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

2. Take g = 10 m/s2 where ever required in this paper. PART-A Select the correct alternative. (More than one is/are correct) [9 × 6 = 54] There is NEGATIVE marking. 1 markwillbe deducted for eachwrong answer. Q.1 The function f (x) is defined for x  0 and has its inverse g (x) which is differentiable. If f (x) satisfies  ) x ( g 0 dt ) t ( f = x2 and g (0) = 0 then (A) f (x) isan odd linear polynomial (B) f (x) issome quadratic polynomial (C) f (2) = 1 (D) g (2) = 4 Q.2 Consider a triangleABC in xyplane with D, E and F as the middle points ofthe sides BC, CAandAB respectively. Ifthe coordinates ofthe pointsD, E and Fare (3/2, 3/2); (7/2, 0) and (0, –1/2) thenwhich ofthefollowing are correct? (A) circumcentre ofthe triangleABC does not lie insidethe triangle. (B) orthocentre, centroid, circumcentre and incentre oftriangleDEF are collinear but oftriangleABC are noncollinear. (C) Equation ofa line passes throughthe orthocentre oftriangleABC and perpendicular to its plane is k̂ ) j ˆ î ( 2 r      (D) distancebetween centroid and orthocentre ofthe triangleABC is 3 2 5 . Q.3 Ifa continuous functionf (x)satisfies the relation,   x 0 dt ) t x ( t f =  x 0 dt ) t ( f +sinx+ cosx– x–1, for allrealnumbers x, then whichofthe following does not hold good? (A) f (0) = 1 (B) f ' (0) = 0 (C) f '' (0) = 2 (D)   0 dx ) x ( f = e ROUGHWORK
3. Q.4 Stepwise hydrolysis ofP4O10 takes place via formation of (A) Tetrametaphosphoric acid (B) Tetrapolyphosphoric acid (C) Pyrophosphoric acid (D) Orthophosphoric acid Q.5 Monochlorinationof(S)-2-chlorobutane cangive (A) (S)-1,2-dichlorobutane (B) (R)-1,2- dichlorobutane (C) (2R, 3S)-2,3-dichlorobutane (D) (2R,3R)-2,3-dichlorobutane Q.6 Select the correct statement about the compound NO[BF4] (A) It has 5  and 2  bond (B) Nitrogen-oxygenbondlength is higher thannitric oxide (NO) (C) It is a diamagnetic specie (D) B–Fbond length in this compound is lower thanin BF3. ROUGHWORK
4. ROUGHWORK Q.7 A blast breaks a bodyinitiallyat rest ofmass 0.5 kg into three pieces, two smaller pieces ofequalmass andthethird double the massofeither ofsmallpiece.After the blast the two smaller massesmoveat right anglesto oneanother with equal speed. Find thestatementsthat is/aretruefor this case assumingthat the energyofblast is totallytransferred to masses. (A)Allthe three pieces share the energyofblast equally (B) The speed ofbigger mass is 2 times the speed ofeither ofthe smaller mass (C) The directionofmotionofbigger mass makes an angle of135°with the directionofsmaller pieces (D) The bigger piece carries double the energyofeither piece. Q.8 You wish to lift a heavy block through a height h by attaching a string of negligible mass to it and pulling so that it moves at a constant velocity. You have the choice of lifting it either by pulling the string (i) vertically upward or (ii) along a frictionless inclined plane (see diagram).Which one of the following statements is true? (A) The magnitude of the tension force in the string is smaller in case (i) than in case (ii). (B) The work done on the block by the tension force is the same in both cases. (C) The work done on the block by the tension force is smaller in case (ii) than in case (i). (D) The work done on the block by the gravitational force is smaller in case (ii) than in case (i). Q.9 The wiresAand B shown in the figure are made of the same materialand have radii rA and rB respectively. The block between them has a mass m. When the force F is mg/3, one of the wires breaks. (A) A breaks if rA = rB (B) A breaks if rA < 2rB (C) Either A or B may break if rA = 2rB (D) The lengths ofAand B must be known to predict which wire will break
