14_01_2012_XII_ABCD_PCM_ST_2_Code_A

7/30/2019 14_01_2012_XII_ABCD_PCM_ST_2_Code_A

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Class: XII (A1&A2) Date: 15/01/2012 Time: 3 Hours. Max. Marks: 243

VERY IMPORTANT

A. The question paper consists of 3 section (Section-1 contains Physics, Section-2 contains Chemistry and

Section-3 contains Mathematics). Please fill the OMR answer Sheet accordingly and carefully.

B. Each Section contains (15 uestions in Part-A, 1 question in Part-B and 5 questions in Part-C) and total

number of pages are 16.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 the Invigilator.

INSTRUCTIONS

PART-A

1. Q.1 to Q.9 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 bubble corresponding to the correct answer and zero mark if no bubble are darkened. In all other

cases, minus one (1) markwill be awarded.

2. Q.10 to Q.12 are Paragraph type. Based upon the paragraph 3 single correct typequestions have to be

answered. Each of these questions 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 bubble corresponding to the correct

answer and zero mark if no bubble are darkened. In all other cases, minus one (1) markwill be awarded.

3. Q.13 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 3 marks if you have darkened only the bubble corresponding to the correct

answer and zero mark if no bubble are darkened. No negative marks will be awarded in this section.

PART-B

4. Q.1 is Matrix Match type question. Each question has Four statements (A, B, C, D) given in

Column-I and Five statements (P, Q, R, S, T) given in Column-II. Any given statement in Column-I

can have correct matching with one or more statement(s) given in Column-II. For example, if for a given

question, statement B matches with the statement given in Q and R, then for the particular question, againststatement B darken the bubbles corresponding to Q and R in the OMR.

For each row, you will be awarded 4 marks for each row in which you have darkened the bubble(s)

corresponding to the correct answer. Thus Q.1 carries a maximum of 16 marks.

PART-C

5. Q.1 to Q.4 are Integer Type questions. The answer to each question is upto 4 digit ranging from

0 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 25, then for the particular question, against question number

you must fill as 0025 in the OMR. No negative marks will be awarded 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 of the questions must be marked by shading the circle against the question by darkBlack Ball point

Pen only.

USEFUL DATAAtomic weights: 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 : ln 2 = 0.69, ln 3 = 1.09, e = 1.6 1019, me= 9.1 1031 kg ]

Take 0 = 8.85 1012 , g = 10 m/s2 unless otherwise stated

CODEAPECIALTEST-2


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PHYSICS

XII Special Test-2 Code-A Page # 2

PART-A

[SINGLE CORRECT CHOICE TYPE]

Q.1 to Q.9 has four choices (A), (B), (C), (D) out of which ONLY ONE is correct.

Q.1 In a series L-R-C alternating circuit, voltage across AC is V, voltage across AC differs current in phaseby 30, voltage across AD differes current in phase by 60. Voltage across CD will be

A B C D

(A)2

V3(B)

3

V2(C) 2V (D) 3V

Q.2 Two very long wires parallel to the z-axis and a distance

4a apart carry equal currents I in opposite directions asshown in the figure. A cylinder of radius a and length L

has its axis on the z-axis midway between the wires.

Calculate the net upward magnetic flux through half of

the curved cylindrical surface above the xz plane. (2a,0,0)

(2a,0,0)x

z

y

L

(A)

IL0

(B)

3lnIL0

(C)

2lnIL0

(D)2

IL0

Q.3 In the figure shown switch S1

remains connected for a long time and the switch S2

remains open. Now

the switch S2

is closed. Assuming = 10V and L = 1H. Find the magnitude of rate of change of current

in inductor (A/s) just after the switch S2is closed.

A R B 2R C

DEF

L

S1

S2

(A) 5 (B) 10 (C) 20 (D) None of these

Q.4 An object O is kept infront of a converging lens of focal length 30cm behind which there is a plane mirror

at 15cm from the lens.(A) the final image is formed at 60cm from the lens towards right of it

(B) the final image is at 60cm from lens towards left of it.

(C) the final image is at 30cm from lens towards left of it.

(D) the final image is at 30cm from lens towards right of it.


3/16

PHYSICS


Q.5 In figure there are two particles A and B each of mass m. A is con-

nected to ceiling by a light inextensible thread OA and B is connected

to A by light inextensible thread AB. Initially line OB is vertical.

System is released from rest. Initial acceleration of A and B are a1and

a2

respectively. Find the value of2

1

a

a.

