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IIT-JEE 2013NURTURE COURSE : PHASE - [TP, TJ & TK](DATE : 16-02-2012)

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Space for Rough Work

E2/32

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NURTURE COURSE : PHASE - [TP, TJ & TK](DATE : 16-02-2012)

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PART1 : MATHEMATICS

SECTION I (Total Marks : 48)

Single Correct Choice Type (Total Marks : 9)

Single Correct Choice Type contains 3 multiple choice questions. Each question has 4 choices (A),

(B), (C) and (D), out of which ONLY ONE is correct.

1. If a, b, gare roots of equation x3 2x2 1 = 0 and Tn= an+ bn+ gn, then value of11 8

10

T T

T

-is -

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

2. Value of 40C0

40C5

40C1

40C6

+ 40C2

40C7

40C3

40C8

+ ...... 40C35

40C40

is

(A) 80C35 (B)40C35 (C) 0 (D)

40C17

3. If a, b, gare roots of equation 111x3 11x 1 = 0, then (ab)2+ (bg)2+ (ga)2equals

(A) 2332 (B) 1331 (C) 1210 (D) 2442


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Multiple Correct Answer Type (Total Marks : 12)

Multiple Correct Answer Type contains 3 multiple choice questions. Each question has 4 choices (A),

(B), (C) and (D), out of which ONE OR MORE is/are correct.

4. If equations x2+ (k + 1)x + k = 0 and x2 (k + 2)x + 2k = 0 have one root common, then value(s) of

'k' is/are -

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

5. Value of1 1 1 11 1 1 23tan tan sin cos

3 2 5 5

- - - - + + +

is greater than

(A) 2

p(B)

2

3

p(C)

3

4

p(D)

5

6

p

6. Which of the following is/are correct ?

(A) 1 11

cot (x) tan x R {0}x

- - = " -

(B) If : R R such that (x) = sgn(ex) then (x) is an into function.

(C) If : R+R such that (x) = sinx + x then (x) is an odd function.

(D) If : R R such that (x) =x

[x ]

e

ethen (x) is a periodic function .

(where [.] represents greatest integer function)

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Linked Comprehension Type (Total Marks : 27)

Linked Comprehension Type contains 3 paragraphs. Based upon each paragraph, 3 multiple choice

questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY

ONE is correct.

Paragraph for Question 7 to 9

Consider x2 (3a + 1)x + 2a2 + a = 0, a & bare roots.

On the basis of above information, answer the following questions :

7. If a, blies in (0, 9), then

(A)1

a ,92

-

(B) a (0, 4) (C) ( )a 0,9 (D)1

a , 42

-

8. If a, b& 11 are in A.P., then sum of all possible value(s) of 'a' is -

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

9. If one root is greater than 11 and other root is less than 9, then sum of possible integral value(s) of 'a'

is-

(A) 15 (B) 21 (C) 30 (D) 35


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: [1, 7] R,

x 1 1 x 2

(x) 4 x 2 x 4

x 4 4 x 7

+ -

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Let 50C15+ 550C14

+ 1050C13+ 1050C12 + 5

50C11 +50C10

=55Cp

and 5C5+ 6C5

+ 7C5+ ............ + 54C5

= 55Cq, (p, q < 30).

On the basis of above information, answer the following questions :

13. ( )1 1 1sin sin p q cos cos(p) tan tan(q)4

- - -p + + +

equals

(A)13

94

p- (B)

2521

4

p- (C)

119

4

p- (D)

2721

4

p-

14. If sin1(x x2+ x3 x4+ ....... ) + cos1(x2+ x3+ x4+ ....... ) = (p 2q 1)4

p- - , (|x| < 1) then number

of possible real value(s) of x is

(A) 1 (B) 2 (C) 3 (D) more than 3

15. If tan1(2x) + tan1(3x) =q

2(p 3)

p- , then sum of all possible real value(s) of x is

(A) 1 (B) 5

6(C) 0 (D)

1

6


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SECTIONII : (Total Marks : 16)

(Matrix-Match Type)

This Section contain 2 questions. Each question has four statements (A, B, C and D) given in

Column Iand five statements (P, Q, R, S and T) in

Column II. Any given statement in Column I can

have correct matching with ONEor MORE statement(s) given in Column II. For example, if for a given

question, statement B matches with the statements given in Q and R, then for the particular question,

against statement B, darken the bubbles corresponding to Q and R in the ORS.

