Mock Test 1 Paper 1 With Solution 2014

8/10/2019 Mock Test 1 Paper 1 With Solution 2014

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Time: 3:00 Hours Max. Marks: 240VERY IMPORTANT

A. The question paper consists of 3 section ( Section-1 contains Physics, Section-2 contains Chemistry and Section-3contains Mathematics ). Please fill the OMR answer Sheet accordingly and carefully.

B. Each Section contains (15 questions in Part-A, 1 questions in Part-B and 4 questions in Part-D).C. Please ensure that the Question Paper you have received contains ALL THE QUESTIONS in each Section

and PAGES. If you found some mistake like missing questions or pages then contact immediately to theInvigilator.

INSTRUCTIONSPART-A

1. Q.1 to Q.7 are single correct type questions . Each question has four choices (A), (B), (C) and (D) out of which

ONLY ONE is correct. For each question, you will be awarded 3 marks if you have darkened only the bubblecorresponding to the correct answer and zero mark if no bubble are darkened. In all other cases, minus one (1)mark will be awarded.

2. Q.8 to Q.10 are Paragraph type. Based upon the paragraph 3 single correct type questions have to be answered. Eachof these questions has four choices (A), (B), (C) and (D) out of which ONLY ONEis correct. For each question you will beawarded 3 marks , if you have darkenedonly the bubble corresponding to the correctanswerand zero mark ifnobubble aredarkened. In all other cases, minus one (1) mark will be awarded.

3. Q.11 to Q.15 are multiple correct type questions .Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct. For each question, you will be awarded 5 marks if you have darkened only thebubble corresponding to the correct answer and zero mark if no bubble are darkened. No negative marks will be awardedin this section.

PART-B

4. Q.1 is Matrix Match type question. Each question has Three statements (A, B, C) given in Column-I andFour statements (P, Q, R, S) given in Column-II. Any given statement in Column-I can have correct matching with one or more statement(s) given inColumn-II. For example, if for a given question, statement B matches with the statement given inQ and R, then for the particular question, against statement B darken the bubbles corresponding to Q and R in the OMR.For each row, you will be awarded 3 marks in which you have darkened the bubble(s) corresponding to the correctanswer and additional 1 Bonus marks will be awarded if all the answers are correct.Thus Q.1 carries a maximum of 10 marks.

PART-D

5. Q.1 to Q.4 are Integer Type questions . The answer to each question is a upto 4 digit ranging from0 to 9999. The correct digit below the question number in the OMR is to be bubbled.For each question, you will be awarded 5 marks if you darken the bubble corresponding to the correct answer and

zero mark if no bubble is darkened.For example, if for a given question, your answer is 7 or 77 or 777 or 7777, then for the particular question, againstquestion number you must fill as 0007 or 0077, 0777 & 7777 respectively in the OMR. No negative marks will beawarded in this section.

6. Indicate the correct answer for each question by filling appropriate bubble in your answer sheet.7. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed.8. The answers ofthe questions mustbe markedbyshadingthe circleagainst the questionby darkBlack Ball point Pen only.

CODE AM O C K T E S T

PAPER-I

USEFUL DATA

Atomicweights: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 = 65.5, Ti = 48,

Ba = 137, U = 238, Co= 59, B =11, F = 19, He = 4, Ne = 20, Ar = 40 , Mo = 96[Take : l n 2 = 0.69, l n 3 = 1.09, e = 1.6 10 19, m e= 9.1 10 31 kg ]

Take 0 = 8.85 10 12 , g = 10 m/s 2 unless otherwise stated


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Mock Test-1 [Paper-I] Page # 2

PHYSICS

PART-A[SINGLE CORRECT CHOICE TYPE]

Q.1 to Q.7 has four choices (A), (B), (C), (D) out of which ONLY ONE is correct.

Q.1 Asolid cylinder is rolling withslippingonperfectly rough partABasshown. It has angularmomentumLabout A.Find its angular momentum aboutAwhen it reaches the top of the part BC which is perfectlysmooth.

30

C

A B

(A) zero (B) L (C)2L (D)

3L

Q.2 The escapevelocityof a bodyon a planet isVe,if weassume the planet to beisolatedfrom otherbodies.The escapevelocityif weassume that there are others planets too in the surroundings will be(A) > Ve (B) < Ve (C) = Ve (D) Data insufficient

Q.3 In a series LCR, ac circuit, the voltage across each of R, L and C is 100 V, and the current is 5A. If resistance is shortedbymeans ofa conducting wire, the current in circuit will become(A) zero (B) 10 A (C) 20 A (D) (infinite)

Q.4 1 moleofan ideal gas is taken through the processABas shown.The maximum temperature of the gasduring AB is 500 K. If work done byGas is W then ( n2.7=1)

A

BV

P

V 2.7V

(A) W < 5000 J (B) 5000 J < W < 6000 J(C) 6000 J < W < 7000 J (D) W > 7000 J

Q.5 Initially the radioactivity of a sample is three times thatof another.After a half lifeof one of them, thecombined activitybecomes one-third of theinitial combinedactivity. Ratioof their half lives iscloser to(A) log 10 1.5 (B) log 2 3.6 (C) lon e 3.6 (D) log e 1.8

Q.6 In a X-ray tube, the operating voltageV is slightlychanges by V. Then if min is the original cut off wavelength, the spread between k and min changes by:

(A) min VV

(B) min VV

(C) min 2VV

(D) min2VV


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PHYSICSQ.7 A bodymoves with speed 20 m/sec for 10 sec and then with 30m/sec for some distance. The average

speed may be(A) 8 m/sec (B) 15 m/sec (C) 25 m/sec (D) all of these are possible

[PARAGRAPH TYPE]


Paragraph for question nos. 8 to 10A convex lens, a concave mirror and a convex mirror have same

A B C

O I E

EO ITrial-I

Trial-II

magnitude of focal length are available. In the figure shown,these are denoted as optical element E, the real object O andimage (real orvirtual) is denoted as I. Three pointsA,B and Care on a straight line as shown.AC is less than three times thefocal lengthofoptical element.Twotrials areconducted givingresults as shown.Position B is the samefor both trials.

Q.8 In trial-I, E can be :(A) only a convex lens (B) only a concave mirror (C)only aconvex mirror (D) convex lensora concave mirror

Q.9 In trial-II, E is :(A) convex lens (B) concave mirror (C)convex mirror (D)bothconcavemirrorandconvexmirrorarepossible

Q.10 In the case of trial-I, consider the correct element then BC (ie - image distance) can be

(A) 2

AC(B) =

2AC

(C) 2

AC(D) all the three are possible

[MULTIPLE CORRECT CHOICE TYPE]

Q.11 to Q.15 has four choices (A), (B), (C), (D) out of which ONE OR MORE maybe correct.

Q.11 Consider a conductor with a cavityas shown. There is a the charge +Q

Qq

placed outside and a negative charge q inside the cavityto the left of thecentre of cavity. Now choose thecorrect statement (S)(A) Force acting on q must be towards left.(B) Force acting on +Qwill be towards left(C) Force on+ Q will changeif qis displaced slightlyfrom its position.(D) Force onqwill changeif +Qis displaced slightlyfrom its position.

Q.12 ABCDis a regular tetrahedron madeof six conductors, and is moving A

B C

VB

D

in a region ofuniform magnetic field asshown.Now choose the correctoption (S) :(A)V A < V D(B) V B = V C(C) V D > VB(D)V A > V Dhere V A , VB , VC and V D represents potentials at these points.


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PHYSICSQ.13 A force F starts acting on a plank ofmass M on which a small block ofmass m is kept, then

(Allsurfaces are smooth)

m

M F

(A) The acceleration of m w.r.t. plank ismF

(B) The acceleration of m w.r.t ground ismF

(C) time taken by m to seperate from M isFm2

(D) time taken by m to seperate from M isFM2

Q.14 Which ofthe following will havedifferent timeperiodif taken tothe moon?(A)Atorsional pendulum(B)Aphysicalpendulum(C)A spring-mass systemplaced vertically(D)An hourglassclock, which is essentially a vessel filled with liquid emptying through a hole in the bottom.

Q.15 Agirlstopssinginga purenote. She is surprised tohearanechoofhigher frequency, i.e.a highermusical pitch then :

(A) There could besome warm air between the girl and the reflectingsurface.

(B) Therecould be two identicalfixed reflectingsurfaces, at seperation of 2

from thegirl.

(C)The girl couldbe moving towardsa fixed reflector (D) The reflector couldbe moving towards thegirl.


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PHYSICSPART-B

[MATRIX TYPE]

Q.1 has three statements (A,B,C) given in Column-I and four statements (P,Q,R,S) given in Column-II .Anygiven statement in Column-I can have correct matching with one ormorestatement(s) given in Column-II .

Q.1 Considera rectangular vesselcontainingideal liquid which isA B

CD

F

E

P

Q

released onan inclined plane whichmaybe rough/smooth.ABishorizontal,AD isparallel to inclinedandAC isthe freesurfaceof liquid.

Column - I Column - I(A) PQ is smooth (P) Liquid surface is parallel toAB(B) PQ is rough ( > tan ) (Q) Liquid surface is parallel to AD(C) PQ is rough ( < tan ) (R) Pressure at E and E are equal

(S) Pressure at E and F are unequal.

