+2 (PCM) Full Scale Test Paper 17 Feb 2012

[Page No.1] PiSCHOLASTICS: S.C.O 16-17, 1st & 2nd Floor, Sector -20D, Chandigarh. Ph: 6544444, 3910727, 5025027, 9216144327

Date 17– 02 – 2012 Class : 10 + 2 (Physics) M.M: 513 Time: 6 hrs

Test Code – 4015 TEST: Full Scale Test (PCM) Booklet Code: [1]

MARKING CRITERIA

SECTION CORRECT WRONG NOT ATTEMPTED

A + 4 – 1 0

B + 5 –2 0

C +5 0 0

D +8 0 0

INSTRUCTIONS : –

1. Paper contains 3 parts: Physics, Chemistry & Mathematics.

2. Each part contains 4 sections A, B, C & D.

3. Section – A contains One Option Correct Type problems from 1 to 20

4. Section – B One or More than one type questions from 1 to 10

5. Section – C Subjective type questions from 1 to 5

6. Section – D contains Match the column type questions from 1 to 2 without negative marking

scheme.

STUDENT NAME

ROLL NO.

[Page No.2]

Space for Rough work

PiSCHOLASTICS: S.C.O 16-17, 1st & 2nd Floor, Sector -20D, Chandigarh. Ph: 6544444, 3910727, 5025027, 9216144327

Pi Scholastics : Premier Institute for the preparation of IIT-JEE / AIPMT Booklet Code [1]

Part : I (Physics)

SECTION-A (One Option Correct Type Questions)

Current I is flowing along the path ABCD, along the four edges of the cube

(figure-a), creates a magnetic field in the centre of the cube of B0. Find the

magnetic field B created at the center of the cube by a current I flowing

along the path of the six edges ABCGHEA (figure-b)

A

X

D

C

B

Z

F

G

EY

H

A

X

D

C

B

Z

F

G

EY

H

Figure-(a) Figure-(b)

Q.1

(a.)

0B2

3towards corner G

(b.) 0B3 towards corner E

(c.)

0B2

3towards corner H

(d) 0B3 towards corner F

A sphere of radius 10 cm and density 500 kg/m3 is under water of density 1000 kg/m3. The acceleration of the

sphere is 9.80 m/s2 upward. Viscosity of water is 1.0 centipoise. If g = 9.81 m/s2, the velocity of the sphere is :

Q.2

(a.) 9 m/s (b.) 10 m/s (c.) 11 m/s (d.) 12 m/s

Q.3 2 loudspeakers are emitting sound waves of wavelength λ with an initial phase

difference of 2

π. At what minimum distance from O on line AB will one hear a

maxima

3λ

100λ

A

B

O

[Page No.3]




(a.) 25 λ (b.)

15

100λ

(c.) 50λ (d.)

3

25λ

An object is moving with a velocity of k6j3i2 ++ . A plane mirror whose reflecting surface is parallel to y-z

plane is moving with a velocity of kji ++ . What is the velocity of image as seen by a stationary observer?

Q.4

(a.) k4j + (b.) k4j −−

(c.) k6j3i ++− (d.) k6j3 +

The system of two weights with masses m1 and m2 are connected with weightless spring as

shown. The system is resting on the support S. The support S is quickly removed. The

accelerations of each of the weights right after the support S is removed are.

Q5

(a.)

2

2121 m

g)mm(a,0a

+==

(b.)

1

2121 m

g)mm(a,0a

+==

(c.) 0a,

m

g)mm(a 2

1

211 =

+=

(d) a1 = 0, a2 = 0

Find the coordinates of the image of an object placed at origin, which the eye will observe in mirror M2.

(a.) – d, d (b.) d, d (c.) –d, –d (d.) d, –d

[Page No.4]




A smooth wedge of mass m and angle of inclination 60° rests

unattached between two springs of spring constant k and 4k, on a smooth horizontal

plane, both springs in the unextended position. The time period of small oscillations

of the wedge (assuming that the springs are constrained to get compressed along their

length) equals

Q.7

(a.)

k

m

2

11

+π

(b.)

k

m

3

11

+π

(c.)

k

m

3

21

+π

(d.) None of these

A 800µF capacitor is charged at a constant rate of 50 × 10–6 A. The time after which the voltage across the

capacitor becomes 10 v

Q.8

(a.) 160 s (b.) 50 s (c.) 10 s (d.) 500 s

Two conducting spheres of radii R each are given equal charges +Q and are separated by a distance r (>R). (R and r

comparable). The force of attraction (F) between them is:

Q9

(a.)

2

2

r

KQ

(b.)

2

2

)R2r(

KQ

+

(c.)

2

2

2

2

)R2r(

KQF

r

KQ

+>>

(d.)

2

2

)R2r(

KQ

−

[Page No.5]




Electric field at the center of a charged parallel plate capacitor having uniform surface charge density σ on one plate

surface and –σ on another plate is

Q.10

(a.)

04ε

σ

(b.)

0ε

σ

(c.)

02ε

σ

(d.) zero

An elevator is accelerating upwards with an acceleration of 6 m/s2. Inside it a

person of mass 50 kg is standing on a weighing machine which is kept on an

inclined plane having angle of inclination 60°. The reading of the weighing

machine is:

weighing machine

a = 6 m/s2

60°

Q.11

(a.) 40 kg (b.) 160 kg (c.) 80 kg (d.) 50 kg

Two identical balls are set into motion simultaneously from equal heights h.