5. PART-B MATCH THE COLUMN [9 × 8 = 72] There is NEGATIVE marking. 0.5 markwillbe deducted for each wrong matchwithin a question. INSTRUCTIONS: Column-Iand column-IIcontains fourentrieseach. Entries ofcolumn-Iare to be matchedwith some entriesofcolumn-II.Oneormorethanoneentriesofcolumn-Imayhavethematchingwiththesameentries ofcolumn-IIandoneentryofcolumn-Imayhaveoneormorethanonematchingwithentriesofcolumn-II. Q.1 ColumnI ColumnII (A)    x e x 3 t n dt x x n Lim l l is (P) 0 (B)            1 x 1 x x 2 4 e e Lim is (Q) 2 1 (C) n 4 ) 1 n ( sin 1 n 5 . 0 n sin ) 1 ( Lim 2 n n               is where n  N (R) 1 (D) The value ofthe integral                     1 0 2 1 1 dx 2 x 2 x 2 1 tan 1 x x tan is (S) nonexistent
6. Q.2 Consider thematricesA=         1 1 4 3 andB =       1 0 b a andlet Pbe anyorthogonalmatrix and Q = PAP APT and R = PTQKP also S = PBPT and T = PTSKP ColumnI ColumnII (A) Ifwe varyK from 1 to n then the first row (P) G.P. withcommonratio a first columnelementsat Rwillform (B) Ifwe vary K from1 to n then the 2nd row 2nd (Q) A.P. with common difference 2 columnelementsat R willform (C) Ifwe varyK from1 to n then the first row first (R) G.P. with common ratio b columnelementsofT willform (D) Ifwe varyK from3 to n thenthe first row 2nd column (S) A.P. with common difference – 2. elements ofT willrepresent the sumof
7. Q.3 ColumnI ColumnII (A) Given two vectors b and a   such that | b | | a |    = | b a |    = 1 (P) 30° The angle between the vectors b a 2    and a  is (B) In a scalene triangleABC, if a cosA= b cos B (Q) 45° then  C equals (C) In a triangleABC, BC = 1 andAC = 2. The maximumpossible (R) 60° value which the Acanhave is (D) In a  ABC  B = 75° and BC = 2AD whereAD is the (S) 90° altitude fromA, then  C equals
8. Q.4 Matchthe column: ColumnI ColumnII (A) (P) Conformationofmaximumtorsionalstrain (B) (Q) Conformationwithstrongintramolecular hydrogenbond (C) (R) Highest boilingpoint (D) (S) ConformationofminimumVanderWaalstrain
9. Q.5 ColumnI ColumnII (Co-ordinationcompound) (Type ofisomerism shown) (A) Na2[Pt(SCN)2(Ox)2] (P) Ionizationisomerism (B) [CrCl2(NH3)4]NO3 (Q) Linkageisomerism (C) [Pt(NO2)(Gly)(NH3)] (R) Geometricalisomerism (D) K3[Fe(OH)2(C2O4)2] (S) Opticalisomerism Q.6 Match the names ofcarboxylic acids incolumnI withpka valueincolumnII. ColumnI ColumnII (A) Benzoic acid (P) 4.17 (B) Ethanoicacid (Q) 4.14 (C) o-methylbenzoic acid (R) 4.74 (D) p-flourobenzoic acid (S) 3.91
10. Q.7 Aglass diskwhose plane surfaces areparallelis cut asshowninfigure thenthe lenses so obtained are moved apart. What willhappen to a beamofparallelrays falling on to the system. ( f is the focallengthofconverging lens). EFFECT (A) (P) Emergingraysareconverging&imagedistancefromL2<f (B) (Q) Emerging rays are diverging &imagedistancefromL2 < f (C) (R) Emerging rays are converging &imagedistancefromL2 > f (D) (S) Emerging rays are diverging &imagedistancefromL2 > f
11. Q.8 Abodyinitiallymovingtowards right explodesinto two pieces1 and2. Directionofmotionofthe pieces is shown incolumn I and possible mass ratio are shownin column II ColumnI ColumnII (A) (P) m1 > m2 (B) (Q) m1 = m2 (C) , v1 > v2 (R) m1 < m2 (D) (S) Impossible for anymasses
12. Q.9 A projectile islaunched at angle  to horizontalfromL and it hits thetarget T on levelground. ColumnI Column II (A) Magnitude ofradialacceleration (P) Increases (B) Magnitude oftangentialacceleration (Q) Decreases (C) Power deliveredbygravity (R) First increases, then decreases (D) Torque ofgravityabout T (S) First decreases, then increases
13. PART-C SUBJECTIVE: [15 × 10 =150] Q.1 Suppose V =    2 0 2 dx 2 1 x sin x , find the value of  V 96 .
14. Q.2 One of the roots of the equation 2000x6 + 100x5 + 10x3 + x– 2 = 0 is ofthe form r n m  , where m is non zero integer and n and r are relativelyprime naturalnumbers. Find the value of m + n + r.
15. Q.3 Acircle C is tangent to the x and yaxis in the first quadrant at the points Pand Q respectively. BC and AD are paralleltangents to the circle with slope – 1. Ifthe pointsAand B are on the y-axis whileC and D are on thex-axis and the area ofthefigureABCD is 900 2 sq. units thenfindthe radius ofthe circle.
16. Q.4 Let f (x) = ax2 – 4ax+ b(a> 0) be definedin1  x  5. Suppose the average ofthe maximumvalue and the minimumvalue ofthe functionis 14, and the difference betweenthe maximumvalue and minimum value is 18. Find the value of a2 + b2.