PART-D[INTEGER TYPE]

Q.1 to Q.4 are "Integer Type" questions. (The answer to each of the questions are upto 4 digits ) [5 Marks]

Q.1 An unknown cell balances 300cm of wire in a potentiometer circuit, but the balance length reduces to280 cm whena resistanceof28 isadded in parallel with thecell.Astandard cell ofemf 1.1 V balances220 cm on the same potentiometer. Find the balance length (in cm) when 48 resistance is connectedacross theunknowncell.

Q.2 A verylongstraightconducting wire, lyingalong the z-axis, carries a current of2A. The integral d.B iscomputed along the stright linePQ, where P has the coordinates (2 cm, 0,0) and Q has the coordinates( 2cm, 2cm, 0). The integral can be expressed as N 10 7 in SIunits. Find N ?

Q.3 Two identical capacitors with charges Q 0 each are connected as shown. Initial seperation between plates is d 0. Now left plate of upper capacitor and right plateof lower capacitor is moved towards left

with speed V in the direction shown. The current in the circuit then can bewritten as N0

0

dVQ

. FindN.

+Q 0 Q0v

+Q 0 Q0

v

Q.4 Aparticle starts atA with initial speed v 0 = 10 m/sec. It moves along a circular path under the action of a variable force which is always directed towards B.Aand B are end poits of a diameter. Find its speed(in m/sec)when it reaches P.

P

B O A

10m/sec

60


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CHEMISTRY



Q.1 A liquidsystem consists of two immiscible liquids waterand n-butyl chloride distills atone atmosphere pressure. If vapour pressure of water at that temperature is 570 mm of Hg, then the ratio of masses of waterand n-butyl chloride distilled is :(A) 3 : 1 (B) 0.58 : 1 (C) 1 : 1 (D) 1 : 3

Q.2 The incorrect optionamong the following is :

(A)

Cl

=

Cl

Cl

>

Cl

ClCl

(Dipole moment order)

(B) (CH 3)2 C = C = C ( C H 3)2 maximum number of 7 atoms are lie in the same plane(C) CO < CO + < CO 2 (Bond length order)(D) NH 3 > N 2H4 (Basic strength)

Q.3

CH 3

+ O

O

O

3AlCl (A) HClHgZn

(B) HF (C)

OH)ii(

MgBr CH)i(

3

3 (D) H (E)Se or S

(F)The compounds (C)and (F) are respectively.

(A)H C3

O

,H C3

CH 3

(B)COOH

,H C3

H3C OH

(C) H C3 O

,

H C3 H3C OH (D) H C3CH 3

,H C3H3C OH


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CHEMISTRYQ.4 From the graph given below, select the option which correctly matches the orbitals for which the radial

probabilitydistributionisgiven:

4 r 2

(r)

(r)

BA

C

(A) A - 3p, B - 3d, C - 3s (B) A - 3s, B - 3d, C - 4p(C) A - 4p, B - 3d, C - 5f (D) A - 3p, B - 4d, C - 4p

Q.5 During the processofelectrorefining ofcopper, whichof the followingoption is incorrect :(A) Some metalsAg andAu present as impurity settle as anode mud.(B) Dil. CuSO 4 is used as a electrolyte(C) Concentration of dil. CuSO

4shouldbe remain same during theprocess

(D) The impurityof Cu 2O is removed.

Q.6 The compound whichdoesnot give foul smell when heated with CHCl 3 and KOH,is

(A)

NH2

CH 3

(B) CH 3 NH 2

(C)2

NHCMe||

O

(D) NH2 CH

2 CH

2 OH

Q.7

Temperature(C) 500 1000

1000

500

0

1500 1900 2000

M g O

C

C O

F e O

CO CO 2

C CO 2

Using the Ellingham diagram, show the temperature at whichMgO can be reduced tometal bycarbon.(A) below 1500C (B) below 1120C (C) above 1900C (D) below 1600C


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CHEMISTRY[PARAGRAPH TYPE]


Paragraph for question nos. 8 to 10Onordertoanalysephaseequilibriainvolvingonlysolids, thermodynamicdata arerequiredforcalculationof equilibrium constant. From thegivendata, answer thequestions that follow.

combustionH of graphite = 394 kJ/mole

mS graphite = 5.8 J/K mole

combustionH of diamond = 396 kJ/mole

mS diamond = 2.4 J/K mole

Densityof graphite = 2.3 g/mlDensityof diamond = 3.5 gm/mlBoth densitiescan be assumed to be independent of temperature and pressure.Usingthe data given andassuming thatheat capacities of the twoallotropicforms areapproximatelysame, answerthequestionsthat follow.

Q.8 The value of 300G for the reaction C (graphite) C(diamond) is equal to :

(A) 2 kJ (B) 104 kJ (C) 1022 kJ (D) 3.02 kJ

Q.9 The pressureatwhich graphite and diamond will beatequilibrium at a temperature of300 K.(A) 1 bar pressure (B) 10 4 Pa (C) 10 6 Pa (D) 1.7 10 9 Pa

Q.10 At what temperature can the equilibrium be attained between graphiteand diamond at 1 bar pressure.(A) 500 K (B) 200 K (C) 2000 K (D)At no temperature



Q.11 Which of the following options correctlyrepresent concentration ofanaqueous solution ofNH 3 havingMolarity = 4M and density = 2.068 gm/ml?

(A) Molalityof ammoniain solution = 2 (B) Molefraction of ammonia =11.115

4

(C) % w/w of NH 3 = 4% (D) % w/v = 6.8%

Q.12 Inwhich ofthe followingpairs,boththe complexes have not thesamegeometrybut differenthybridisation(A) K 2[NiCl 4] , K 2[Ni(CN) 4] (B) Na 3[CoF 6], [Co(NH 3)6]Cl 3(C) Ni(CO) 4 , K 2[Ni(CN) 4] (D) [Cu(NH 3)4]SO 4, [Ni(NH 3)6]Cl 2

Q.13 Whichof the following is/arecorrect?(A) CH 3 CH = CH CHO undergoes aldol condensation.

(B)

O

Oyields

Oas major product when treated with KOH

(C) Ph CH = CH CHO does not undergo aldol condensation.(D)When an aldehyde and a ketone undergo cross-aldol condensation, it is the -Hofketone which isinvolved in carbanionformation producing majorproduct.


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CHEMISTRYQ.14 Which of the following is / are not possible?

(A) NOF 3 (B) NF 5 (C) OF 4 (D) SnCl 3

Q.15 Which of the followingwould produce iodoform when heated with I 2 and NaOH?

(A)

O

||CHCCHPh 32 (B) CH 2 = CH CHO

(C) CH CH CH CH CH3 2 3

OH OH

(D) PhCCHCPh||||

OO

2

PART-B[MATRIX TYPE]

Q.1 has three statements (A,B,C) given in Column-I and four statements (P,Q,R,S) given in Column-II .Any

given statement in Column-I can have correct matching with one ormorestatement(s) given in Column-II .Q.1 Column I (Reaction) Column II (Major product)

(A) CH 2 = C = CH2 OH3 (P) CH 3COCH 3

(B)

CH OH2

CH OH

CH OH2

+COOH

COOH

240C

(Q) CH 2 = CH CH 2 OH

(C) CH 3 C CH )OH(Hg

3

2 (R) CO 2 is evolved

(S) enol is produced during thereaction whichtautomerises into final product.


Q.1 to Q.4 are "Integer Type" questions. (The answer to each of thequestions are upto 4 digits )

Q.1 A B 2 is a salt of strong baseA(OH) 2 and weak acid, 'HB'. The saturated solution ofAB 2 contains 0.6moles in2Lsolution. IfpOH of thesolution is5.6 and 90% dissociation of the salt takes place then whatis pK

aof weak acid. [ Given : log (0.54) = 0.27]

Q.2 s p mixing isnot possiblein amongthe following :C2 , B2 , NO, CO, NO

+ , C22+, O2

2+ , O2+, N2 , N2

+, N2

[If your answer is 1 so write 0001.]

Q.3 How many moles ofHCHOwould beused by NH 3 to prepare one mole of a compound which is usedin the treatment ofurinaryinfection.Assume 100% efficiencyof the reaction.

Q.4 Which of the followingwill obeySidewick'sE.A.N. rule (or E.A.N. rule) ?(i) K 4[Fe(CN) 6] (ii) K 3[Fe(CN) 6] (iii)Ni(CO) 4 (iv) Fe(CO) 5(v) [Zn(NH 3)4]SO 4 (vi) [Cd(NH 3)4]SO 4 (vii) [Cr(en) 3]Cl3 (viii) [Cr(H 2O)6]Cl3(ix) [Mn

2(CO)

10] (x) [V(CO)

6] (xi) [Fe(CO)

2(NO)

2]

[If your answer is 4 so write 0004.]