While the ball A is thrown horizontally with velocity v, the ball B is just

released to fall by itself. Choose the alternative that best represents the

motion of A and B with respect to an observer who moves with velocity v/2

with respect to the ground as shown in the figure.

A

v/2

B

ground

h h

Q.12

(a.) BA

(b.) BA

(c.) BA

(d.) B

A

[Page No.6]




A uniform solid right circular cone of base radius R is joined to a uniform solid hemisphere

of radius R and of the same density, as shown. The centre of mass of the composite solid lies

at the centre of base of the cone. The height of the cone is h

R

Q.13

(a.) 1.5 R (b.) 3 R (c.) 3R (d.) 32 R

A rigid equilateral triangular plate ABC of side 2 m, is in motion in the x-y plane. At the

instant shown in the figure, the point B has velocity )j8i3(vB +=r

and the plate has

angular velocity k2=ωr

r/s. Find the speed of point A.

X

Y

A B2m

Q.14

(a.) 5 m/s (b.) 4 m/s (c.) 3 m/s (d.) None of these

The wheels on the old-time bicycle shown in figure have radii of 60.0 cm and 10.0 cm. If

the larger wheel is rotating at 12.0 rad/s, what is the angular speed of the smaller wheel ?

Q.15

(a.) 12.0 rad/s (b.) 60.0 rad/s (c.) 72.0 rad/s (d.) 2.0 rad/s

[Page No.7]




A dielectric slab of area A passes between the capacitor plates of area 2A with a constant

speed v. The variation of current (i) through the circuit as function of time (t) can be

qualitatively represented as

Q.16

(a.) i

t

i

t

(b.) i

t

i

t

(c.) i

t

i

t

(d.) i

t

i

t

If the surface of a metal is successfully exposed to radiation of λ1 = 350 nm and λ2 = 450 nm the maximum velocity

of photoelectrons will differ by a factor 2. The work function of this metal is

Q.17

(a.) 2.84 × 10-19

J (b.) 1.6 × × 10-19

J (c.) 3.9 × × 10-19

J (d.) 2.4 × × 10-19

J

A small metal plate (work functionφ) is kept at a distance d from a singly ionized fixed ion. A monochromatic light

beam is incident on the metal plate and photoelectrons are emitted. The maximum wavelength of the so that the

photoelectrons may go round the ions along a circle is

Q.18

(a.)

dhc8

ed8

0

20

επ

+φπε

(b.)

20

0

edhc8

dhc8

+φεπ

επ

(c.)

−

φ

n

ehc

2

2

(d.)

φ

πε

hce

d8 0

A uniform ball of radius r rolls without slipping down from the top of a sphere of radius R. The angular velocity of

the ball at the moment it breaks off the sphere will be (neglect initial velocity of ball)

Q.19

(a.)

2r

g)rR(

17

10 +

(b.)

2r

g)rR(

10

7 +

(c.)

2r

g)rR(5 +

(d.)

2r

g)rR(

5

2 +

[Page No.8]




A particle of mass m is attached to one end of string of length l while the other end is fixed to a point height h

above the smooth horizontal table. The particle is made to revolve in a circle on the table so as to make n revolutions

per second. The value of n if the particle is in contact with the table will be-

Q.20

(a.)

h

g

2

1

π

(b.)

l

g

2

1

π

(c.)

h2

g

2

1

π

(d.) None of these

SECTION-B (One or More than one Type Questions)

Mark the correct statement(s) for the situation shown :

r

R

Neutral isolated spherical conductor with spherical cavity

r1

C

Q.1

(a.) If a point charge q is placed inside the cavity but not at centre, then potential of the conductor is

R4

q

0πε

(b.) If a point charge q is placed at the centre of cavity, then potential of the conductor will be zero

(c.) If a point charge q is placed inside the cavity but not at centre the then potential of the conductor will be

R4

q

0πε

−+

1r

1

r

1

R

1

(d) If a point charge q is placed inside the cavity but not at centre, then potential at the center of the conductor due

to charges on the outer surface of conductor is R4

q

0πε

[Page No.9]




A constant external torque τ acts for a very brief period ∆t on a rotating system having moment of inertia I. Q.2

(a.) The angular momentum of the system will change by τ ∆t.

(b.) The angular velocity of the system will change by

I

t∆τ

(c.) If the system was intially at rest, it will acquire rotational kinetic energy

I2

)t( 2∆τ

(d) The kinetic energy of the sytem will change by

I

)t( 2∆τ

In a region there exist a magnetic field B0 along positive x-axis. A metallic wire

of length 2a and one side along x-axis and one side parallel of y-axis is rotating

about y-axis with a angular velocity ω. Then at the instant shown.

z

y

P

RB

a

ax

ω

Q

Q.3

(a.) Potential difference across PQ is O (b.) Potential difference across PQ is

20 aB

2

1ω

(c.) Potential difference across QR is

20 aB

2

1ω

(d) Potential difference across QR is B0ωa2

[Page No.10]




Find the acceleration of the three masses A, B and C shown in figure. Friction

coefficient between all surfaces is 0.5. Pulleys are smooth. (Given mA = 1kg,

mB = 1kg, mC = 2kg.) CB

A

Q.4

(a.)

9

g7a1 =

(b.)

9

g7a2 =

(c.)

18

g7a3 =

(d.)

18

ga2

7=

In the circuit shown R1 = R2 = 10 Ω and resistance per unit length of wire PQ = 1Ω/cm and

length PQ =10 cm. If R1 is made 20 Ω the to get zero deflection in galvanometer. S is

midpoint of wire PQ.