A

B

53

37

O

(A)5

1(B)

5

2(C)

5

3(D)

5

4

Q.6 Two co-axial rings of same radius R = 10 cm are placed parallel to the y-z plane, such that x-axis is the

axis of the rings. Ring 1 carries a current of 2 Amp and ring 2 carries a current of 1 Amp as shown in the

figure. The separation between the rings is d = 50 cm. Find the magnitude of

0

xd.B

, where B

is the

net magnetic field due to both rings at any point on the x-axis.

y 1 Amp

x

z

10 cm 10 cm

2 AmpRing-1

Ring-2d = 50 cm

(A) +1 Amp (B) 1 Amp (C) +3 Amp (D) None of these

Q.7 A wheel of radius R = 2m performs pure rolling on a rough horizontalsurface with speed v = 10 m/s. In the figure shown angle is angular

position of poitn P on wheel from where dirt released from wheel reaches

the maximum height from ground. Find the value of sec.

(A) 2 (B) 2

(C) 5 (D) 4

Q.8 A tunnel is dug along the diameter of the earth. There is a particle of mass mat the centre of the tunnel.

Find the minimum velocity given to the particle so that it just reaches to the surface of the earth.

(A) R

GM

(B) R2

GM

(C)R

GM2(D) it will reach with the help of negligible velocity


4/16

PHYSICS


Q.9 A certain series RC circuit is formed using a resistance R, a parallel plate capacitor without dielectric

having a capacitance C = 2F and a battery of emf E = 3V. The circuit is completed and it is allowed to

attain the steady state. After this, at t = 0, half the gapping between plates of the capacitor is quickly filled

with a dielectric of constant K = 2 as shown in the figure. The system is again allowed to attain a steady

state. What wi l l be the heat generated (i n Joule) between t = 0 and t = ?d/2

K=2

d

(A) 1 (B) 2 (C)4

3(D)

4

27

[PARAGRAPH TYPE]


Paragraph for question nos. 10 to 12

A U tube containing two different liquid of densityand 2 is fixed vertically on a rotating table as shown

in the figure. Initially table is at rest and table can rotate about a vertical axis passing through the centre

of the table. The interface of two liquids of densitiesand 2 respectively lies at the point A in a U tube

at rest. The height of liquid column above A is3

8a, where AB = 2a. The cross-sectional area of the tube

is S. Now the table is whirled with angular veloityabout a vertical axis as shown in figure such that the

interface of the liquids shifts towards B by3

2a, then at this instant find

Q.10 Find PBPA.

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

Q.11 Find the force exerted by liquidon 2 at the interface. (Neglect atmospheric pressure)

(A)Sag

4

9(B)Sag

3

29(C) Sag

10

9(D)Sag

10

29

Q.12 Find the value of.

(A)a4

g9(B)

a32

g9(C)

a8

g9(D)

a16

g9


5/16

PHYSICS


[MULTIPLE CORRECT CHOICE TYPE]

Q.13 to Q.15 has four choices (A), (B), (C), (D) out of which ONE OR MORE may be correct.

Q.13 The displacement versus velocity equation of a particle moving in a straight line is given as x = 2v

( and are constants). Choose the correct answer.

(A) the particle is in simple harmonic motion

(B) time period of the particle is 2

(C) amplitude of the particle is

(D) maximum velocity of the particle is

Q.14 Which of the following statements is/are true

(A) work done by kinetic friction on a rigid body may be positive

(B) a uniform sphere rolls up an inclined plane without sliding. The friction force on it will be up the

incline. (only contact force and gravitational force is acting)

(C) a uniform sphere rolls down an inclined plane without sliding. The friction force on it will be up the

incline. (only contact force and gravitational force is acting)(D) a uniform sphere is left from rest from the top of a rough inclined plane. It moves down the plane with

slipping. The friction force on it will be up the incline.

Q.15 In an organ pipe (which may be closed or open) of 99 cm length, standing wave is set up whose equation

is given by longitudinal displacement. x = (0.3 mm) cos [(2/0.8) (z + 0.01m)] cos 400 t

where z is measured from the top of tube in metres and t is in second. Take end correction = 1cm.

Choose the correct statements.

(A) the upper end and lower end of tube are open and closed respectively.

(B) the upper end and lower end of tube are closed and open respectively.

(C) the air column is vibrating in third harmonic

(D) the air column is vibrating in second overtone.