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MATHEMATICS




Q.1 Suppose f : R R bea continuous function such that f(3x) = f(x) x R and f(2) = 5, then value

of 5

2

dx)x(f sgn is equal to

(A) 0 (B) 1 (C) 3 (D) 3

Q.2 Suppose g is the inverse function of a differentiable function f and G(x) =)x(g

42 . If f(5) = 3 and

f '(5) = 1251

then G'(3) is equal to(A) 1 (B) 2 (C) 4 (D) 8

Q.3 If log a (x2 2x) > log a (2x 3), where the point (a, 2) lies between the lines x 2y + 3 = 0 and

x 2y + 4 = 0 then the set of values of x is equal to

(A)

,23

(B) (1, 3) (C) (2, 3) (D) ( , 0) (2, )

Q.4 Let 1v , 2v and 3v are three unitvectors in a plane such that theyareequally inclined toeach other and

if k 1 = 3221 vv.vv

, k 2 = 1332 vv.vv

and k 3 = 2113 vv.vv

then the value of (k 1 + k 2 k 3) is equal to

(A)43

(B)43

(C)46

(D)49

Q.5 A bagcontains three red,six blueand fourgreen dice. 2 diceare selectedat random, thentheprobabilitythat one dice is blue and other is red given that theyare ofdifferent colour

(A)4

1(B)

3

2(C)

3

1(D)

2

1

Q.6 A shopkeeper sells three varitiesofperfumesand hehaslarge number ofbottlesof the samesize ofeachvariety in his stock. There are five places in a row in his showcase. The number of different ways of displayingthe threevarities ofperfumesin the show case are(A) 240 (B) 210 (C) 150 (D) 90

Q.7 The distance between the directrices of the ellipse (4x 8) 2 + 16y 2 = 210y3x is(A) 12 (B) 16 (C) 18 (D) 20


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MATHEMATICS


[PARAGRAPH TYPE]


Paragraph for Question no. 8 to 10

Consider the parabola x 2 = 4yand circle x 2 +(y 5 ) 2 = r 2 (r > 0). Given that the circle touches the

parabola at the points P and Q. Let R be the point of intersection of tangents to parabola at P andQ and S be the centre of circle.

Q.8 Which ofthe following statement(s) is/are TRUE?

(A) Centroid of PQR is

97

,0 .

(B) Distance between chord PQ and directrix of the parabola is34

.

(C) Area of PQR is33

40.

(D) The common tangents to the circle and parabola intersect at (0, 3).

Q.9 The equationof the circlewhich passes through the vertex of the parabola x 2 = 4y and touches itat the point M ( 4, 4) , is(A) x 2 + y2 10x 18y = 0 (B) x 2 + y2 8x 16y = 0(C) x 2 + y2 + 8x = 0 (D) x 2 + y2 8y = 0

Q.10 Tangents drawn from the point A(1, 1) to the circle x 2 + y2 4x + 6y 1 = 0 touch the circleat the

points B and C. If thecircumcircleof the ABC cuts theauxiliarycircleof hyperbola 1 b

y

4

x

2

22

orthogonally, then b 2 is equal to(A) 1 (B) 2 (C) 3 (D) 5



Q.11 Let f(x) = ax 2 + bx + c where a, b, c R and a 0. If c2 + 4ac 2bc < 0, then which of thefollowing is/arecorrect?(A) f (x) = 0 has equal roots (B) f(x)= 0 has imaginary roots

(C) f(x) = 0 has real and distinct roots (D) one root of f(x) = 0 lies in ( 2, 0)

Q.12 Consider f(x) =

xsin

x)x(sincoscos3

1

, then

(A) )x(f Lim0x

does not exist (B) f(x) has removable discontinuityat x =

(C) jump of discontinuity at x = is31

. (D) f(x) is discontinuous at all x = n , n I


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MATHEMATICS


Q.13 In ABC,a=4 ,b=c= 22 .Apoint P moves within the triangle such that the square of its distancefrom BC is half the rectangle contained byits distances from the other two sides. If the locus of P is aconic, then

(A) locus of P is parabola (B) locus of P is ellipse with eccentricity32

(C) locus ofP is hyperbola with eccentricity23

(D) centre of conic is

32

,0

Q.14 Consider a ABC whose circumcircle is | z | = r in the argand plane with A, B, C be represented bycomplex numbers a,b, c respectively. The foot of altitudes fromA, B,C meet the opposite sideat D,Eand F and the altitudes whenproduced meet the circle | z | = r atL, M and N respectivelythen which of followingis/arecorrect?

(A) centroid of LMN isabc3

)acc b ba( 222222

(B) the mirror image of orthocentre of ABC with respect to BC lies on | z | = r.

(C) the mirror image of orthocentre of ABC with respect to BCisa bc

.

(D) none of these

Q.15 Tangentsare drawn fromP(2, 0)to y 2 = 8x, radiusofcircle (s) that would touch these tangentsand thecorresponding chord of contact can be equal to

(A) 4 (B) 124 (C) 24 (D) 424

PART-B[MATRIX TYPE]

Q.1 has three statements (A, B,C) given in Column-I and four statements (P, Q, R, S) given in Column-II .Any givenstatement in Column-I canhavecorrect matchingwith one ormore statement(s) given in Column-II .

Q.1 Column-I Column-2

(A) If , , are roots of x 3 x + 2 = 0, then the value of (A)21

( ) ( ) + ( ) ( ) + ( ) ( ) is

(B) In ABC, if incentre I is the mid point of median (B)41

through Athen the valueof 2C

sin is

(C) If z 1, z2 C then the maximum value of 21

2121

zzzzzz

(C) 3

is equal to (S) 2


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MATHEMATICS




Q.1 Let G(x) be a non-negative continuous function on R such that G(x) + G

3

1x = 5,

then calculate the value of integral1200

0

dx)x(G .

Q.2 Find the sum of an infinite geometric series whose first term is 2013

1k 0x 2013

k 2xtan

x

Lim

and whose commonratio is the value of )xsinx1(n2

eeLim 23

xxtan

0x

33

l

.

[Note : where {k} denotes fractional part of k.]

Q.3 If k

3 j

2i

V1 and k

c j

bi

aV2 where a, b, c {1,0,1, 2,3} thenfind the numberofnon-

zero vectors 2V whichare normal to 1V .

Q.4 Let A =

2x35x2

, B = c5 ba2 , C = 2x41x5

andD=

412

be four given matrices, where a, b, c and x R.

Given that t r (AB) = t r (DC) x R where t r (A) denotes trace of matrix A, then if

k

c j

bi

aV1 , k

30 j

105i

2V2 and k

V3 then find the value of 321 VVV[Note : [k ] denotes greatest integer less than or equal to k.]


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MATHEMATICS


ROUGHWORK


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Time: 3:00 Hours Max. Marks: 249

VERY IMPORTANT

A. The question paper consists of 3 section ( Section-1 contains Physics, Section-2 contains Chemistry and Section-3contains Mathematics). Please fill the OMR answer Sheet accordingly and carefully.

B. Each Section contains (15 questions in Part-A, 1 questions in Part-B and 4 questions in Part-D).C. Please ensure that the Question Paper you have received contains ALL THE QUESTIONS in each Section

and PAGES. If you found some mistake like missing questions or pages then contact immediately to theInvigilator.

INSTRUCTIONSPART-A

1. Q.1 to Q.7 are single correct type questions . Each question has four choices (A), (B), (C) and (D) out of whichONLY ONE is correct. For Q.1 to Q.4, you will be awarded 3 marks and for Q.5 to Q.7, you will be awarded4 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble aredarkened. In all other cases, minus one (1) mark will be awarded.

2. Q.8 to Q.10 are Paragraph type. Based upon the paragraph 3 single correct type questions have to be answered. Eachof these questions has four choices (A), (B), (C) and (D) out of which ONLY ONEis correct. For each question you will beawarded 3 marks , if you have darkenedonly the bubble corresponding to the correctanswerand zero mark ifnobubble aredarkened. In all other cases, minus one (1) mark will be awarded.

3. Q.11 to Q.15 are multiple correct type questions .Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct. For each question, you will be awarded 5 marks if you have darkened only thebubble corresponding to the correct answer and zero mark if no bubble are darkened. No negative marks will be awardedin this section.

PART-B4. Q.1 is Matrix Match type question. Each question has Three statements (A, B, C) given in Column-I and

Four statements (P, Q, R, S) given in Column-II. Any given statement in Column-I can have correct matching with one or more statement(s) given inColumn-II. For example, if for a given question, statement B matches with the statement given inQ and R, then for the particular question, against statement B darken the bubbles corresponding to Q and R in the OMR.For each row, you will be awarded 3 marks in which you have darkened the bubble(s) corresponding to the correctanswer and additional 1 Bonus marks will be awarded if all the answers are correct.Thus Q.1 carries a maximum of 10 marks.

PART-D

5. Q.1 to Q.4 are Integer Type questions . The answer to each question is a upto 4 digit ranging from0 to 9999. The correct digit below the question number in the OMR is to be bubbled.For each question, you will be awarded 5 marks if you darken the bubble corresponding to the correct answer and

zero mark if no bubble is darkened.For example, if for a given question, your answer is 7 or 77 or 777 or 7777, then for the particular question, againstquestion number you must fill as 0007 or 0077, 0777 & 7777 respectively in the OMR. No negative marks will beawarded in this section.

6. Indicate the correct answer for each question by filling appropriate bubble in your answer sheet.7. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed.8. The answers ofthe questions mustbe markedbyshadingthe circleagainst the questionby darkBlack Ball point Pen only.