R1R2

12V

PS

Q

G

R

Q.5

(a.) The jockey at P can be moved towards right 2 cm.

(b.) The jockey at Q can be moved towards right 2 cm.

(c.) The jockey at S can be moved towards left a distance 5/3 cm

(d) The jockey at all positions fixed and R1 should be made 20 Ω.

A cubical box dimension L=5/4 metre starts moving with an acceleration

5.0a =r

m/s i from the state of rest. At the same time, a stone is thrown from the

origin with velocity kvjvivV 321 −+=r

with respect to earth. Acceleration due

to gravity gr

= 10m/s2 )j(−

. The stone just touches the roof of box and finally falls

at the diagonally opposite point then :

Q.6

(a.) v1 =

2

3

(b.) v2 = 5 (c.)

4

5v3 =

(d.)

2

5v3 =

[Page No.11]




A particle of mass m moves in a conservative force field along x axis where the potential energy U varies with

position coordinate x as U=U0 (1–cosax), U0 and a being positive constants. Which of the following statement is true

regarding its motion. Its total energy is U0 and starts from x = 0.

Q.7

(a.) The acceleration is constant (b.) It's speed is maximum at the initial position

(c.) It's maximum x coordinate is

a2

π

(d) It's maximum kinetic energy is U0

Figure shows a square current carrying coil of edge length L. The magnetic field on the coil is

given by jL

xBi

L

yBB 00 +=r

where B0 is a positive constant.

iy

x

Q.8

(a.) If coil is free to rotate about x axis torque on the coil is given by iiAB

2

10

(b.) If coil is free to rotate about y - axis torque on coil is given by jiAB

2

10−

(c.) Resultant force on coil is zero.

(d) Equation for the torque Brr

×µ where µ is magnetic moment of coil is not valid on the coil.

As shown in figure BEF is a fixed vertical circular tube. A block of mass m starts moving in the

tube at point B with velocity V towards E. It is just able to complete the vertical circle, then C

R

F

E

60°B

Q.9

(a.) velocity at B must be Rg3 (b.) velocity at F must be Rg2 .

(c.) Normal reaction at point F is 2mg. (d) The normal reaction at point E is 6 mg.

[Page No.12]




A narrow steel rod of length ‘L’ is rigidly clamped at its mid-point and transverse standing waves of frequency ‘f’ are

set up in it. The speed of transverse waves in the rod is ‘c’. Then,

Q.10

(a.) The free ends of the rod must be antinodes.

(b.) The fundamental frequency of the rod is c/(L)

(c.) The second overtone frequency of the rod is 5c/(2L)

(d) ‘f’ can be any integral multiple of the fundamental frequency.

SECTION-C (Subjective Type Questions)

Q.1 Slide rail of length 2L are fixed on a horizontal plane at a distance l from

each other. These ends are connected by two identical ideal batteries with emf

E by resistanceless wires (see figure). On the rails a rod of mass m, which

may slide along them. The entire system is placed in a uniform vertical

magnetic field B. Assuming that the resistance of the rod is R and the

resistance per unit length of each of the rails equal to ρ, find the period of

small oscillations (in sec.) arising from shifting the rod from the equilibrium

along the rails. Neglect friction, internal resistance of batteries and induced

emf in the rod.

[Take : B = πT , ε = π volt, l = 0.5m, L = 1m, ρ = 1Ω/m, R = 0.25 Ω, m =

100 gm. ]

B

lm, R

2L

ε ε

[Page No.13]




Q.2 A 0.5 kg block slides from point A on a horizontal track with an initial speed of 3 m/s towards a weightless spring

of length 1 m and having a force constant 2 N/m as shown in figure. The part AB of the track is the frictionless &

the part BC has co-efficient of static & kinetic friction as 0.22 & 0.20 respectively. If the distance AB & BD are 2

m and 2.14 m respectively. Find the total distance (in cm) through which the block moves before it comes to rest

completely [g = 10 m/s2 ]

m3 m/s

A B D C

k

Q.3 A positive charge +q1 is located to the left of a negative charge –q2. On a line passing through the two charges, there

are two places where the total potential is zero. The reference is assumed to be at infinity. The first place is between

the charges and is 4.00 cm to the left of the negative charge. The second place is 7.00 cm to the right of the negative

charge. If q2 = –12 µC, what is the value of charge q1 in µC.

Q.4 A uniform stick of mass m and length l spins around on a frictionless horizontal plane, with

its Centre of Mass stationary. A mass M is placed on the plane, and the stick collides

elastically with it, as shown (with the contact point being the end of the stick). What should

M (in kg) be so that after the collision the stick has translational motion, but no rotational

motion? take m = 24 kg.

M

m

l

Q.5 A square loop of area 2.5 × 10

-3 m

2 and having 100 turns with a total resistance of 100 Ω is moved

out of a uniform magnetic field of 0.40 T in 1 sec with a constant speed. Then what is the work

done, in pulling the loop (in µJ).

[Page No.14]




SECTION-D (Match the Column Type Questions)

Column-I Column- II Q1

(i.) A wave pulse is given by y =

)1)t2x((

1022

3

+−

× −

travels in +ve x direction.The shape of pulse is

drawn at t = 0.

(a.)

x

y

(ii.) The switch is closed at t = 0, y = magnetic field

energy, x = time.

(b.)

x

y

(iii.) A uniformly charged ring kept in yz plane with

centre at origin. y = electric field at a point on

x-axis, x = x coordinate.