6/16

PHYSICS


PART-B

[MATRIX TYPE]

Q.1has Four statements (A,B,C,D) given in Column-IandFive statements (P,Q,R,S,T) given in Column-II.

Any given statement in Column-Ican have correct matching with one or more statement(s) given in Column-II.

Q.1 Column-I Column-II

(A) Angular momentum of system (P) System :An electron revolving around

is conserved about centre of nucleus in hydrogen atom in ground state.

circular path. Event :A photon corresponding to first line oflyman series is incident on it at t = 0

and is absorbed.

(B) Mechanical energy of system (Q) System : A ball.

can increase for t > 0. Event : It is projected on a rough surface with

some angular velocity at t = 0 as shown

0 0

= v /Rv

0

(C) Kinetic energy of system reamins (R) System :A small ball. It is attached to a cord

constant. passing through a hole on a frictionless

horizontal surface and rotating as shown.

Event : The cord is slowly pulled inside by

an external agent at t = 0.

System particle

(D) Speed of system's centre of (S) System :An electric dipole free in space.

mass can increase for t > 0. Event : At t = 0 a charge is brought near it.

(Consider the centre of dipole as the centre of

the circular path.)

(T) System :A charged ball is revolving in a

circular path made on a smooth horizontal table.

Event :A uniform magnetic field is switched

on in vertically upward direction at t = 0 which

gradually increases in magnitude.


7/16

PHYSICS


PART-C

[INTEGER TYPE]

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

Q.1 The energy of a K-electron is tungsten is 20 keV and of an L-electron is 2 keV. The wavelength of

k

X-ray photon emitted when a K-electron is knocked out is ___________ (pm).

Q.2 The moment of inertia of a disc of inner radius a and outer radius b and having mass M about z-axis is of

the form (A0 B0 10

2) kg-cm2. Find the value of B0/A0.[Given M = (2 0.02)kg, a = (5 0.05) cm, b = (7 0.07)cm.]

Q.3 For the circuit shown in figure, charge on the 5F capacitor is _______ (in C).

Q.4 One mole of an ideal monoatomic gas is taken through a cylic process ABCDA. It is given that

A

B

V

V=

C

D

V

V= K. It is also given that the total work done by gas in one cyclic process ABCDA is equal

to zero. Using the details given in the diagram. Find the value of 4 lnK.

Given. :AB = isothermal expansion

BC = isochoric cooling

CD = isothermal expansion.

DA = Adiabatic compression.

The temperature of upper isotherm is 2T and of lower isotherm is T.


8/16

CHEMISTRY


PART-A



Q.1 The unit cell of the hexagonal close packing can be divided into three equivalent smaller unit cell. What

will be the number of tetrahedral voids and packing fraction of each such smaller unit cell.

(A) 6, 74% (B) 2, %3

74(C) 2, 74% (D) 6, %

3

74

Q.2 Which of the following has the least tendency to form peroxide?

(A) Li (B) Ba (C) Na (D) Sr

Q.3OH

42SOH.conc

reagent

s'Baeyer Product(s).

Total diols formed after final reaction are

(A) 6 (B) 5 (C) 4 (D) 8

Q.4 If magnitude of energy of electron in first Bohr orbit of hydrogen atom is x J and the Planck's constant is

6.6251034 J sec then what will be the expression of frequency of revolution of electron in 3rd Bohrorbit of He+

(A) Hz10625.627

x834

(B) Hz

10625.627

x234

(C) Hz10625.63

x234

(D) Hz

10625.63

x834

Q.5 Which of the following reactions would not produce the same gas which is produced by electrolysis of

fused NaH using inert electrodes?(A) CaH

2+ H

2O (B) Pb + NaOH

(C) SiH4

+ H2O (D) ZnO + NaOH

Q.6

OH

/SOH 42

/Se

etemperaturhigh

SOH.conc 42

Final product is

(A)

SO H3

(B)SO H3

(C)

SO H3

(D)

SO H3


9/16

CHEMISTRY


Q.7 Isotherms of a real gas is represented as shown in diagram at three temperature T1, T

2, T

3. From the

graph, predict in which case gas-liquid transition will involve only one phase throughout.