CODE AM O C K T E S T

PAPER-II

USEFUL DATA

Atomicweights: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 = 65.5, Ti = 48,

Ba = 137, U = 238, Co= 59, B =11, F = 19, He = 4, Ne = 20, Ar = 40 , Mo = 96[Take : l n 2 = 0.69, l n 3 = 1.09, e = 1.6 10 19, me= 9.1 10 31 kg ]Take 0 = 8.85 10

12 , g = 10 m/s 2 unless otherwise stated


16/60

PHYSICS

Mock Test-1 [Paper-II] Page # 16


Q.1 to Q.4 has fourchoices (A), (B), (C), (D) out of whichONLY ONE is correct. [3 Marks]

Q.1 A squareloop isplaced inanexternaluniform fieldasshownin (a).The torqueacting is.Now imaginea branchisremoved but still samecurrent inrestofthe branches. The new torqueabout c in (b) will be

B

(a)

I C

B

(b)

I C

(A) zero (B) 43

(C) (D) 4

Q.2 Twoelectric bulbs with rated powersP1 andP2 at samerated voltageare connected inseries acrossasource. One of themgives lessthanrated power. The other one will give(A) less thanthe rated power (B) more thantherated power (C) equal to the ratedpower (D) canbeanyof theabove

Q.3 Themutual inductanceof twoco-axial coilsof small radiiatlargedistancexbetweenthemisproportionalto

(A) x1 (B) 2x1 (C) 3x1 (D) 4x1

Q.4 InYoung'sdoubleslitexperimentford=0.001cm,D=1minterferencepattern isobtainedforradiationsof wavelengths 5000Aand 5800A. Which of the following isnearest to3rd maxima forwavelength5000A(A)2nd maxima for 5800A (B) 3rd minimafor5800A(C)3rd maxima for 5800A (D) 3rdminimafor 5000

Q.5 to Q.7 has fourchoices (A), (B), (C), (D) out of whichONLY ONE is correct. [4 Marks]

Q.5 Ina standingwave, the phase difference atany timet,between two particles of themediumseperatedbya distance x(A) depends on x and t (B) depends on x but independent of t(C) depends on t but independent of x (D) independent of both xandt


17/60

PHYSICS


Q.6 Twolayers of insulatorsare keptasshown.Hot surface ismaintainedat1000C.ABC isanimaginarystraight line inwhich D andE aremidpointsofABand BC.If l1 < l2 andat steadystate temperaturesat D and E are 875C and 600C then

A

C

coldsurface

l1 l2

Hotsurface

D B Ek 1

k 2

(A) k 1 > k 2 (B) k 1 = k 2 (C) k 1 = 1.3 k 2 (D) k 1 < 1.2 k 2

Q.7 The accuracyof a cesium clock is 1 part in1011. What can be the maximum difference between twosuch clocks operating for about 3200 years (1011 sec.).(A)practicallynodifference (B) 1 sec(C) 4 sec. (D) 2 sec.

[PARAGRAPH TYPE]

Q.8 to Q.10 has fourchoices (A), (B), (C), (D) out of whichONLY ONE is correct.

Paragraph for question nos. 8 to 10Considera cylindricalvesselof radiusR and lengthL.Ifone molecule ispresent in it thenthemotionof that one moleculecan bedescribed byradialandAxialvelocities asshown. Now consider N identicalmolecules.Eachmoleculehas a mass m.ApplyassumptionsofKTG, lawofequipartitionofenergyandanswerthefollowingquestion (Kisboltzmann's constant and T isabsolute temperature)

vr

va

Q.8 Which of the following iscorrect expressionfor rms speedof radialcomponentsofthe gas sample

(A) mKT

(B) mKT2

(C) m2KT

(D) mKT3

Q.9 Which ofthe following iscorrect expressionfor rms speed ofaxial componetofgas smaple

(A) mKT

(B) mKT2

(C) m2KT

(D) mKT3

Q.10 Which of the followingexpressioncan beusedtogivethe pressure?

(A)LR 2

)v(mN2

2rmsa (B)

Lr )v(mN

2

2rmsa (C)

LR 4)v(mN

2

2rmsa (D)

LR )v(mN2

2

2rmsa


18/60

PHYSICS



Q.11 to Q.15 has four choices (A), (B), (C), (D) out of whichONE OR MORE may be correct.

Q.11 Acapacitor ofcapacitance C is connected to two voltmetersA and B.A is anideal voltmeter havinginfinite resistance, whileB has resistanceR.Thecapacitorisunchargedandthen theswitchSisclosedat t = 0, (Assume thatbattery is ideal)

AB

S

C

(A) readings ofB andA will be andzeroatt=0(B)during time interval (0 t < ) reading ofB andAare changing(C)readingofAandBwillbeequalatt=RCln2(D) noneof these

Q.12 Hydrogenatoms absorbsradiation of wavelength0 andconsequentlyemit radiationsof 6 differentwavelengthsofwhich twowavelengthsaregreater than0.(A) The final excited state of the atomsisn = 4(B) The initial stateof the atomsmaybe n = 2(C)Theinitialstateoftheatomsmayben=3(D)Therearethree transitionsbelongingtoLymanseries.

Q.13 Ansustained interferencepatternis formed onthescreen, whenlight from twodifferent monochromaticsourcesare allowedto interfere.Then, it is true that,(A) frequencies of light fromthe two sources are equal toeachother (B) the sources are coherent

(C) the sources shouldbelocated inthe samemedium(D) the pathdifferenceshouldeitherbeanevenor, anodd multipleof 2 ,where is the wavelengthof light

Q.14 Athinrigiduniform ciruclardiscrollswithout slippingonahorizontalrigid surface (or theground).At acertain instant,itsposition with respect togroundframeisasshown inthefigure.

Y'

B

O' Y X'

X

Y

Ground frame

AC

D

(A) sectorABChas greater kineticenergythansectorADCwith respect togroundframe(B) sector BO'Chas greater kineticenergythansector CO'Dwith respect toground frame(C)sector BO'Chas the samekinetic energyassectorAO'Bwith respect toground frame(D)all thesectorsAO'B,BO'C, CO'DandAO'Dhave samekinetic energywith respect to the centre of mass frame


19/60

PHYSICS


Q.15 A targetobject isplacedatthebottomofa tank ofdepth 20m, andfilledwitha liquidofdensity500 gm/cc.Another objectofdensity100gm/cc isdropped ontoit, from a heightof45m fromthe upper surfaceoftheliquid.(takeg=10m/s2) (Neglect viscous force)

45m

(A)Thesecond object collides with thetarget(B) The seocndobject doesnot collidewith the target(C)The least separation betweenobject and target is 11.25 m.(D) The retardation of the object in the liquid is40m/s2.

PART-B[MATRIX TYPE]

Q.1 hasthree statements (A,B,C) giveninColumn-I andfour statements(P,Q,R,S) given inColumn-II .AnygivenstatementinColumn-I canhave correctmatchingwithoneormorestatement(s) giveninColumn-II .

Q.1 ColumnAlistsdifferent typeofmethodstousedifferentphysicalquantiteswhilecolumnBlistsnamefor instrument thatare usedin these methods.

Column - I Column - II

(A) Determinationofgusingsimplependulum (P) Vernier calipers

(B) DeterminationofYoung'smodulusof steel (Q) Stop clock

bySearle'method.(C) Focal length of a concave mirror using (R) Screw gauge.

uvmethod

(S) Optical Bench


Q.1 to Q.4 are "Integer Type" questions. (The answer to eachof thequestionsare upto 4 digits ) [5 Marks]Q.1 Radiation from hydrogengas excited tofirst excited state isusedfor illuminating certainmetallic plate.

Whenthe radiation fromsomeunknown hydrogenlikegas excited to the samelevel isusedtoexposethesame plate, it is foundthat thede-Broglie wavelength of thefastest photoelectron has decreased2.3 times. It isgiven that the energycorresponding to the longest wavelengthof the Lymanseries of theunknown gas is 3 times the ionization energyof hydrogengas (13.6 eV). Find the work function of metallic plate in eV. (Take(2.3)2 = 5.25).


20/60


21/60


CHEMISTRY


Q.1 to Q.4 has four choices (A), (B), (C), (D) out of which ONLY ONE is correct. [3 Marks]

Q.1 For two reactions :A BandC D; activation energies are20Kcaland30 Kcal respectively. Whichof the following options must be true regarding rate constants TIK and

TIIK where

TIK and

TIIK are rate

constant for the first andsecond reactions at temperatureT kelvin respectively.

(A) 300II300I K K (B)

300II

350I K K (C) 300

II

310II

300I

310I

K

K

K

K (D) 500

II

450II

500I

450I

K

K

K

K

Q.2 [Co(dien)Cl 3]Which of the following is correct optionforabove complex?(i) fac and mer geometrical isomers(ii)Optical active geometrical isomers(iii)Octahedral complex(iv) Low spin complex(A) TFTT (B) FFTT (C) TTTT (D) FTTT

Q.3 The correct order of relative rate ofacidic hydrolysis of the following compounds is :

O O

(I)

O O

(II)O

O O

(III)F

O O

(IV) NH

2

(A) I > IV > II > III (B) IV > III > II > I(C) I > III > IV > II (D) I > II > III > IV

Q.4 [Pt(NC) 2(NO 2)2] has manytotal isomers are possible for the complex?(A) 19 (B) 4 (C) 8 (D) 16

Q.5 to Q.7 has four choices (A), (B), (C), (D) out of which ONLY ONE is correct. [4 Marks]

Q.5 Identifythe statements which is incorrect w.r.t. surfacephenomenon.(A)Asol, prepared byaddingexcessAgNO 3 solution in KIsolution when subjected to electro-phoresiswill show coagulation near cathode.

(B) The conductivity of a soap solution decreases steeply at CMC.(C)Tyndalleffect will be more prominent in gold solutionas compared to rubber solution.(D) Extent of physisorption increases with increase in temperature initial and then decreases withtemperature.