(c.)

dx

dy= 0 at x = 0 as well as atlarge values of x.

[Page No.15]




(iv.) A liquid drop falling starts down in presence of

air resistance y = kinetic energy of the drop. x =

time.

(d.)

x

y

(e.)

x

y

A homogeneous field of magnetic induction B is perpendicular to a sufficiently long

track of width l which is horizontal. A frictionless conducting resistanceless rod of

mass m straddles the two rail of the track as shown in the figure. Entire arrangement

lies in horizontal plane. For the situation suggested in column-II match the

appropriate entries in column-I.

AD

B

C

Column-I Column- II

Q.2

(i.) A is a battery of emf V and internal resistance R. The rod

is initially at rest

C

D

(a.) Energy is dissipated.

[Page No.16]




(ii.) A is a charged capacitor. The system has no resistance. The

rod is initially at rest.

Q 0–Q0

(b.) The rod moves with a constant

velocity after a long time.

(iii.) A is an inductor with initial current i0. It is having no

resistance.

i 0

(c.) After a certain time interval rod will

change its direction of motion.

(iv.) A is a resistance. The rod is projected to the right with a

velocity V0

(d.) If a constant force is applied on the

rod to the right, it can move with a

constant velocity.

(e.) The rod stops after some time in

absence of an external force.

[Page No.17]




Part: II (Chemistry)

SECTION-A (One Option Correct Type QUESTION)

Two flasks X and Y of volumes 250 mL and 300 mL respectively at the same temperature are connected by a

stopcock of negligible volume. The flask X contains nitrogen gas at a pressure of 660 Torr and the flask Y

contains neon gas at a pressure of 825 Torr. If the stopcock is opened to allow the two gases to mix, the partial

pressure of neon gas and total pressure of the system will be

(a.) 300 Torr, 700 Torr (b.) 400 Torr, 700 Torr

Q.1

(c.) 450 Torr, 750 Torr (d.) 300 Torr, 750 Torr

At temperature ‘T’K, Kp for the reaction of CO2 with excess of hot graphite to form CO is 9 atm. The mole per

cent of CO in the equilibrium mixture of gases at temperature ‘T’ is

Q.2

(a.) 14.3% (b.) 25% (c.) 75% (d.) 85.7%

0.2 g sample of benzoic acid C6H5COOH is titrate with 0.12 M Ba(OH)2 solution. What volume of Ba(OH)2

solution is required to reach equivalence point? (Molar mass of benzoic acid = 122)

Q.3

(a.) 6.82 mL (b.) 13.6 mL (c.) 17.6 mL (d.) 35.2 mL

Nodal planes of π-bond(s) in CH2 = C = C = CH2 are located in

(a.) All areas in molecular plane

Q.4

(b.) Two in molecular plane and one in the plane perpendicular to molecular plane which contains C − C σ -

bond

[Page No.18]




(c.) One in molecular plane and two in the plane perpendicular to molecular plane which contains C − C σ-

bonds

(d.) Two in molecular plane and one in the plane perpendicular to molecular plane which bisects C − C σ-

bonds at right angle

O2F2 is an unstable yellow orange solid and H2O2 is a colourless liquid, both have O − O bonds, and O − O bond

length in H2O2 and O2F2 respectively, are

Q.5

(a.) 1.22 Å, 1.48 Å (b.) 1.48 Å, 1.22 Å (c.) 1.22 Å, 1.22 Å (d.) 1.48 Å, 1.48 Å

Silicon dissolves in excess of HF due to formation of Q.6

(a.) SiF4 (b.) SiH4 (c.) H2SiF6 (d.) H2SiF4

Which of the following orders is correct with respect to the decreasing p-character of the hybrid orbitals of the

central atoms in the following compounds?

(I) C3O2 (II) (HPO3)3 (III) B3N3H6

Q.7

(a.) I > III > II (b.) II > III > I (c.) III > II > I (d.) II > I > III

An exothermic reaction, has an activation energy of 27 kJ/mol of A. The heat of the reaction is 60 kJ. The

activation energy for the reverse reaction is

B A→ is

Q.8

(a.) 33 kJ (b.) 87 kJ (c.) 27 kJ (d.) 54 kJ

[Page No.19]




Which of the following reaction has zero activation energy?

(a.) HClHClCCH 34 +→+ && (b.) lC2Cl2&→

Q.9

(c.) 3333 CHCHHCHC −→+ && (d.) lCClCHClClHC 33

&& +−→−+

The reaction, 2NO + 2H2 → N2 + 2H2O

Has been assigned to follow following mechanism;

I. NO + NO N2O2 (fast)

II. N2O2 + H2 → N2O + H2O (slow)

III. N2O + H2 → N2 + H2O (fast)

The rate constant of step II is 1.2 × 10-4 mol L−1 min-1 while equilibrium constant of step I is 1.4 × 10-2. What is

the rate of reaction when concentration of NO and H2 each is 0.5 mol L-1?

(a.) 2.1 × 10-7 mol L-1 min-1 (b.) 3.2 × 10-6 mol L-1 min-1

Q.10

(c.) 3.5 × 10-4 mol L-1 min-1 (d.) None of these

Q.11

Which of the following is correct regarding above reaction?

;AH→

+

R R

O

BH→

+

R

R

O

[Page No.20]




(a.)

(b.)

(c.)

(d.)