1. Let (n) = ( )n

nk

k 1

k C=

, n N. Then

Column-I Column-II

(A)1 (10)sin sin

1000-

(P) 5 2p

(B)1 (9)cos cos 3

1000- +

(Q) 5 p

(C)1 (8)tan tan 4

100- -

(R) 2p 5

(D)1 (7)cot cot 1

100- +

(S) 6 2p

(T) 2p 6

(where [.] denotes greatest integer function)


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2. Column-I Column-II

(A) Fundamental period of4 42x 2x 4x(x) sin cos

3 3

= + + p (P) 1

isa

bp where 'a' is a prime, then

a b

3

+

is greater than (Q) 2

(where {.} denotes fractional part function) (R) 3

(B) Number of integers in range of6 4 2

6(x)

x x x 2

=

+ + +

, is (S) 4

(C) Number of even factors of 960 not divisible by 4, is (T) more than 4

(D) Number of different values of x satisfying

sin1(x2 4x + 4) + cos1(x) =2

p, is


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SECTIONIII : (Total Marks : 16)

Integer Answer Type (000 to 999)

This Section contains 4 questions. The answer to each of the question is a three digit integer, ranging

from 000 to 999. The bubble corresponding to the correct answer is to be darkened in the ORS.

1. Number of positive integral values of 'k' such that equation x2 (k 3)|x| + 2k 10 = 0 has 2 distinct

real solutions, is

2. If p, q & r are different prime numbers and a, b are natural numbers such that their LCM is p 3q3r2

and HCF is pr, then number of possible ordered pairs (a,b) is

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3. Let A = {1, 2, 3, 4, 5}. If : A A is a one-one function such that (x) x "x domain, then

the number of possible such different functions that can be defined, is

4. Let A = {1, 2, 3, ........, 15}. The number of different subsets of A containing 4 elements such that

no two consecutive integers lie in the subset, is

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PART2 : PHYSICS




(B), (C) and (D), out of which ONLY ONEis correct.

1. A container has an ideal gas at pressure P. Assuming the mass of a molecule is m and all the molecules

are moving with same speed v in random directions. The expression for number of collisions per

second which the molecules make with unit area of container wall is

(A)P

mv(B)

3

2

P

mv(C)

3

2

P

mv(D)

3

2

P

mv

2. A rod of length lis rotating with angular velocity wand translating such that ucm= wl/2. The distance

covered by the point B when the rod completes one full rotation is

w

ucm

A

B

(A) pl (B) 8 l (C) 4 l (D) 2 pl


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3. A particle of mass m is projected with speed u inside a fixed uniform horizontal ring as shown in the

figure. The collisions of the particle with the surface of the ring are perfectly elastic and friction is

absent. Choose the INCORRECT statement.

30A

m

O

(A) The particle will be able to come back to A only after infinite number of collisions with the surface

(B) The particle will be able to come back to A after a time of3 3R

uafter its projection from A.

(C) The particle will be coming back to A after a time of6 3R


(D) The particle will be coming back to A after a time of9 3R


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4. In a standard projectile motion on a horizontal plane, power of gravitational force

(A) varies linearly with time

(B) is constant throughout

(C) is negative for the first half, positive for the rest half

(D) is zero for the whole path

5. A uniform rod kept vertically on the rough ground falls from rest. Its foot does not slip on the ground.

Then

(A) no part of the rod can have acceleration greater than g in any position.

(B) at any position of the rod, different points on it have different accelerations.

(C) each point on the rod has different accelerations at different positions of the rod.

(D) the maximum tangential acceleration of any point on the rod, at any position is 1.5 g.


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6. One end of an ideal spring is fixed at point O and other end is attached to a small disc of mass m which

is given an initial velocity v0perpendicular to its natural length on a smooth horizontal surface. If the

maximum elongation in spring is

0

4

l

then (l0= natural length and k = stiffness of spring)

k,l0

v0

o

(A) velocity at maximum elongation,04

5

vv=

(B) velocity at maximum elongation, 03

4

vv=

(C)0

0

5

12v =

l k

m

(D)0

012

kv

m=l


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ONEis correct.


Two friends A and B (each weighing 40 kg) are sitting in a frictionless well having vertical circular

smooth wall. They subtend angle 90 at the centre of well. A rolls a ball of mass 40 kg in clockwise

direction on the platform base towards B along the wall of the well which B catches. Then similarly B

rolls the ball towards A anticlockwise and A catches it. The ball has a fixed speed of 5 m/s.

(Neglect catching and throwing time).

A

B

5m/s

7. Find the total impulse by the wall of well on whole system by the time ball travels from A to B

(A) 200 kg-m/s (B) 400 kg-m/s (C) zero (D) None of these

8. Find the angular displacement of A till he meets B

(A) 150 (B) 60 (C) 90 (D) 180

9. When A meets B they catch each other and now they move together i.e. perfectly inelastic collision. What

will be the velocity when they (A+B) throw the ball after catching it

(A) 2.5 m/s (B)5

3m/s (C)

50

11m/s (D) None of these


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An ideal gas with the ratio of its specific heats = g, undergoes a process in which its internal energy U

is given by U = aVawhere a and aare constants.