P

V

C

B

A

F

T1

T2

T3E

D

G

H

I

(A) ADEG (B) ACIH (C) BADE (D) BCI

Q.8 Ph

O O

/HO

.)eq2(

Ni/H2 HI/PdRe J (Final product)

J is

(A)

Ph

(B)Ph

(C)

Ph

(D)

Ph

Q.9 When blood containing "Haemoglobin" as the colloidal partial is subjected to electro osmosis. The

dispersion medium moves towards the anode. Hence, the incorrect statement will be

(A) Fe(OH)3 solution on mixing with haemoglobin in blood can cause coagulation(B) As

2S

3solution can cause coagulation in blood on mixing.

(C) In electrophoresis of blood, movement of colloidal particle will be towards cathode.

(D) NaCl on mixing in blood can cause coagulation.


10/16

CHEMISTRY


[PARAGRAPH TYPE]


Paragraph Question No. 10 to 12

Sodium azide (NaN3) is an ionic compound. The N

3 group is symmetric with NN bond distance of

1.2 . It is highly soluble in water. Sodium azide as a product is prepared by a two-step process calledWislicenus reaction.

Step 1 : 2Na (s) + 2NH3

(g) 2NaNH2

(s) + H2

(g)

Step 2 : 2NaNH2

(s) + N2O (g) NaN

3(s) + NaOH (s) + NH

3(g)

For heavy metals less reactive metals form thermally less stable azide.NaN

3is unstable and decomposes due to shock / jerk as:

2NaN3 2Na + 3N

2

This property finds application in car airbags. The vital component of the airbag system is a sensor that

can detect head - on collision as different from car coming across a bump or a pothole.

When a car decelerates very quickly, as in a head-on crash, the NaN3

pellet gets 'jerked' strong enough

to evolve vast quantities of N2

gas. This nitrogen gas fills into a nylon bag (attached with car steering) at

a velocity of nearly 200 miles per hour. It takes 40 mill seconds for full inflation. Subsequently, the

inflated airbag slowly deflates by allowing N2to escape through its 'holes'.

Sodium which is a potential hazard, and is formed as a by-product of the above jerk, is 'Scavanged' by

SiO2 kept in the same chamber forming sodium silicate.Sodium azide is also employed as a reactant tomake acyl azide.

RCOCl + NaN3 RCON

3+ NaCl

Heating acyl azide followed by hydrolysis is an important rearrangement reaction in organic chemistry

called Curtius reaction. This is used in the preparation of pure primary amines.

Q.10 NaN3

exists but Na3N is highly unstable. This can be best explained by:

(A) Resonance stabilization of N3 ion.

(B) High electropositivity of Na atom.

(C) Na+ is unable to stabilize the very high charge density of N3.

(D) Non-existence of conjugate base of NH2

Q.11 If X = Solid product in Step

1 of Wislicenus reactionY = Solid by-product in Step2 of Wislicenus reactionZ = Product of Curtius reaction done on acyl azide

Choose the correct basicity order:

(A) X > Y > Z (B) X > Z > Y (C) Y > X > Z (D) Z > Y > X

Q.12 The correct order of thermal stability of the given azides is

(A) AgN3

> AuN3

>CuN3

(B) AgN3

< AuN3

< CuN3

(C) AuN3

< AgN3

< CuN3

(D) AuN3

= AgN3

= CuN3


11/16

CHEMISTRY




Q.13 Which of the following solutions are isotonic with respect to 0.5 M NaCl solution having degree of

dissociation = 0.8.

(A) 153.9 gm of Sucrose dissolved in 500 ml of solution.

(B) 0.3 M aq. Na2SO

4solution undergoing 100 % ionization

(C) 1.8 % w/w aq. NaOH solution undergoing 100 % ionization.

(D) 1.2 M benzoic acid in a solution of benzene where the acid dimerizes to an extent of 50 %.

Q.14 Choose the reactions which would liberate nitrogen gas?

(A) Ca(OCl)Cl + NH3

medium

aqueous ? (B) NH3 + PbO

?

(C) NH3

(excess) + Cl2

? (D) NH

4Cl + NaNO

2

?