The product of I− with −4MnO in acidic medium is Q.12

(a.) I2 (b.) −3IO (c.) IO− (d.) −

4IO

The set of reagents required for the change

(a.) (1) NaNO2 + H2SO4 (2) Sn/HCl (3) H3PO4/∆

(b.) (1) Sn/HCl (2) NaNO2 + HCl (3) H2O

(c.) (1) NH4HS (2) H3PO2/∆ (3) NaNO2 + HCl

Q.13

(d.) (1) NH4HS (2) NaNO2 + H2SO4 (3) H2O

NO2

NO2

NO2

OH

; are

R R

R

OH

‘ B = A =

R

OH

R R

O

R

R

OH

‘ B = A =

R

O

R

R

OH

‘ B = A =

R

R R

R

OH

‘ B = A =

R

OH

[Page No.21]




For the molecule PF4CH3 which of the following structure is the most stable considering that CH3 is more

electropositive than phosphorus?

(a.)

(b.)

Q.14

(c.)

(d.)

COMPREHENSION (Next Three Questions)

Hydrogen peroxide can be prepared by the action of dil H2SO4 or H3PO4 on barium peroxide or by bubbling carbon

dioxide through a thin paste of barium peroxide. On an industrial scale, it can be prepared by hydrolysis of

peroxodisulphuric acid obtained by electrolysis of 50% H2SO4 or an equimolar mixture of H2SO4 and ammonium

sulphate. The strength of H2O2 solution can be expressed in a number ways namely normality, molarity, per cent

strength and volume strength. Volume strength refers to the volume of O2 produced at NTP by decomposition of 1 mL

of H2O2 solution. H2O2 acts as an oxidizing as well as reducing agent both in acidic and basic media.

The correct increasing order of the acidity of CO2, H2O and H2O2 is

(a.) CO2 < H2O2 < H2O (b.) H2O < H2O2 < CO2

Q.15

(c.) H2O < H2O2 > CO2 (d.) H2O2 > CO2 < H2O

P

F F

F

F CH3

P

F F

F F

CH3

P

CH3

F

F F

F

P CH3

F

F F

F

[Page No.22]




The volume of 10 volume H2O2 solution that decolourises 200 mL of 2N KMnO4 solution in acidic medium is Q.16

(a.) 112 mL (b.) 336 mL (c.) 200 mL (d.) 224 mL

Hydrolysis of one mole of peroxodisulphuric acid produces

(a.) Two moles of Sulphuric acid

(b.) Two mole of peroxomonosluphuric acid

(c.) One mole of Sulphuric acid, and one mole of peroxomonosulphuric acid

Q.17

(d.) One mole of Sulphuric acid, one mole of preoxomonosulphuric acid and one mole of hydrogen peroxide.


In the following reaction sequence product, I, J and L are formed. K represents a reagent.

The structure of the product I is

(a.)

(b.)

Q.18

(c.)

(d.)

Hex-3-ynal → → →+

)K(

OH.3

ether/Mg.1CO.2

PBr.2

NaBH.1)J()I(

3

2

3

4

)L(2

4

H

quinolineBaSO/Pd →

H3C

O

Cl

Br Me Br Me

Br

Me Br Me

[Page No.23]




The structures of compound J and K, respectively

(a.)

(b.)

Q.19

(c.)

(d.)

The structures of product L is

(a.)

(b.)

Q.20

(c.)

(d.)

SECTION-B (One Or More Than One Correct Type Question)

Which of the following alcohols respond to iodoform test?

(a.)

(b.)

Q.1

(c.)

(d.)

CH − CH3

OH

CH2 = CH − CH

OH

CH3 − CH2 − CH − CH2

OH

CH3 − CH − CH3

OH

Me CHO

Me

CHO

Me CHO CHO

Me

COOH and CH3SO2Cl Me

COOH and SOCl2

Me

O

Me OH and SO2Cl2 COOH and SOCl2 Me

[Page No.24]




25 mL of H2O2 solution were added to excess of acidified solution of KI. The iodine so liberated required 20 ml

of 0.1 N Na2S2O3 for titration. Then the strength of H2O2 is

Q.2

(a.) 0.08 N (b.) 0.136% (c.) 0.448 volumes (d.) 0.004 M

Following two equilibria are simultaneously established in a container.

PCl5(g) PCl3(g) + Cl2(g)

CO(g) + Cl2(g) COCl2(g)

If some Ni(s) is introduced in the container establishing another equilibrium

4CO(g) + Ni(s) Ni(CO)4 (g)

Which among the following statements is/are definitely true about this system? (a.) COCl2 concentration decreases as the new equilibrium is established

(b.) As Ni is a solid it will not have any impact on the existing two equilibrium reactions.

(c.) PCl3 concentration decreases to re-attain the equilibrium

Q.3

(d.) PCl5 concentration increases to attain the new equilibrium

Which of the molecules is/are not planar? Q.4

(a.) F2C = C = CF2 (b.) F2B − CH = CH−BF2 (c.) CH3CH2SOCH3 (d.) H2N − NH2

Choose the correct statement (a.) Molar enthalpy is and extensive property

(b.) First law of thermodynamic suggest that the internal energy of an isolated system is constant

(c.) The work of reversible, isothermal expansion of a perfect gas is W = − p∆V

Q.5

(d.) Maximum expansion work is achieved in a reversible change.