10. If the internal energy of the gas is to increases by DU, find the amount of heat DQ, needed to be given:-

(A) DQ = DU (B)U

Q g D

D =a

(C) DQ = = DU 1 g

+ a (D) DQ = DU

11

g - + a

11. The work DW performed by the gas when its internal energy increases by DU :-

(A) DW = DU (B)U

W g D

D =a

(C)( 1) U

W g - D

D =a

(D) DW = 0

12. The molar specific heat C of the gas during the process :-

(A)R

C1

=g - (B)

RC=

a(C)

vCC g=

a(D)

R RC

1= +

g - a


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A large mass M is released from rest at the top of an inclined plane of angle qand friction coefficient

m. At the same time, a pendulum consisting of a small mass m and (massless) string of length L is released

at height L (horizontally). The large mass slides down the incline and smoothly onto the table, continues

across the frictionless table, and collides with the pendulums mass just as the pendulum has reached

the bottom of its swing and is approaching the large mass. The two masses stick together after the

collision.

M

m

q

h

peg m

L

L

smooth\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

13. Assuming the mass M is released at a height h, what is the its velocity when it reaches the flat part of

the table?

(A) ( )2 1 tangh m q+ (B) ( )1 cotgh m q+ (C) ( )2 1 cotgh m q- (D) ( )1 tangh m q-

14. For what initial height h of the mass M will the combined mass come to rest immediately after the

collision? [Take m=0]

(A)

2

2

mL

M(B)

2 2

2

m ML

M

+ (C)

2

2

ML

m

(D)

2

2 2

mL

m M

+

15. What must the initial height h have been in order for the pendulum of the combined mass to complete

the vertical circle in the counterclockwise direction? [Take m=0 and M = 2m ]

(A)( )

2

2 3 5

8

Lh

+= (B)

( )2

3 2 5

4

Lh

-= (C)

( )2

3 2 5

9

Lh

+= (D) none


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(Matrix-Match Type)


Column Iand five statements (P, Q, R, S and T) in Column II. Any given statement in Column I can




1. In column-I condition on velocity, force & acceleration of particle is given. Resultant motion is described

in column-II. ur

= initial velocity (non-zero), Fr

= resultant force and vr

= instantaneous velocity.

Column-I Column-II

(A) . 0v F=

rr

all the time, F

r

= constant and (P) Path will be circular

vr

& Fr

are coplanar. (Q) Speed may increase

(B) . 0u F=rr

and Fr

= constant (R) Speed may decrease

(C) 0u F =rr

and Fr

= constant (S) Path will be straight line

(D) 2 3u i j= -r

and acceleration is ( ) 6 9a k i j= -r (T) Path will be parabolic

(where k is a positive constant)

2. A body of mass m1 collides one dimensionally with another stationary body of mass m

2. The coefficient of

restitution is e. Find the correct combination of options of column II to satisfy the condition of column I.

Column I Column II

(A) After the collision, velocity of the second body is maximum when (P) e =1

(B) After the collision, momentum of the second body is maximum when (Q) m1>>m

2

(C) After the collision, kinetic energy of the second body is maximum when (R) e = 0

(D) After the collision, kinetic energy of system is minimum when (S) m1

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1. A boat is traveling east at 12 m/s. A flag flaps at 53N of W at the bow of the boat. Another flag on shore

flaps due north. Find the speed (in m/s) of the wind as measured on land.

2. Suppose the average density of raindrops is 1000kg/m3and their average falling velocity 8 ms1.

Calculate the energy (in kJ) transferred by rain to each square metre of the surface at a place which

receives 100 cm of rain in a year.


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3. Figure shows an ideal gas. Its pressure, volume & temperature are P0, V

0& T

0respectively. Thin U-

tube contains mercury. It was observed that there was a difference of 40 cm in the level of mercury

column in two limbs. Now the gas is heated to temperature 1.5 T0and simultaneously mercury was

added in limb B to maintain the level of mercury in limb A at its original position. Find the new

difference in the level of mercury in limb A & B (in cm). [Take : Patm

= 76 cm of Hg]

Gas

B

A40cm

4. Figure shows a container having adiabatic walls and a freely movable separator which is highly

conducting. The separator divides the cylinder in two equal parts A and B each containing 2 moles of

ideal monoatomic gas at temperature 300 K. Now a heater is switched on in part A, find the heat

supplied (in kJ) by heater till pressure in part A is doubled. [ Take R =25

3SI units]

A

T0

T0

V0

V0

B

Heater


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PART3 : CHEMISTRY




(B), (C) and (D), out of which ONLY ONEis correct.

