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JEE 2013LEADER & ENTHUSIAST COURSE(DATE : 13-04-2013)

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USEFULDATA

AtomicNo. H=1,B=5,C=6,N=7,O=8,F=9,Al=13,P=15,S=16,Cl=17,

Br=35,Xe=54,Ce=58,

Atomicmasses: H=1,Li=7,B=11,C=12,N=14,O=16,F=19,Na=23,Mg=24,

Al=27,P=31,S=32,Cl=35.5,Ca=40,Fe=56,Br=80,I=127,

Xe=131,Ba=137,Ce=140,

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Path to success KOTA (RAJASTHAN)


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PART-1 : PHYSICSSECTIONI

(i) Single Correct Answer Type

This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and

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

1. An optical fibre of refractive index n is surrounded by air.A light ray enters the end of the fibre as shown

in figure. The largest value of permitted, if the ray in the fibre is incident on the wall at critical angle for

the fibre-air interface is given by

Air

(A) 1/ 2

2sin n 12

(B) 1/ 2

2cos n 12

(C)

1/ 2

2

1sin 1

2 n

(D)

1/ 2

2

1cos 1

2 n

2. Two identical isosceles thin prisms of prism angle A and refractive index are placed with their basestouching each other. This system acts as a converging lens. What is the focal length of this system for

parallel rays at a distance h from the base of the prism ?

A

h

h

(A) 2h

1 A (B) h

1 A (C) h

2 1 A (D) None of these

BEWARE OF NEGATIVE MARKING

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3. The flow of charge through switch S when it is closed is :-

+ 2F

+ 6F

q

+ 3F

q

q

(A) Zero (B) q/4 (C) 2q/3 (D) q/3

4. Consider the arrangement of three plates X, Y and Z each of the area A and separation d. The energy stored

when the plates are fully charged is :-

X

Y

Z

d

d

V

(A)

2

0AV

2d

(B)

2

0AV

d

(C)

2

02 AV

d

(D)

2

03 AV

2d

5. A ray of light makes normal incidence on the diagonal face of a right-angled prism as shown in figure such

that the ray strikes the surface AB of the prism after entering the prism. If = 37 then the angle of de-

viation is (sin 37 = 3/5) :-

90

AIR

AIR

90

= 5/3

A

B C

(A) 53 (B) 127 (C) 106 (D) 90


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(ii) Multiple Correct Answer(s) Type


(D) out of which ONE or MORE are correct.

7. In the figure shown the radius of curvature of the left & right surface of the concave lens are

10 cm & 15 cm respectively. The radius of curvature of the mirror is 15 cm

\\\\

\\\\\\\\\\\\\\\\\\\\\

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

Glass(n=3/2)

water(n=4/3)

air

(A) modulus of equivalent focal length of the combination is 18 cm

(B) modulus of equivalent focal length of the combination is 36 cm

(C) the system behaves like a concave mirror

(D) the system behaves like a convex mirror

8. An equilateral prism ABC is placed in air with its base side BC lying horizontally along X-axis as

shown in the figure. A ray given by 3 z + x = 10 is incident at a point P on face AB of prism :-

60

P

A

CB

(0,0,0,)x

y

z

(A) For =2

3the ray grazes the face AC.

(B) For =3

2finally refracted ray is parallel to z-axis.

(C) For =2

3the ray emerges perpendicular to the face AC.

(D) For =3

2finally refracted ray is parallel to x-axis.


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9. An electrical circuit is shown in the given figure. The resistance of each voltmeter is infinite and each

ammeter is 100. The charge on the capacitor of 100 F in steady state is 4 mC. Choose correct

statements (s) regarding above circuit :-

V2

200

[idealcell]

A1

A2

V1 C 900

100

(A) Reading of voltmeter V2

is 16 V

(B) Reading of Ammeter A1

is 0A and A2

is 1/25 A.

(C) Reading of voltmeter V1 is 40V(D) EMF of the ideal cell is 66 V.

10. Inside a parallel plate capacitor of capacitance C (without dielectrics) dielectrics are filled which have

dielectric constant k1and k

2such that k

1> k

2. The capacitor is now connected to a battery of voltage V

then :-

K1 K2

A/2 A/2

(A) New capacitance of the capacitor will be1 2k k C

2

(B) Field in dielectric 1 will be more than the field in dielectric 2

(C) Surface charge density on the capacitor plates will be uniform

(D) Field in both the dielectric regions will be the same.


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(iii) Paragraph Type

This section contains 3 multiple choice questions relating to one paragraph with three questions

on paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is

correct.

Paragraph for Questions 11 to 13

A ray of light travelling in air is incident at an angle of incidence i 90 on a long rectangular slab of a

transparent medium of thickness y0. The medium has a variable refractive index of (x) = 2x/a1 e

x 0 , where 'a' is a positive constant.

y

y0

i = 90

Air

Medium

( = 1)

Air ( = 1)x

11. In the above situation if y0= a/2, the coordinates of the point where the ray intersects the upper surface

of the slab-air boundary are :-

(A)

2 aae ,2

(B)

aa n2,

2(C)

a a

n2,2 2

(D)

a2a,

2

12. In the previous question, the angle made by light ray with +ve x-axis at the upper surface of slab air

boundary, inside the medium is :-

(A) /4 (B) /3 (C) tan1(2) (D) tan1

12

13. If y0

= a, the light ray will :-

(A) Emerge out from the upper surface of slab-air boundary

(B) Emerge out from the lower surface of slab-air boundary

(C) Never emerge out of the slab

(D) Move in a close loop inside the slab

SECTION II & SECTION III

Matrix Match Type Integer Answer Type

No question will be asked in section II and III


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SECTIONIV

Integer Answer Type

This section contains 7 questions. The answer to each question is a single digit Integer, ranging from

0 to 9.