Q.6 Which is/are correct option regarding PF 5?(i)All the bond lengths of PF 5 are seems to be equal.(ii) It shows berrypseudorotation.(iii) Structure ofPF 5 is trigonal bi pyramidalandsquare pyramidalduringpseudorotations.(iv)All bondangles are not equal(A) TTTT (B) TTTF (C) FTTT (D) FTTF


22/60


CHEMISTRY

Q.7O

OEtOH

H N 42 'X' (the most stable product)

'X'is:

(A) N

N(B)

NH

N(C)

NH

N

(D)

NH

NH

[PARAGRAPH TYPE]


Paragraph for question nos. 8 to 10Salt (A) reacts with NaOHgivesgas (B) and compound(C), compound(C) onreaction with Zn in thesolution gives gas (B), salt (A) ondecomposition gives two neutral oxide (D) and (E), (D) on reactionwithP 4 gives dehydratingagent (F).

Q.8 What is covalencyofcentral atom 'F' ?(A) 5 (B) 4 (C) 3 (D) 2

Q.9 Hybridisation ofsalt 'A' is:(A) sp 3 (B) sp 2 (C) both (A) & (B) (D) None

Q.10 The oxidation state ofcentral atomin compound 'D' is :(A) 1 + (B) 2 (C) 1 (D) 2 +



Q.11 Which of the followingstatements is/are incorrect regardingdefectsin solid?(A)AgBr(s) crystals show both schottkyand frenkel defects.(B) Impuritydefect bydopingArsenic in Silicon yields 'P' type semiconductor.(C)Doping in crystal introducesdislocationdefects.(D) Metaldeficient defect canoccur with extra anions present in the interstitial voids.


23/60


CHEMISTRYQ.12 Whiichofthe followingalkenegives sameozonolysisproduct?

CHOCHO

CHO

O

(A) (B)

(C) (D)

Q.13 Which option(s) is/are correct for SF 4?(A) l .p-b.p & b.p-b.p repulsion(B) It has see-saw structure

(C) 2zd orbital is participation in hybridization.

(D) 22 yxd orbital is takingpart in hybridization.

Q.14 Consider the reaction given below:

CH 3 CHDCONH 2 + PhCO N* H2 OHBr 2 ?

The products obtained are :

(A) CH 3CHDNH 2 (B) CH 3CHD N* H2 (C) PhNH 2 (D) Ph N

* H2

Q.15 Which option(s) is/are correct ?(A) K 4[Fe(CN) 6] has 10 total isomers. (B) K 3[Fe(CN) 6] has 10 total isomers.(C) K 4[Fe(CN) 6] has 7 linkage isomers. (D) K 3[Fe(CN) 6] has 7 linkage isomers.


24/60


CHEMISTRYPART-B

[MATRIX TYPE]

Q.1 has three statements (A,B,C) given in Column-I and four statements (P,Q,R,S) given in Column-II .Anygiven statement in Column-I can have correct matching with one ormorestatement(s) given in Column-II .

Q.1 Column-I Column-II

(A) Ratio of critical temperature to that (P) Dependent on type of gasof Boyle's temperature

(B) Slope of PV vs V graph at Boyle's (Q) 1temperature for low to moderate pressure

(C) Slope of compressibilityfactor(Z) vs (R) is a constant value for anygas pressure(P) at high pressure andnormal temperature (S) 1


Q.1 to Q.4 are "Integer Type"questions. (The answer to each of the questions are upto 4 digits ) [5 Marks]

Q.1 How many millimoles of NH 3 must be added to one litre of 0.016 M Ag+ solution to just prevent

precipitation ofAgBr when [Br ] in the solutionis 10 6 M.[Given Ksp ofAgBr = 10 13 M2 and K in stability ofAg(NH 3)2

+ = 10 8 M2]

Q.2 (a) Doubling the concentration of substratedoubles the rate ofS N2 reaction.(b) Addition ofmixtureof ethanol and H 2O in reactionmixture increases rate ofS N1 mechanism.

(c) IncreasingthenumberofR groupsonthe C bondedto the leaving group increases the tendency. of S N2 reaction.(d) Increasing the concentration of nucelophile increase the rate of S N1 reaction.Write 1 in OMR sheet if the statement is correct and 2 if it is incorrect. For example it all arecorrect write 1111 as Answer in OMR sheet.

Q.3 Fe 2(SO4)3 where reacts with excess of KCN first give ppt than excess of KCN will give complex (A).What is primaryvalency., secondaryvalency, E.A.N. respectively.

Q.4 Consider the reaction givenbelow: NH

2

NH2

condistionacidicmildC50;HNO.eq1 2

?

Find the total number ofdegreeof unsaturation in themain product formed.


25/60

MATHEMATICS




Q.1 Tangentsdrawn from every point on the line y x + 2 = 0 toparabolay 2 = 4xsuch thatchordsofcontact pass throughthe fixedpoint, the co-ordinate of thispoint is(A) (2, 2) (B) ( 2, 2) (C) (2, 2) (D) ( 2, 2)

Q.2 Radical centre of the circles drawn on the sides of triangle formed by lines 3x 4y + 6 = 0,x y + 2 = 0 and 4x + 3y 17 = 0 as diameter is(A) (0, 0) (B) ( 2, 3) (C) ( 2, 3) (D) (2, 3)

Q.3 The product of the series(1 + cot 7) (1 + cot 9) (1 + cot 11)...(1 + cot 45) (1 cot 52) (1 cot 54)...(1 cot 88) is

(A) 221

(B) 220

(C) 219

(D) 218

Q.4 The function f is defined for all non-zero real numbers such that 2f(x) + 3f

x1

= 5x,

then equation f(x) = f( x) is satisfied by(A) no real numbers (B) exactly one real number (C) exactlytwo real numbers (D) all non-zero real numbers


Q.5 Let f : [0, ) R be a continuous andstrictly increasing function such that

f 4 (x)=x

0

32 dt)t(f t x > 0. Thearea enclosed by y = f(x), the x-axis and the ordinates atx = 1 and

x = 4 i s

(A)4817

(B)4865

(C)48

257(D)

48235

Q.6 A variable line x cos + y cot = a where a is constant meets the x-axis and y-axis at A and B

respectively. The locus of a point R which divide the line segmentABexternally3 : 5 is given by(A) 100 x 2 36y 2 = 225a 2 (B) 100 x 2 36y2 = 225a 2

(C) 36 x 2 100 y 2 = 225a 2 (D) 36 x 2 100 y2 = 225a 2

Q.7 Let f(x) =

0x,0

0x,xtanx1

cosx

m

n

.

If f(x) is continuous but non-derivable at x = 0 then

(A) n m (B) m < n m + 1 (C) n < 2m (D) n < 2m + 1


26/60

MATHEMATICS


[PARAGRAPH TYPE]


Paragraph for question nos. 8 to 10

For all x 27

,27

, let f(x) = 1}x{21,x

21

}x{0,]x[

.

[Note : [x] denotes greatest integer less than or equal to x and {x} denotes fractional part of x.]

Q.8 )x(f Lim

23

x is equal to

(A) 1 (B)23

(C) 0 (D) does not exist

Q.9 Number of solution(s) of the equation f(x) =25

is equal to

(A) 2 (B) 3 (C) 4 (D)infinite

Q.10 If L is the number of points of discontinuity and M is the number of points of non-differentiabilityof the function f(x), then(L+ M)is equal to(A) 18 (B) 20 (C) 21 (D) 22



Q.11 Let 321 v,v,v

be three vectors such that 15vv 32

and 1v1 , 1v2 , 4v3 .

If 32 v2v

= 1vk then k can be(A) 4 (B) 2 (C) 2 (D) 4

Q.12 If P( , 2) falls inside the angle made bythe lines y =2x

,x >0 an d y =3 x ,x >0 th en can be

(A)31

(B)21

(C)43

(D)35

Q.13 The function f(x)= )1x(x 31

(A) has vertical tangent at x = 0.

(B) area enclosed by curve with x-axis from x = 1 to x = 1 is23

.

(C) is concaveup in (0, ).

(D) is decreasing for x

41

, .


27/60

MATHEMATICS


Q.14 Let r be a position vector of a variablepoint in cartesian xy-plane such that )r j

10i

8(r

= 40

andM=max2

j

3i

2r ,m=min2

j

3i

2r , then(M + m) is less than or equal to

(A) 9 (B) 18 (C) 27 (D) 28

Q.15 If the middle term of 12

xsinx1

x

is16

6237, then the value of sin 1 (sinx) is/are

(A)4

(B)3

(C)4

(D)3

PART-B[MATRIX TYPE]

Q.1 has three statements (A, B,C) given in Column-I and four statements (P, Q, R, S) given in Column-II .Any givenstatement in Column-I canhavecorrect matchingwith one ormore statement(s) given in Column-II .

Q.1 Column-1 Column-II

(A) Thesum of thecoefficients in theexpansion of (P) 8012

3x15x1531

(17x 17x 5 + 3) 2013 is

(B) If {x} represents fractional part of 'x' (Q) 5

then9

0

dx}x{ is equal to (R) 4

(C) Let f(x) = x + tan 3x and g(x) = f 1(x) (S) 3

then the value of 56

14

'g .


28/60

MATHEMATICS




Q.1 Consider f(x) = sin 1

5x23x

, g(x) =

5x bax

2

2

. If )x(g)x(f Limx =0and

)x(g)x(f Lim0x

=4

, then findthe value of (5a + 3b 2).