[Page No.25]




Without performing a calculation, estimate where the standard entropies of the following reactions are positive? (a.) Ala − Ser − Thr − Lys − Gly − Arg − Ser →

sinTryp Ala − Ser − Thr − Lys + Gly − Arg

(b.) N2(g) + 3H2(g) → 2NH3(g)

(c.) ATP4− (aq) + 2H2O(l) → ADP3− (aq)+ −24HPO (aq) + H3O+(aq)

Q.6

(d.) Sugar + water → solution

The energy diagram represents the reaction occurring with and without a

catalyst……..

Which of the following statements are incorrect?

(a.) E4 is the activation energy for the reverse catalysed reaction

(b.) The forward reaction, with catalyst, is endothermic

(c.) The enthalpy change of reaction is (E2 − E3)

Q.7

(d.) The enthalpy change of reaction is reduced by using a catalyst

For a process to be spontaneous

(a.) (∆Gsystem)T, p = 0 (b.) ∆Ssystem + ∆Ssurrounding > 0

Q.8

(c.) ∆Ssystem + ∆Ssurrounding < 0 (d.) (∆Gystem)T,p < 0

E3

E4

E2

E1

Energy

Progress of reaction

[Page No.26]




The diagram illustrates the energy changes of a set of reactions. Which of the

following statements are correct?

(a.) The enthalpy change for the reaction P → R is -33 kJ mol-1

(b.) The enthalpy change for the transformation R →Q will be endothermic

(c.) The enthalpy change for the transformation R → Q will be exothermic

Q.9

(d.) The enthalpy change for the transformation S → P will be + 42 kJ mol-1

The standard reduction potentials of some half cell reactions are give below:

PbO2 + 4H+ + 2e− Pb2+ + 2H2O; E° = 1.455 V

+− + H8MnO4 + 5e− Mn2+ + 4H2O; E° = 1.51 V

Ce4+ + e− Ce3+; E° = 1.61 V

H2O2 + 2H+ + 2e− 2H2O; E° = 1.71 V

Pick out the correct statement.

(a.) Ce4+ may oxidize Mn2+ to −4MnO

(b.) −4MnO may oxidize Pb to PbO2

(c.) H2O2 may oxidize Mn2+ to −4MnO

Q.10

(d.) PbO2 may oxidize Mn2+ to −4MnO

P

R

Q

S

∆H = −134 kJ mol-1

∆H = −75 kJ mol-1

∆H

= +

92

kJ m

ol-1

[Page No.27]




SECTION-C (SUBJECTIVE TYPE QUESTION) Q.1 Among (i) addition of CaCO3 (s) (ii) addition of CaO(s), (iii) addition of CO2 (iv) addition of N2 at constant

volume (v) addition of N2 at constant pressure (vi) increase in temperature (vii) increase in pressure (viii)

addition of HCl and (ix) addition of NaOH, in how many cases equilibrium

CaCO3(s) CaO(s) + CO2(l)

Will shift in forward direction?

Q.2 In the nelson cell the asbestos lining was not proper and during electrolysis of brine solution the lining was

teared and the products were reacted. As a result, two products containing chlorine atoms are formed. Sum of

the oxidation states of both the chlorines in the products formed is……………

Q.3 For the balanced redox reaction, OH2BrO2Mn2BrH8MnO2 23

224 ++→++ −++−

If molecular weight of −4MnO , Br2 be Mx & My respectively and equivalent weight be

2

y

1

x

n

Mand

n

M

respectively, the value of n2 − n1 is ………….

Q.4 What is the number of moles of hydrocarbon formed when one mole of aluminum carbide is dissolved in water?

Q.5 Find the total number of isomeric products formed when n-hexane undergoes monochlorination.

[Page No.28]




SECTION-D (MATCH THE COLUMN TYPE QUESTION) (Items of Column- I can match one or more than one Items of column- II with individual marking scheme)

The van der waal’s constants a and b of a real gas are 3.6 L2 atm mol-2 and 0.05 L mol-1, respectively. If 200 g

gas (molecular mass 40) is placed in 10 L vessel at 300 K.

Match the following

Column-I Column- II

Q.1

(i.) Pressure correction (atm) (a.) 0.25

(ii.) Free space for the molecules to move about (L) (b.) 0.0125

(iii.) Actual volume of the gas molecules per mole

(L)

(c.) 0.9

(iv.) Effective volume occupied by total gas

molecules (L)

(d.) 9.75

Match the compounds given in column I with corresponding products / tests in column II

Column-I Column- II

Q.2

(i.) 4-(hydroxymethyl) phenol (a.) Bakelite formation

(ii.) Acetyl acetone (b.) Ceric ammonium nitrate

(iii.) 1-phenylethanol (c.) Haloform test

(iv.) Phenol (d.) FeCl3

[Page No.29]




Part : III (Mathematics)

SECTIONSECTIONSECTIONSECTION----A (One Option Correct Type A (One Option Correct Type A (One Option Correct Type A (One Option Correct Type Question)Question)Question)Question)

If ,100

74

wz2yx

zx2yx

=

+−

++ then the values of x, y, z, w are

Q.1

(a.) 2, 2, 3, 4 (b.) 2, 3, 1, 2 (c.) 3, 3, 0, 1 (d.) None of these

Among (i)

−

∞→

−

∞→ x

xsinseclim)ii(and

xsin

xseclim 1

x

1

x

Q.2

(a.) (i) exists, (ii) does not exist (b.) (i) does not exist, (ii) exist

(c.) both (i) and (ii) exist (d.) neither (i) nor (ii) exists

Let

>+

≤≤−−−=

1xif,x

1log1

1x1if,x11)x(f

2

is

Q.3

(a.) Continuous and differentiable at x = 1

(b.) Continuous but not differentiable at x = 1

(c.) Neither continuous nor differentiable at x = 1

(d.) None of these

The value of

nn

n a

b1alim

+−

∞→(a > b, b > 0) is equal to

Q.4

(a.) a b (b.) b a (c.) b (d.) a

[Page No.30]




∫+++ 322 )x1(x1

dxxis equal to

Q.5

(a.) C)x11ln(

2

1 2 +++ (b.)

