NE CRRECT ANSWER) Q Two capacitors of capacitance C and C are charged to a potential difference of V and