Q.2 If c < 2 and the system of equations x + y 2z = 0, 2x + y cz and bx + 2by c z = 0has non-trivial solution then if range of b is (m, n) then findvalue of 24(n m).

Q.3 If 16 l 2 + 9m 2 = 24 l m + 6l + 8m + 1 and the line mx + l y = 1 is tangent to circle S 1 = 0,then the equation of circle S 2 = 0 which touches S 1 = 0 at (0, 0) and passingthrough (3,1) is given by

x2 + y2 ax by + c = 0 then find the value of (3a + 4b + 5c).

Q.4 In ABC, medians ADand BEare drawn. If DAB =6

and ABE =3

then find the value ofADAD

if area of ABC is33

32sq. units.


29/60


30/60

HINTS & SOLUTIONS Page # 148

Mock Test-1PAPER-2

P H Y S I C S

PART-AQ.1 C Q.2 D Q.3 C Q.4 B Q.5 B

Q.6 D Q.7 D Q.8 B Q.9 A Q.10 BQ.11 A, B, C Q.12 A, B, D Q.13 A, B Q.14 A, B, C, D Q.15 B, D

PART-B

Q.1 (A) P,Q (B) R (C) S]

PART-DQ.1 0003 Q.2 0038 Q.3 0004 Q.4 0008

C HEM IS TRY

PART-AQ.1 A Q.2 A Q.3 D Q.4 A Q.5 DQ.6 A Q.7 B Q.8 A Q.9 C Q.10 AQ.11 BCD Q.12 AB Q.13 ABC Q.14 ADQ.15 ABCD

PART-BQ.1 (A) Q,R (B) Q,R (C) PQPART-DQ.1 0072 Q.2 1122 Q.3 3635 Q.4 0006

MATHEMATICS

PART-AQ.1 B Q.2 D Q.3 B Q.4 C Q.5 CQ.6 D Q.7 B Q.8 D Q.9 A Q.10 CQ.11 AD Q.12 CD Q.13 ABCD Q.14 BCD Q.15 BD

PART-B

Q.1 (A) S, (B) Q, (C) P

PART-DQ.1 0004 Q.2 0020 Q.3 0016 Q.4 0004


31/60


HINTS & SOLUTION


32/60


Mock Test-1PAPER-1

P H Y S I C S

PART-A

Q.1[Hint. When it reaches at toppart of BConlyrotational velocitywill beremaining. ]

Q.2[Hint. Other planetswill also exert attractiveforces soVe will be more. ]

Q.3

[Hint. XL = XC, I = R V

= . ]

Q.4[Hint. W will beless than thatcalculated for isothermal process.

Wisothermal = 1 (R) (500) l n 2.7 < 5000 J at 500 K.

Q.5[Hint. A(tA) B(tB)

A

Btt

00

A

00

)2(A3

2

Att

A3A0tA

Btt

00 )2(A3

2A

= )A3A(31

00 . Ans. ]

Q.6

[Hint. min = evhc

min = 2VV

and k does not change. ]

Q.7[Sol. Averagespeedisalways less than maximumspeed and greaterthenminimum speed. ]

Paragraph for question nos. 8 to 10[Hint.(i) Onlya concavemirror can formimageon sameside.

Q.11[Hint. Force on q due to inner induced charges will be towards left and force on Q due to outer induced

charges will also be towards left. ]

Q.12[Hint. VA VD = positive

VB = VC as v||l VD > VB. ]


33/60


Q.14[Hint. gwillchange]

Q.15[Hint. vapp> vactonlyif distancebetween sourceand observer decreases. ]

PART-DQ.1Sol. The emf of the cell or the masured potential difference is proportional to the balance length on the

potentiometer.Theemfof theunknowncell is foundtobe1.5Vandits internal resistancecanbefoundasfollows:

2828r 5.1

= drop across 280 cm of wire

=1.4(involt) r = 2

Thecurrent throughthe48 resilstance, whenit isconnected across theunknown cell, is

i = A2485.1

= 0.03A, and the balance length = 200 48 0.03 = 288 cm.

Q.2

Sol. PAQ

d.B = RBQ

d.B

PCR

0d.B

and0d.B

= R 4R 2 I0 = 16 )2)(104(

7

= 10 7 S.I. units.

(2,2,0)Q

BAP C

R x

I = 2A4

(2,0,0)

Q.4

[Sol. Fromconservation ofangular momentumabout B2R 10 = RV sin 30V=40m/sec. ]


34/60


35/60


CH3

HO

H C3

(D)

H

CH3

O

H C3 OH)ii(MgBr CH)i(

3

3

CH3

CCO

CH2CH2H2C

(C)

H+

CH3

H C3

H

CH3

H C3

(E)

S

or Se

CH3

H C3

(F)

Q.4Sol. From the graph

Ahas 2 radial nodes 4pB has 0 radial node 3dC has 1 radial node 5f

Q.5[Sol. During theprocessofelectro-refiningofcopper, the impuritiesofsilverand gold isremoved asa anode

mud. ]

Q.6Sol. Carbylamine reaction (Isocyanide test) isgivenby1amine

(A)

NH2

CH3

Positiveisocyanidetest

(B) CH3 NH2 Positiveisocyanidetest

(C) 2 NHCMe||

O

Negativeisocyanide test

(D) NH2 CH2 CH2 OH Positiveisocyanidetest

Q.7[Sol. At T > 1900C

MgO + C Mg + CO G = veItmeans above1900C,MgO can bereduced to metal bycarbon. ]


36/60


Q.8[Sol. C(graphite) C(diamond)

)Diamond(C)graphite(Cr HHH = 394 (396)= + 2.0 kJ/mol

)Graphite(m)Diamond(mr SSS = 2.4 5.8 = 3.4 J/K-mole

STHG= 2.0 300 ( 3.4 10 3)= 2.0 + 1.02 = 3.02 kJ ]

Q.9[Sol. dG = VdP SdT = VdP

P

1

G

G

dPV)G(d

GP G = V (P 1)

0 3020 = diamondgraphite d

md

m (P 105)

(since1atm=105 Pa)

3020 = 12 5.31

3.21

10 6 (P 105)

P = 105 +2.112

105.33.23020 6

= 1.6881 109 Pa 1.7 109 Pa Ans. ]

Q.10[Sol. Equilibriumpressureis1.7 109 Pa.Hence,at1 bar, equilibriumcannotbeattainedatanytemperature.]

Q.11Sol. Molarityof NH3 solution=4M

dsolution = 2.068 g / ml1 L solutionhas 4molesofNH3 =68g

Massof solution= 2068gMassofsolvent = 2000 g

24

m = 24

= 2

11.1154

1820004

4X3 NH

% 100206868

ww

= 3.3


37/60


% 1001000

68vw

= 6.8

Q.12[Sol. Hybridisation Geometry

(A) K 2[NiCl4] sp3 tetrahedralK 2[Ni(CN)4] dsp2 squareplanar

(B) Na3[CoF6] sp3d2 octahedral[Co(NH3)6]Cl3 d2sp3 octahedral

(C) Ni(CO)4 sp3 tetrahedralK 2[Ni(CN)4] dsp2 squareplanar

(D) [Cu(NH3)4]SO4 dsp2 squareplanar [Ni(NH3)6]Cl2 sp3d2 octahedral ]

Q.13

Sol. (A) CH CH = CH CHO3 H

C

Aldol condensation

(B)

O

O

O

IntramolecularAldol condensation

(C) Ph CH = CH CHO

Habsent NoAldol condensation

(D) Aldehyde + Ketone OH CrossAldol condensation(involvedincarbanion)

Q.14[Sol. Due to the absence of vacant oforbital inN andO, NF5 and OF4 are not possible. ]

Q.15

Sol. (A)

O||CHCCHPh 32 Positiveiodoformtest

(B) CH2 = CH CHO Negative iodoformtest

(C) CH CH CH CH CH3 2 3

OH OH

Positiveiodoformtest

(D) PhCCHCPh||||

OO

2 Negative iodoformtest


38/60


PART-BQ.1

Sol. (A) CH2 = C = CH2 OH3

HOH||CHCCH 22 (Enolic)

O||

CHCCH 33

Keto form

(B)

CH OH2CH OHCH OH2

+COOH

COOH

240C

CH2

CH2 OH

CH

[Allyl alcohol]

(C) CH3 C CHreactionKucherov

)OH(Hg

3

2

enolic

3

HOH||

CHCCH O||

CHCCH 33

PART-DQ.1Sol. (90%dissociation)

AB2 A+2 + 2B 0.3 M 0 00.3(10.9) 0.3 0.9 2 0.30.9 M = 0.54 M

pOH = 7 21 pK a 21 log C

5.6 = 7 21

pK a 21

log (0.54)

pK a + log 0.54 = 2.8 pK a = 3.07 3

Q.2[Sol. species 15p,due to the lessenergygap between s and p orbital spmixingispossible.

C2 , B2 , NO, CO, NO+, N2 , N2+, N2 Not possible in O22+, O2+ ]

Q.3Sol. (CH2)6 N4 Utropine

6HCHO + 4NH3 (CH2)6 N4


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Q.4[Sol. K 4[Fe(CN)6] Ni(CO)4 Fe(CO)5 [Zn(NH3)4]SO4

[Cd(NH3)4]SO4 [Mn2(CO)10] [Fe(CO)2(NO)2]Will obeys sidewickE.A.N. rulebetween E.A.N. isequal tonearest inert gas atomicnumber. ]

MATHEMATICS

PART-AQ.1[Sol. Given

f(3x) = f(x)

f (3x) = f(x) =

3xf = .......... =

n3xf

as n ; 3n

03xn

f(3x) = f(0) f(x) is a constant function. f(x) = 5 x R

)x(f sgn = 1.