Cx112 2 +++

(c.) C)x11(2 2 +++ (d.) None of these

Let f(x) be a polynomial satisfying f(0) = 2, f'(0) = 3 and f"(x) = f(x). Then f(4) is equal to Q.6

(a.)

4

8

e2

)1e(5 +

(b.)

4

8

e2

)1e(5 −

(c.)

)1e(5

e8

4

−

(d.)

)1e(5

e28

4

+

If f(x) = eg(x) and g(x) = ∫ +

x

2 4t1

dtt, then f'(2) is equal to

Q.7

(a.) 2/17 (b.) 0 (c.) 1 (d.) Can’t be determined

Area enclosed by the graph of the function y = ln2 x – 1 lying in the 4th quadrant is Q.8

(a.)

e

2

(b.)

e

4

(c.)

+e

1e

(d.)

−e

1e4

If ,4

3π<α<

πthen

α+α

2sin

1cot2 is equal to

Q.9

(a.) 1 + cot α (b.) − 1 − cot α (c.) 1 − cot α (d.) − 1 + cot α

[Page No.31]




If at each point of the curve y = x3 − ax2 + x + 1, the tangent is inclined at an acute angle with the positive

direction of the x-axis, then

Q.10

(a.) a > 0 (b.) a ≤ 3 (c.) 3a3 ≤≤− (d.) None of these

A rectangle ABCD has its side AB parallel to line y = x and vertices A, B and D lie on y = 1,

x = 2 and x = −2, respectively. Locus of vertex ‘C’ is

Q.11

(a.) x = 5 (b.) x − y = 5 (c.) y = 5 (d.) x + y = 5

If the radius of the circumcircle of the triangle TPQ, where PQ is chord of contact corresponding to point

T with respect to circle x2 + y2 − 2x + 4y − 11 = 0, is units, then minimum distances of T from the director

circle of the given circle is

Q.12

(a.) 6 (b.) 12 (c.) 26 (d.) 2412 −

If the distance between two parallel tangents drawn to the hyperbola 149

y

9

x22

=− is 2, then their slope is

equal to

Q.13

(a.)

2

5±

(b.)

5

4±

(c.)

2

7±

(d.) None of these

A series is such that its every even term is ‘a’ times the term before it and every odd term is c times the term

before it. The sum of 2n term of the series is (the first term is unity)

Q.14

(a.) ( )( )ac1

a1c1 nn

−

−−

(b.) ( ) ( )ac1

ac1a1 nn

−

−+

(c.) ( )( )ac1

a1c1 nn

−

++

(d.) ( ) ( )ac1

ac1a1 nn

+

++

[Page No.32]




The A.M. between two positive numbers a and b is twice the G.M. between them. The ratio of the numbers is Q.15

(a.) ( ) ( )32:32 −+ (b.) ( ) ( )32:32 −+

(c.) ( ) ( )13:13 −+ (d.) None of these

If |z2 + iz1| + |z1| + |z2| and |z1| = 3 and |z4| = 4, then area of ∆ABC, if affixes of A, B and C are z1, z2

and [(z2 − iz1)/(1 − i)] respectively , is

Q.16

(a.)

2

5

(b.) 0 (c.)

2

25

(d.)

4

25

The coefficient of a8b4c9d9 in (abc + abd + acd + bcd)10 is Q.17

(a.) 10! (b.)

!9!9!4!8

!10

(c.) 2520 (d.) None of these


Tangents are drawn to the parabola y2 = 4x from the point P(6, 5) to touch the parabola at Q and R. C1 is a circle

which touches the parabola at Q and C2 is a circle which touches the parabola at R. Both the circles C1 and C2

pass through the focus of the parabola.

Area of the ∆PQR equals Q.18

(a.)

2

1

(b.) 1 (c.) 2 (d.)

4

1

Radius of the circle C2 is Q.19 (a.) 55 (b.) 105 (c.) 210 (d.) 210

[Page No.33]




The common chord of the circles C1 and C2 passes through the Q.20

(a.) incentre (b.) circumcentre

(c.) centroid (d.) orthocentre of the ∆PQR

SECTION-B (One Or More Than One Correct Type Questions)

If a, b and c are all different from zero such that ,0c

1

b

1

a

1=++ then the matrix

+

+

+

=

c111

1b11

11a1

A is

Q.1

(a.) Symmetric

(b.) Non-singular

(c.) Can be written as sum of a symmetric and a skew symmetric matrix

(d.) None of these

Which of the following functions f has/have a removable discontinuity at the indicated point?