Q.15 Na2C

2

HCl

)ex(ICH)ii(

)ex(NaNH)i(

3

2

42 BaSOPd/H

Zn/OH)ii(

O)i(

2

3

Final product can be obtained by

(A)OH/H)ii(

mCPBA)i(

2

4HIO

(B) H2C = CH

2

HO/OH)ii(

THF.BH)i(

22

3

Cu

(C)

O||

OHCCH3 2SOCl 33

)OCMe(LiAlH

(D) H3CBr

DMSO

KCN

OH/H)ii(

HCl/SnCl)i(

2

2


12/16

CHEMISTRY


PART-B

[MATRIX TYPE]

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


Q.1 Column I Column II

(Reaction) (Laboratory test for final product)

(A) Mg2C

3

OH2 (P) Final product(s) can reduce Tollen's reagent

(B)

O||

NHCCHCH 223 OH/HHO/CHF

OH)ii(

LAH)i( 23

2

(Q) Final product(s) can give violet colour with

neutral FeCl3

(C)

OO||||

OMeCCHCCH 23

O|| ClCCH)ii(

MeO)i(

3

)ii(

OH/H)i( 2

(R) Final product(s) can give Haloform test

(D) 3

3

AlCl

ClCHPh|CH

42

2

SOH)ii(

/O)i(

(S) Final product(s) can liberate CO2

on reaction

with NaHCO3

(T) Final product(s) gives a product with

Hg2+ / H+ /H2O which can give Haloform test

PART-C

[INTEGER TYPE]

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

Q.1 All the substances involved in the reaction given below can undergo combustion reaction and theircombustion enthapies at 300 K are given below,

2A (g) + B(g) 3C(g) + D (g)

Given: AHocombustion =1000 cal/mol CHocombustion =500 cal/mol

BHocombustion =2000 cal/mol DH

ocombustion =100 cal/mol

Take : R = 2 Cal mol1 K1

If the reaction occurs in a constant volume container at 300 K and the reaction obeys first order withrespect to A and if A reduces to half its initial amount in 69.3 sec. then calculate "abcd"

where ab = heat released when 2 103 mole of A has reacted at 300 K (in cal)cd= rate at which heat is released initially (in cal/sec.) if initially 1 mole of A is present.


13/16

CHEMISTRY


Q.2 Find the number of species containing XOX linkage (where X is central atom).N2O4 , S4O6

2 N2O

5, B

2O

3, Cl

2O

7, Cr

2O

72, P

4O

8, H

2S

2O

7, H

2S

2O

6, H

3P

3O

9If your answer is 5, write the answer as 0005.

Q.3 A saturated solution of sparingly soluble base Fe(OH)3

is found to have a specific conductance of50 104 ohm1 m1. Calculate the value of a four digit number "abcd" whereab = 3 1016 times solubility product of Fe(OH)

3cd = 6104 times solubility of Fe(OH)

3in a solution of pH = 10.

Given : 3eqFeCl

= 15 103S m2 eq1

NaCleq

= 13 103 S m2 eq1

NaOHeq

= 23 103 S m2 eq1

Q.4 100 ml solution of I2

is added with 100 ml 0.2 M NaOH. After sufficient time for disproportion tocomplete, excess of NaOH is back titrated with HCl and 25 ml of 0.1 M HCl was consumed. Calculatemillimoles of I

2initially taken rounded off to nearest integer.


14/16

MATHEMATICS


PART-A



Q.1 If kjy3i3xa 22 and kx4j3ib

be perpendicular vectors for x, y R, then the

range of values of x and y will be respectively

(A)

3

1,

3

1;3,1 (B)

3

1,

3

1;1,

3

1(C)

1,

3

1;1,0 (D)

1,

3

1;1,0

Q.2 The value of nnnnnnn

1011......4321Lim

is equal to

(A) 0 (B) 1 (C) 11 (D) 11!

Q.3 Let normal drawn to the parabola y2 = 4x at the point P(4, 4) intersects the parabola at the point Q.

If normal drawn to the parabola at Q intersects the same parabola at R, then the arithmetic mean of

abscissae of points P, Q and R is equal to

(A)27

238(B) 0 (C)

27

175(D)

27

338

Q.4 Let f(x) be a differentiable function satisfying f '(x) = f(x) with f(0) = 1, and g(x) satisfies

f(x) + g(x) = ex (x + 1)2. If1

0

dx)x(g)x(f = ae2 + b, then the value of (a + b) is

(A) 1 (B) 2 (C) 3 (D) 4

Q.5 The equation of the line passing through M(1, 1, 1) and intersects at right angle to the line of intersection

of the planes x + 2y4z = 0 and 2xy + 2z = 0 isa

1x =

b

1y =

c

1z , then a : b : c equals

(A) 5 :1 : 2 (B)5 : 1 : 2 (C) 5 :1 :2 (D) 5 : 1 : 2

Q.6 The value of definite integral dxxcos

xsine4

03

xcos

12

equals

(A) 41ee

22 (B) 2

ee2

(C) 4

1e4

(D) 2

1e2

Q.7 Locus of the feet of perpendiculars drawn from points (1, 2) and (3, 4) on a variable tangent to the conic