5

2dx)x(f sgn =

5

2dx = 3. Ans. ]

Q.2[Sol. f(5) = 3 f 1(3) = 5

g(3) = 5

g '(y) =)x('f

1 g '(3) = )5('f

1= 125

G'(x) =)x(g

)2)(4(3 g'(x)

G '(3) = )x(g8

3 g '(x) =125

8

125 = 8. Ans. ]

Q.3[Sol. Since (a, 2) lies between x 2y + 3 = 0 and x 2y + 4 = 0

(a 1) a < 0 a (0, 1)loga(x2 2x) > loga(2x3)x2 2x < 2x 3 x2 4x + 3 < 0x (1, 3) .......(1)

but x2 2x > 0 x(x 2) > 0 x ( , 0) (2, ) ..........(2)

2x 3 > 0 x > 23

........(3)


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41/60


e = 21

aeea

= distance from (2, 0) to 10y3x = 0

2a 2

a=

2

1002 = 6.

2a3

= 6 a = 4.

Distance betweendirectrices =ea2

= 218

=16. Ans. ]

Q.8[Sol.(i) Putting x2 = 4y in equationof given circle, we get 4y+ y2 10 y + (25 r 2 ) = 0

y2 6 y + (25 r

2) = 0Asparabola is tangent to circle, sodiscriminant ofabove equation must bezero.

36 = 4(25 r 2) r = 4 = radius of circle.Let y = mx + c be tangent to x2 = 4y, so on solving we get

y

x

R (0, 3)

Q P

S

M

O

23

13

, 23

13

,x2 4mx 4c = 0Put discriminant tozero, weget m2 = c (condition of tangency)

y = m x m2 is tangent to parabola x2 =4y.But byapplyingconditionof tangencyofabove tangentwith thegiven circle, weget

4m1

|m5|2

2 m4 6m2 9 = 0 (m2 3)2 = 0 m = 3 .

Points of contact to the parabola will be

211 m

1,m2P &

222 m

1,m2Q i.e.

31,

32P &

31,

32Q .

Equation ofcommontangentswill bey = 3x3 which intersect at R (0, 3)

Center of circle is S(0, 5) & equationof chord PQisy =31

.

Equationsof latus-rectumand directrix ofparabolawill bey= 1 and y= 1 respectivelywhich are at

distances 32

and 34

respectively. Also distance SM= 31

5 = 3

14

.

Clearly centroid of PQR is

67,0 and area of PQR is

3320 . ]

Q.9[Sol. The equation of tangent atM( 4,4) to the parabolax2 =4y,is

x ( 4) = 2 (y + 4) 2x + y + 4 = 0Let the required circle be (x + 4)2 + (y 4)2 + (2x +y + 4) = 0

y

O (0,0)x( 4, 4)

M

x = 4y2

As above circle passes through (0,0), so 16 + 16 + (4) = 0 4 = 32 = 8

Hence required equation of circle is x2

+ y2 8x 16y= 0Ans. ]


42/60


43/60


h2 + 3

k

34k 2 = 4

h2 + 3

94

32k

2

= 4

h2 + 32

32k

= 4 + 3

4

91632k

316h

2

2

= 1.

91632y

316x

2

2

= 1

e = 32

and centre =

32,0 , Ans. ]

Q.14[Sol. BOC = 2A

in ABE, ABE= 2 AA

N(n)

A(a) M(m)

C(c)B(b)

L( )l

D

EF O

AOM = 2AA2ie

bc

)A2(iema

ie bmac

= 1

m = bac

.

Similarlyl = a

bc

n = cab

.

centroid of LMN =

abc3

acc b ba 222222. Ans. ]

Q.15[Sol. Point P( 2,0)clearly liesondirectrix of y2 = 8x.Thus, slopesofPAandPBare 1 and 1 respectively.

EquationofPA: y = x + 2EquationofPB: y = x 2


44/60


45/60


46/60


=

30x x

xxtanLim21

2

22

xxtanxxxtan

= 331

21

= 21

S =

2

11

1= 2. Ans. ]

Q.3[Sol. 0VV 21 a 2b + 3c = 0

Now if a = 1 then 3c 2b = 1.c = 1 and b = 1 only.a = 1; b = 1 = c.

if a =0 then 2b = 3c b = c = 0

Hence k

0 j

0i

0V2 is Null vector..

a = b = c= 0 is rejected.If a = 1 then 2b 3c = 1 b = 1 and c = 1 and b = 2 and c = 1 satisfy it.

If a = 2 then 2b 3c = 2 b = 1 and c = 0 satisfy it.

If a = 3 then b = 0 and c = 1and b = 3 and c = 1 satisfy it.

6 suchvectors are possible. ]Q.4

[Sol. AB =

222 cx15 bx3ax6 c25 b5a10

cx10 bx2ax4

DC =

222

x164x20x41x5x82x10

Since, tr (AB) = tr (DC) x R 4ax 5b 15cx2 = 10x 1 + 16x2 x R 4a = 10 ; 5b = 1 ; 15c = 16

a = 25

; b = 51

; c = 1516

.

k

1516 j

51i

25V1

k

30 j

10i

52V2

k

V3

321 VVV =100301052

15165125= 102

5 5

152

= 25 252

321 VVV = 24. Ans. ]


47/60


PAPER-2

P H Y S I C S

PART-A

Q.1Sol. Force actingonwires willnot changehenceabout c remainssame.

Q.2Sol. Voltageacrossthe other one can begreaterequal or less thanrated.

Q.3

Sol. = 22/3222

0 R )xR (2

iR 3x1

for x < < R.

Q.4

Sol. dnDy

y = dD

21n

Q.5Sol. Ina loop theyhavenophase difference but consecutiveloops havea differenceof .

Q.6

Sol.2

TT BA = TD

2TT CB = TE and

1

1BA Ak )TT(l

=2

2CB Ak )TT(l .

Paragraph for question nos. 8 to 10[Hint. There are two degrees of freedom along radial direction and onlyone degree of freedom along axial

direction. ]

Q.11Sol. Voltage across C changesduringcharging henceVA andVB bothcahnges.

VA

=VB

E

t

e1 = 2E

t = RC l n 2.

Q.14Sol. Upper portionparticles havegreaterspeed then lowerportion particles.


48/60


Q.15[Hint. ma= f up mg

ma = gvv

bg b

a = g

1

b then apply v2

= u2

+ 2as.]

PART-D

Q.1Sol. K 1 = 3 MeV

we have,10.2 = W + K max, 1 ...(i)

and 10.2Z2 = W + K max, 2 ...(ii)

Also de-Broglie = mK 2hh

2

1=

1

2

K K

= 2.3 K 2 = 5.25 K 1 ...(iii)

Also10.2Z2 = energycorresponding to longest wavelengthof teh Lyman series = 3 13.6 Z = 2 From equations (i), (ii) and (iii)

W = 3 eV

Q.2Sol. The collision doesnot alter the verticalcomponent ofthe velocityofeitherball, so

30cosu50

+ 30cosu7.050

= 1030sinu2

u 38m/s

Q.3Sol. Ina doubleslit interference pattern,thedistancex ofdarkfringe from thecentral achromaticfringeis

x = dD

(2n + 1)2 , n = 0,1,2, .....

= 1n275000 (where n = 0,1,2, ....)

Thus in the range 4000 8000 the absent wavelengths are 6818, 5769, 5000, 4421.

Q.4Sol. P = v2

dtmdv

v = v2

t

0

v2

v dtmvdv0

0


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ln2= m t

t =2lnm

t = 693.0693.024

t = 8 seconds

C HEM IS TRY

PART-AQ.1Sol. A B C D

KCal20EIa KCal30E IIa

III aa EE T

IK > T

IIK 300

II300I K K 300II350I K K 350

II350I K K ( Since 300II350II K K )

Also 300I

310I

K K

< 300II

310II

K K

& 500II

450II

500I

450I

K K

K K

12

T

T

K K

(whenT2 > T1) will behigher for the reaction which has higherEa.

Q.2[Sol. [Co(dien)Cl3]

Coordination number =6,Hybridisation : d2sp3It can show fac-mer isomerismduetopresenceofplaneofsymmetryit's isomerareopticallyinactive.]

Q.3Sol. RateofacidicHydrolysis Stabilityof Carbocation

O O

H O O

H

O

Intermediatecarbocation

Stabilityof carbocationI

I

I 2 NHOR F Relativerate

O O O O

(I) (II) (III) (IV) NH2 OR F


50/60


Q.4[Sol.

Linkages Geometrical isomer[Pt(CN)2 (NO2)2] 2[Pt(CN)2(NO2) (ONO)] 2[Pt(CN)2(ONO)2] 2

[Pt(CN)(NC)(NO2)2] 2[Pt(CN)(NC)(NO2)(ONO)] 3[Pt(CN)(NC)(ONO)2] 2[Pt(NC)2(NO2)2] 2[Pt(NC)2(NO2)(ONO)] 2[Pt(NC)2(ONO)2] 2Allareopticallyinactive.]