(a.) 2xat

2x

8x2x)x(f

2

−=+

−−=

(b.) 7xat

|7x|

7x)x(f =

−

−=

(c.) 4xat

4x

64x)x(f

3

−=+

+=

Q.2

(d.) 0xat

x9

x3)x(f =

−

−=

[Page No.34]




Let S be the set of real values of parameter λ for which the equation f(x) = 2x3 − 3(2 + λ)x2 + 12λx has

exactly one local maximum and exactly one local minimum. Then, S is a subset of

Q.3

(a.) (−4, ∞) (b.) (−3, 3) (c.) (3, ∞) (d.) (−∞, 0)

Parabola y2 = 4x and the circle having it’s centre at (6, 5) intersect at right angle. Possible point of

intersection of these curves can be

Q.4

(a.) (9, 6) (b.) ( )8,2 (c.) (4, 4) (d.) ( )32,3

In the nth row of the triangle

Q.5

(a.) Last term =

2

1 n (n + 1)

(b.) First term =

2

1 (n

2 − n + 2)

(c.) Sum =

2

1 n (n

2 + 1)

(d.) Sum =

2

1 n

2 (n + 1)

1 2 3 4 5 6 7 8 9 10 ………………………….

………………………..

[Page No.35]




In the following figure AB, DE and GF are parallel to each other and AD,

BG and EF are parallel to each other. If CD : CE = CG : CB = 2 : 1, then

the value of area (∆AEG) : area (∆ABD) is equal to

Q.6

(a.) 7/2 (b.) 3 (c.) 4 (d.) 9/2

Consider a set of points in the space which is at a distance of 2 units from the line 2

2z

1

1y

1

x +=

−

−=

between the planes x − y − z + 3 = 0 and x − y − z − 2 = 0.

Q.7

(a.) The volume of the bounded figure by points R and the planes is ( )π33/10 cube units.

(b.) The area of the curved surface formed by the set of points R is ( )3/4 π sq. units.

(c.) The volume of the bounded figure by the set of points R and the planes is ( )3/20 (π cubic

units.)

(d.) The area of the curved surface formed by the set of points R is ( )π3/10 sq. units.

Consider the planes 3x − 6y + 2z + 5 = 0 and 4x − 12y + 3z = 3. The plane 67x − 162y + 47z + 44 = 0 bisects

that angle between the given planes which

Q.8

(a.) Contains the origin (b.) Is acute (c.) Is obtuse (d.) None of these

Q.9 The probability that a married man watches a certain TV show is 0.4 and the probability that a married

women watches the show in 0.5. The probability that a man watches the show, given that his wife does,

is 0.7. Then

D

A B

C E

F G

[Page No.36]




(a.) The probability that married couple watches the show is 0.35

(b.) The probability that a wife watches the show given that her husband does is 7/8

(c.) The probability that atleast one person of a married couple will watch the show is 0.55

(d.) None of these

If α, β are the roots of the quadratic equation ax2 + bx + c = 0 then which of the following expression

will be the symmetric function of roots

Q.10

(a.)

β

αlog

(b.) 5252 αβ+βα

(c.) tan (α − β) (d.) ( )2

2

log1

log β+

αl

SECTIONSECTIONSECTIONSECTION----C (Subjective Type Questions)C (Subjective Type Questions)C (Subjective Type Questions)C (Subjective Type Questions)

Q.1

If A + B + C = π, and

1CcotCsin

1BcotBsin

1AcotAsin

2

2

2

=∆ Find ∆ + 5.

Q.2 If f(x) is a twice differentiable function such that f(a) = 0, f(b) = 2, f(c) = −1, f(d) = 2, f(e) = 0, where a < b <

c < d < e, then find the minimum number of zero of g(x) = (f’(x))2 + f”(x) f(x) in the interval [a, e]

Q.3

If the value of integral ( )∫π −

+2/

0

4xcosxsin dx is

k

1 then the numerical quantity k should be

[Page No.37]




Q.4 If (1 − P) (1 + 3x + 9x

2 + 27x

3 + 81x

4 + 243x

5) = 1 − P

6, P ≠ 1, then find the value of

x

P

Q.5 Find the integral part of the greatest root of equation x3 − 10x

2 − 11x − 100 = 0.

SECTIONSECTIONSECTIONSECTION----D D D D (Match The Column Type Questions)(Match The Column Type Questions)(Match The Column Type Questions)(Match The Column Type Questions)

(Items of Column(Items of Column(Items of Column(Items of Column---- I can match one or mo I can match one or mo I can match one or mo I can match one or more than one Items of columnre than one Items of columnre than one Items of columnre than one Items of column---- II with individual marking scheme) II with individual marking scheme) II with individual marking scheme) II with individual marking scheme)

Column-I Column- II Q.1

(i.) If

dx

dyx = x2 + y − 2, y(1) = 1, then y(2) equals

(a.) 1

(ii.) Let

( ) ( )∑= ++++

9999

1n44 1nn1nn

1S , then

S equals

(b.) 2

(iii.) Let G(x) = ∫ ∫

+

x

0

x )x(fdt)t(fe dx where f(x)

is continuous on R. If f(0) = 1, G(0) = 0 then

G’(0) equals

(c.) 3

(d.) 4

[Page No.38]




Column-I Column- II Q.2

(i.) If |z1| = 2 and (1 − i) z2 + (1 + i) 28z2 = ,

then the minimum value of |z1 − z2| equals

(a.) 5

(ii.) The value of the definite integral

( )∫

π

π ++

2

4

xcosxsinxcosxsin2xcosxsin

dx

equals

(b.) 4

(iii.) If f(x) =

( )3

2

1x23log

9−

−then the value of

‘a’ which satisfies f-1 (2a − 4) = 2

1, is

(c.) 3

(iv.) The locus of the point (h, 2k − 3) where (h, k)

lies on the curve x2 − y2 = 16 is a conic C. The

square of eccentricity of the conic C equals

(d.) 2

(e.) 1

+2 (PCM) Full Scale Test Paper 17 Feb 2012

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