2|)i43(z||)i21(z| is

(A) 1|)i32(z| (B) 4|)i32(z| (C) 2|)i1(z| (D) 1|)i1(z|


15/16

MATHEMATICS


Q.8 For

2,

2x , let g(x) =

x

0

dttcos . If f(x) =

n

1r

1r2

n)x(gLim1 then the range of f(x) is

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

Q.9 If the polynomial y = x3 + px2 + qx + r (p, q, rR) has three real roots in the interval (0, 2) then therelation which must be correct, is

(A)2 < p + q + r < 0 (B)1 < p + q + r < 1

(C)

1 < p + q + r < 2 (D) p + q + r > 1

[PARAGRAPH TYPE]


Paragraph for question nos. 10 to 12

C1is the locus of a point P which moves such that the sum of square of its distances from a pair of straight

lines xy4x3y + = 0 is 25. A, B, C and D are four points in order from where pair of tangentsdrawn to the curve C

1are perpendicular but product of their slopes 1.

Q.10 The equation of tangent to curve C1

passing through the origin is

(A) 3x + 4y = 0 (B) 3x

4y = 0 (C) 4x + 3y = 0 (D) 4x

3y = 0

Q.11 If P1

and P2

are two points on C1

such that A, P1, P

2and C are collinear then |AP

2CP

2| is equal to

(A) 6 (B) 12 (C) 10 (D) 5

Q.12 If (xi, y

i), i = 1, 2, 3, 4 denote co-ordinates of the points A, B, C & D then

4

1i

ii )yx( is equal to

(A) 25 (B) 30 (C) 32 (D) 34



Q.13 Consider the bijective functions f : DfC

fand g : D

gC

gwhere f is a function satisfying the

relation f(x) +

x

1f = x3 and g(x) =

2

1(sin1x + cosec1x + tan1x + tan12x + tan13x).

Which of the following relationdoes not hold good?

(A) Df D

gand C

f= C

g(B) D

f= D

gand C

f C

g

(C) Df D

gand C

f C

g(D) D

f= D

gand C

f= C

g.

Q.14 Let f(x) =

0x,1

0x,|x|x2

x2

then which of the following statement(s) is/are true?

(A) f(x) is continuous at x = 0. (B) f(x) is derivable at x = 0.

(C) )x(fLim0x

does not exist. (D) f(x) is discontinuous at x = 0.


16/16

MATHEMATICS


Q.15 In which of the following conditions a unique plane can be determined?

(A) Plane passing through a given point and parallel to a given line not contained in plane.

(B) Plane passing through a given point and containing a given line provided point lies on the line.

(C) Plane passing through a given point and containing a given line provided given point does not contain

in the line.

(D) Plane parallel to a given plane and passes through a given point.

PART-B

[MATRIX TYPE]

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


Q.1 Column-I Column-II

(A) Let z = (cos 12 + i sin 12 + cos 48 + i sin 48)6. (P) 0

Then the Im (z) is equal to

(B) If dx|xsinx|

2

0

222

k3 then the value of k is (Q) 2

(C) The number of positive integral ordered pair (x, y) for (R) 4which cot1x + cot1y = tan12 is

(D) From a point (h, k) if three normals are drawn to y2 = 4x (S) 5

and if the tangents drawn to the parabola at the feet ofthese

form an equilateral triangle then h equals (T) 7

PART-C

[INTEGER TYPE]

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

Q.1 Find the number of points of intersection of curves |z1 | + | zi | = 4 and | 2z1i | = 14 .

Q.2 Let F, f, g, h are differentiable functions such that

F(x) =

0x,0

0x,)0(hx

1cos1)0(g

x

1sinx)0(g)0(f

and )x(f)x('ht)x(h)x('gt)x(g)x('f 2 = 0 t R.Find the value of f3(x) + g3(x) + h3(x)3f(x) g(x) h(x) at x = 5.

Q.3 If the area bounded by the curve f (x) = cos1

]x[sin2

sin and x-axis from x = 0 to x = 2 is

k, then find the value of k.Note :- {k} and [k] denote fractional part and greatest integer functions of k respectively.

Q.4 Let area of triangle ABC is 32 sq. units, and C = 15. If side AB is of minimum length,

then find the value ofAC

BC.

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