Q.5Sol. (A) AgI /Ag+ positivelychargedsolution(excessAgNO3)

(B) Factual information(C) Tyndalleffectismoredominatingin lyophobicsolution(D) Extent ofphysisorption decreases with increasein temperature.

Q.6

[Sol.

Fa

P

Fa

F

F b

F

PF

F

F

F

Fsquare pyramidal

Fa

P

Fa

F

F

F

Due to the berry - pseudolation it seems to likeall the PF bondlength inPF5 aresame.]

Q.7

Sol. NHOH

NO

H H N

H N2

Q.8,9,10[Sol. NH4 NO3 (A) + NaOH NH3(B) + H2O + NaNO3 (C)

N O + H O(D)

2 2

N2O + P4 P4O10 + N2Covalencyof phosphorous is5.

P

P

P

OO

O

O

PO

O

O

O

O

O N2O Oxidation state of N is +1 NaNO3 + Zn + 2NaOH Na2ZnO2 + H2 NaNO3 on reduction gives NH3 gas(B)]


51/60


Q.11Sol. DopingasbySi yield 'n' typesemiconductor

Anion cannot occupyinterstitial voidsasanion isbiggerinsize.

Q.12

Sol. (A)O OO O Ozonolysis H

HH

OOO

OC

(B)O

O

O O

O

O

O HH

OH

(C)

O

O

O

O

O

O O

H

H

O

(D)

O

O

O

O Ozonolysis OO

OO

H

Q.13

[Sol. S

F F

FF

sp3d,dz2 orbital takepart in hybridisation ]

Q.14

Sol. CH3 CHDCONH2 + PhCO N* H2

OH/Br 2 Hoffmann Degradation(HoffmannBromamidetest)

CH3 CHD + NH2 + Ph N* H2


52/60


53/60


CH3X > RCH2X >

R |

XHCR >R |

XCR |R

(d) Increasingconcentration ofnucleophile doesnot effectrateofS N1Rate = K [Substrate]

S N1 is independentofnucleophile concentration.Q.3[Sol. Fe2(SO4)3 + KCN(Xs)

K 3[Fe(CN)6] (A)Oxidationstate(Primaryvalency)=3Coordinationnumbers(Secondaryvalency) = 6 ]

Q.4

[Ans. NH

N N ]

MATHEMATICS

PART-AQ.1[Sol. Let P (t + 2, t) be a point on y x + 2 = 0.

Tangentsare drawn to parabola y2 = 4x from P(t + 2, t)

chord ofcontact isgiven byyy1 = 2(x +x1)yt = 2(x + t + 2)

(x + 2) + 2t

(2 y) = 0

point is (2, 2). Ans. ]

Q.2[Sol. Radical centre is the point of intersectionof perpendicular lines i.e., orthocentre of triangle. Since the

triangle formedbygiven linesisa right .Orthocentre will bepoint ofintersection of 4x + 3y 17= 0 and 3x 4y + 6 = 0 i.e., (2,3). Ans. ]

Q.3[Sol. Using (1 + cot ) (1 cot (45 + ) ) =2

The given expressionsimplifies to(1+ cot 45)219 = 220. Ans. ]

Q.4

[Sol. 2f(x) +

x1f 3 = 5x .........(1)

x x1


54/60


x1f 2 + 3f(x) = x

5.......(2)

Solving(1)and(2)

f(x)=x5

x1015 2

f(x)=f(x)

x5x1015 2

=x5x1015 2

(15 10x2)

x52 = 0 x2 = 2

3

x = 23 . Ans. ]

Q.5

[Sol. f 4(x)=x

0

32 dt)t(f t

differentiatingbothsideswrtx,4 f 3(x)f '(x)=x2 f 3 (x)

f'(x)=4x2

Integrate both sides:

f(x)= C12x3 , since f(0) = 0

C = 0.

f(x)=12x3

A = 0

1

3dx

12x

+4

0

3dx

12x

10 4

A =4

0

40

1

4

48x

48x

A =484

481 = 48

257. Ans. ]


55/60


Q.6

[Sol. h = 53seca503

h = 2a5

sec .........(1)

k = 5305tana3

y

x

B(0, a tan )

A(a sec , 0)

R(h,k)3

B(0, a tan ) A(a sec ), 0 R(h,k)

3

5O

5

k = 2a3

tan ........(2)

sec2 tan2 =22

a3k 2

a5h2

= 1

2

2

2

2

a9

k 4

a25

h4 = 1.

36x2 100y2 = 225a2. Ans. ]

Q.7

[Sol.m

m

n

0xx

xxtan

x1cosx

Lim

=

x1cosxLim mn

0x

n m > 0 so that f(x)is continuous at x = 0But f(x)is non-derivableat x = 0, so

f '(0) =xx

xxtan

x1cosx

Limm

m

n

0x

=

xcosxLim 1mn

0x

n m 1 0 for f '(0) not existing n m 1. Ans. ]

Paragraph for question nos. 8 to 10

[Sol.

12 32 52 721 2 3 121 322 523 72

13/2

2

5/2

37/2

0

x

y


56/60


L = 7, M = 14 (L+ M) = 21. Ans. ]

Q.11

[Sol. 15vv 32

15sinvv 32 sin =

415

cos = 41

.

132 vk v2v

21

2232 vk v2v

3223

22 vv4v4v

= 212vk

16 + 4 4 32 vv cos = k 2

20 4 (1) (4) 41

= k 2

k 2 = 16 k = 4. Ans. ]

Q.12[Sol. We musthave

2 3 < 0 ( 3) < 0 (0, 3) .......(1)

and 2 2

> 0

21 > 0

y-axis

x-axis

y=3x

P( , ) 2 y = x2

O(0,0)

< 0 or > 21

........(2)

(1) (2) gives

3,21 . Ans. ]

Q.13

[Sol. f(x) = )1x(x31

f'(x)= 1x4x3

1

32

f(x) is increasingfor x >41

and decreasing for x


57/60


f'(x)= 32

31

x31x

34

f '(x) does not exist at x = 0f ' (0 )andf'(0+) both tends to .

vertical tangent atx = 0.

f"(x)=

x1x2

x9

232 .

f"(x)=0atx= 21

(Inflectionpoint)

Graph of f(x) is

1/21/4

(1,0)0 .

A =

0

1

31

34

dxxx +

1

0

31

34

dxxx

A =

0

1

34

73

x43x

73

+

1

0

34

73

x43x

73

A = 0

43

73 +

43

73

A = 289

282112

A = 2842

= 23

. Ans. ]

Q.14

[Sol. Let j

yi

xr r j10i8r = 40

x2 + y2 + 8x 10y + 40 = 0circle with centre C( 4, 5) and radius= 1. (4,5) C

P(2,3)

M=max 2

j

3i

2r

= max 22 )3y()2x( = 218 m=min 22 )3y()2x( = 218 (M + m) = 18. Ans. ]

Q.15 I


58/60


[Sol. Middle term = 12C6 x66

xxsin

= 166237

sin6x =6

23

sin x = 23

sin 1s inx= 3 . Ans. ]

PART-BQ.1[Sol.

(A) Put x = 1 to get sum of the coefficients2012

31

(3)2013= 3. Ans.

(B)9

0

dx}x{ = 9

0

dxxx

=

4

1

9

4

1

0

9

0

23dx2dx1dx0

2

3x

= 18 13 = 5. Ans.

(C)

4

f = 14

f '(x) = 1 + 3 tan2x sec2 x

f '

4 = 1 + 3(1)

2 22 = 7.

g '

14

=

4'f

1= 7

1

56 g '

14 = 7

56 = 8. Ans. ]


59/60


PART-DQ.1

[Sol. )x(g)x(f Limx = 0

65x2

3xsinLim 1

x

65x baxsinLim 2

21

x

Hence sin 1(a)= 6

a = 21

Now, as

5x23x

sinLim 1

0x = sin 1 53

5x baxsinLim 2

21

0x = 4

53sin 1

5 bsin 1 = tan 1 1 tan 1

53

5 bsin 1 =

501sin 1

b = 21

b2 = 21

5a + 3b2 = 25

+ 23

= 4. Ans. ]

Q.2[Sol. The given systemisconsistent if

=c b2 bc12211

= 0

3bc + c 10b = 0

c = 1 b3 b10

Since c < 2

1 b3 b10

< 2

01 b3 2 b6 b10


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01 b32 b4

b

21,

31

m = 31

, n = 21

n m = 65

24 (n m) = 20. Ans. ]Q.3[Sol. 16l 2 + 9m2 = 24l m + 6l + 8m + 1

25 (l 2 + m2) = (3l + 4m + 1)2

22

m

1m43l

l

= 5

Equation of S1 = 0 is (x + 4)2 + (y + 3)2 = 52S1 : x2 + y2 + 8x + 6y = 0

Equationof familyofcircletouching S1 =0at(0,0)isgivenbyS2 : (x 0)2 + (y 0)2 + (4x + 3y) = 0S2 = 0 passes through (3, 1)9 + 1 + (12 + 3) = 0

= 1510

= 32

.

S2 : x2 + y2 3x8

2y = 0

a = 38

; b = 2 ; c = 0

3a + 4b + 5c = 8 + 8 + 0 = 16. Ans. ]Q.4

[Sol. Area of ABG = 31

Area of ABC

2

1AG BG =

33

32

3

1

)60cotAG()AG(21

= 3932

30

60

A

G

E (AG)2 = 964

8

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Mock Test 1 Paper 1 With Solution 2014

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