17. Q.5 If the            bx 1 ax 1 x 1 1 x 1 Lim 3 0 x existsand has the valueequalto l, thenfind the valueof b 3 2 a 1   l .
18. Q.6 Calculate the Hvaporization [CH3COOH( l )] in kJ/mol Given data Hsolution [KF. CH3COOH(s)] in glacial acetic acid = –3 kJ/mole Hsolution [KF(s)] inglacialacetic acid = +35 kJ/mole The strength ofH-bond between F–(g) and CH3COOH (g) = +46 kJ/mole Lattice enthalpyof KF.CH3COOH(s) = +734 kJ/mole Lattice EnthalpyofKF(s) = +797 kJ/mole
19. Q.7 The gaseousdecomposition reaction A(g)  2B(g) + C(g) is observedto first order over the excess ofliquidwater at 25°C, it is found that at the end of10min, the totalpressure ofsystemis 188 torr and after verylong time it is 388 torr. Calculate rate constant ofthe reaction(inhr–1) Given : vapour pressure of H2O at 25° is 28 torr (ln2 = 0.7, ln3 = 1.1, ln10 = 2.3)
20. Q.8 When1 moleofA(g) is introducedina closed rigid 1 litre vesselmaintained at constant temperature the following equilibriaare established. A(g) l B(g) + C(g) : 1 C K C (g) l D(g) + B(g) : 2 C K The pressure at equilibriumis twice the initialpressure. Calculatethe value of 1 2 C C K K if eq eq ] B [ ] C [ = 5 1
21. Q.9 Totalentropychange (system+ surrounding) for the process H2O (l,–8°C) H2O (s, –8°C) at 1 atm and – 8°C is 1 J/K mol. Find Cp,m (H2O, l) in J/K mol. Given : Hmelting(at –8°C) = + 5784.95 J/mol, Hmelting(at 0°C) =6006 J/mol Cp,m(H2O, s) = 36 J/K mol ln       265 273 = 0.03
22. Q.10 The equilibriumconstant Kp for the reaction N2O4 (g) l 2NO2(g) is 4.5 at temperature T. What would be the average molar mass (in gm/mol) ofanequilibriummixture ofN2O4 & NO2 formed bythe dissociationofpure N2O4 at a total pressure of2 atmat temperature T.
23. Q.11 Arocket isprojected straight up andexplodes into three equallymassive fragments just asit reaches the top ofitsflight (refer figure). Oneofthe fragmentsisobserved to come straight downin 2sec,while the other two take4secto cometo ground, aftertheburst. Find theheighth(inm)atwhichthefragmentation occurred.
24. Q.12 BoardAis placed on board Bas shown. Bothboards slide, without moving withrespect to eachother, along africtionlesshorizontalsurface at aspeed 6 m/s. Board Bhits aresulting boardC "head-on".After the collision, boards B and C stick together and boardAslides on top ofboard C and stops its motion relative to C in the positionshown on the diagram. What is the length (in m) of eachboard?All three boards have the same mass, size and shape. The coefficient ofkinetic friction between boardsAand C and between boardsA& B is .
25. Q.13 Asideview ofasimplifiedformofverticallatchB is asshown. Thelower memberAcan be pushed forward in its horizontalchannel. The sides of the channels are smooth, but at the interfaces ofAand B, which are at 45°withthehorizontal, there exists a static coefficient offriction=0.4. What is theminimumforce F(inN) that must be appliedhorizontallytoA to start motionof the latch B if it has a mass m= 0.6 kg ?
26. Q.14 The essentialelements ofone formofsimple speed governorare asshown: to a vertical shaft a horizontalrod is mounted symmetricallyand on the horizontal rod are freely sliding brake shoes. When the shaft turns at a frequency of rotation f = 10 Hz, the brake shoes press against the inner surface ofa stationarycylindricalbrake drum. Ifthe brake shoes are each ofmassm= 1kg, and their thickness dimension is negligible compared to the inner radius ofthe brake drumr =0.1 m, and the coefficient ofsliding friction between the shoes and the drumis = 0.5, find the power required inwatt to turnthegovernor shaft. [Take: 2 = 10]
27. Q.15 Aring ofmass m= 1kg canslide over asmoothverticalrod.Alight string attached to the ring passing over a smooth fixed pulleyat a distance ofL = 0.7 mfromthe rod asshownin the figure.At the other endofthe string massM = 5 kgis attached, lying overa smooth fixed inclined plane ofinclinationangle37°. The ring isheld in levelwith thepulleyand released. Determine the velocityofring (inm/s) when the string makes an angle (  37°) withthe horizontal. [sin37°=0.6]