1. In a reversible reactionl

2

k

kA B , the initial concentration of A & B are a& bmole/L respectively.

If 1

2

k

k>

b

athen the equilibrium concentration of A is

(k1= forward rate constant ; k

2=backward rate constant)

(A) a +1 2

1 2

k a k b

k k

-

+ (B) a 1 2

1 2

k a k b

k k

-

+ (C) a + 2 1

1 2

k b k a

k k

-

+ (D) None

2. Which of the following has higher number of POP linkages

(A) P4O

6(B) P

4O

10

(C) both have equal number POP linkage (D) None of these

3. The number of degree of unsaturation is :

(A) 10 (B) 15 (C) 18 (D) 14


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4. The reaction,

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

is present at equilibrium. Choose the correct statement(s) -

(A) If q is (+)ve then reaction moves forward upon increasing temperature

(B) If q is ()ve then reaction moves forward upon increasing temperature

(C) If q is (+)ve then reaction moves forward upon decreasing temperature

(D) If q is ()ve then reaction moves backward upon decreasing temperature

5. In which of the following compound/ions the dp-ppis not present

(A) N3 (B) NO

2+ (C) SO

2(D) HPO

32

6. In which case, Istcompound having more enol content than 2ndcompound-

(A)

,

(B)

(C)

(D)

,

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ONEis correct.


A sample of excited H-like species when bombarded by photons of wavelength 54nm gets excited to

another excited state. In returning back to ground state it emits total six different types of photons. Out

of six different photons three have wavelength less than 54 nm

H

1Use : 90 nm

R

=

7. Final excited state of H-like species -

(A) 3 (B) 4 (C) 2 (D) None

8. Initial excited state of H-like species-

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

9. Determine atomic no. of H-like species -

(A) 2 (B) 3 (C) 5 (D) 6


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The repulsion theory is given as lone pairlone pair > lone pairbond pair > bond pairbond pair. Where

the bond pair indicates the single bond pair.

10. The reason behind the above order is

(A) lone pair and bond pair both are consisting of two electron

(B) lone pair is attracted by only one atom while bond pair is attracted by two atom.

(C) The direction of lone pair moment is always outward direction.

(D) None of these

11. In which of the following case the FBrF angle is less than 90

(A) BrF3

(B) BrF4 (C) BrF

5(D) (A) and (C) both

12. In which of the following cases, the shape of the species is exactly perfect tetrahedral

(A) SiHF3

(B) SiH2F

2(C) SiH

3F (D) SiH

4


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Paragraph based on structure of five compounds are given above.

13. The compounds show geometrical isomerism :

(A) A, C, D only (B) B, C, D only (C) A, B, C, D, E (D) C, D only

14. The compounds show positional isomerism :

(A) A, B, C, D only (B) B, C, D only (C) A, B, C, D, E (D) A, C only

15. The compounds having degree of unsaturation > 1 :

(A) A, B, C, D (B) B, C only (C) B, D only (D) A, B only


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(Matrix-Match Type)


Column Iand five statements (P, Q, R, S and T) in Column II. Any given statement in Column I can




1. Match the column :

Column-I Column-II

(A) Boyle's temperature (P) Depends on 'a' and 'b'

(B) Compressibility factor (Q) Depends on identity of real gas

(C) Real gas with very large molar volume (R) The temperature at whichdZ

= 0dP

at low pressure region.

(D) Critical temperature (S) PV = nRT

(T)8a

27R.b.


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2. Match the column :

Column-I (Compound) Column-II (Isomerism)

(A)

and

(P) Functional isomers

(B)

and

(Q) Geometrical isomers

(C)

and

(R) Position isomers

(D)

and

(S) Chain isomers

(T) Degree of unsaturation in both

compound is =1


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1. In a H-like atom for an electron revolving in nthorbit, the variation of log10

KEversus log10

Z is

plotted as following -

log Z10

log

KE

10

O

A

where Z is atomic number & KE is kinetic energy of electron (in eV). If OA = log10

3.4 then find

the value of principle quantum number of the electron.

2. Calculate the value of screening constant sfor last electron of Y (Atomic No.= 39)

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3. Number of geometrical isomers of the given compound is :

C6H

5CH=CHCH=CHCH=CHCOOH

4. Find the number of s-bond in the given molecule.

C6H

6

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Name of the Candidate

I have read all the instructions and shall

abide by them.

Signature of the Candidate

Form Number

I have verified all the information filled

in by the Candidate.

Signature of the Invigilator


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