1. Two identical conducting spheres of radius r separated far apart are joined through resistor R & a switch

S. Initially switch is open and one of the spheres is provided with a charge +Q0. If switch S is closed at

t = 0 then. If charge on sphere B at time65rR

t26k

is given bynQ a 1 e

(where a & n are constant),

find the value of n.

+++

+

+

+

+

+

+

+

++ ++

++

+

+

+

+

+

++

rS R

A B

2. An equi-convex lens of focal length 10 cm (at t = 0) and refractive index (g

= 1.5) is placed in a liquid

whose refractive index varies with time as (t) = 1.0 +1

10t. If the lens was placed in the liquid at

t = 0 after what time (in sec) lens will act as concave lens of focal length 20 cm.

3. For the circuit shown in the figure. Find the emf (in V) of the unknown battery E. The ammeter repre-

sented by the symbol A can be considered perfect (i.e. no resistance) and it reads the current in the wire

to be7

A11

in the direction shown.

4V

6

12V

E

A

711

A


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4. In the figure shown, O is a point object placed above the lens L of focal length 10 cm. The distance

between the object O and its image formed in the plane mirror is n 20 cm find n.

O

15cm

1mWater n=4/3

Plane mirror

L

15cm

5. Four wire of equal length 2m are arranged as shown in the figure. Wires 2, 3 and 4 are of equal cross

sectional area and wire 1 is of half the cross section of these wires. The distance (in m) pointer at point

5 must be moved to get null point is given by . Fill 12 in OMR sheet.

G

5

31

6

2 4

7

8

x



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6. Find out the net emf of the three batteries between A & B when the point P is the null point, measured

by the potentiometer arrangement shown in the figure.

r1

a b

A

4V 6.5

2V

6V

1

1B

G

P

r2

7. A thin bi-convex lens of refractive index 3/2 and radius of curvature 50 cm is placed on a reflecting convex

surface of radius of curvature 100 cm. A point object is placed on the principle axis of the system suchthat its final image coincides with itself. Now few drops of a transparent liquid is placed between the mirror

and lens such that final image of the object is at infinity. The refractive index of the liquid used is given

by . Fil l 6 in OMR sheet.



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PART-2 : CHEMISTRY

SECTIONI


This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and(D), out of which ONLY ONE is correct.

1. Which of the graph is correct representation for the elementary reaction of type A + 2B C

(A) conc.

time

ABC

(B) conc.

time

AB

C(C) co

nc.

time

A

B

C

(D) conc.

time

A

B

C

2. 50 ml of 0.1 M KI solution is completely oxidized by atmospheric oxygen according to the following

equation-

4H+ + 4I + O2 2l

2+ 2H

2O

I2

formed then quickly reacts with I to form I3

I2

+ I I3

What will be the final concentration of I3 in the solution -

(A) 0.025 (B) 0.033 (C) 0.01 M (D) 0.066 M

3. Degree of hardness for aqueous 104M Ca(HCO3)

2solution will be -

(A) 10 ppm (B) 20 ppm (C) 16.2 ppm (D) 8.1 ppm


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4. Find the element having highest 1st ionisation energy -

(A) Tl (B) Al (C) In (D) Ga

5. Choose the correct option regarding theHNN bond angle in HN3molecule -

(A) less than 10928' (B) In between 10928' and 120

(C) Approximately 150 (D) Just greater than 120

6.

HBr(1eq)

HBr(1eq)

80C

80C

(A)

(B)

(A) Both A and B are

Br

(B) A is

Br

& B is

Br

(C) A is

Br

& B isBr

(D) A is

Br

& B isBr


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7. Based on the following graph mark the correct option for the reaction : A P

(A) III order reaction

(B) Rate constant is 0.5 (mol/L)1n

sec1

time (min)

1[A]

2

45

(C) [A]0

= 0.5 M

(D) Reaction complete in finite time

8. In which of the following compound 2 2x yd orbital is not involved for the hybridisation of their central

atom -

(A) I3+

(B) [BrF4]

(C) I3

(D) [AsF4]

9. Which of the following properties are showing the correct order in the given option -

(A) SiH4

< GeH4

< PbH4

: Boiling point order

(B) Li2CO

3< K

2CO

3< Cs

2CO

3: Solubility order in water

(C) He > Ar > Xe : Solubility order in water

(D) SiCl4

35 < SiCl4

37 : Boiling point order

10. Find out incorrect stability order in the following carbocations-

(I)

(II)

(III)

(IV)

OH

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


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This section contains 3 multiple choice questions relating to one paragraphs with three questions


correct.


From the following data answer the question :

Reaction A + B P

[A] M [B] M

at 300 K at 400 K

2.5 104

3.0 105

5.0 104

2.0 103

5.0 104

6.0 105

4.0 103

1.0 103

6.0 105

1.6 102

Initial rate (M sec1

)

11. The order with respect to A is -

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

12. The value of rate constant at 300 K is (M2 sec1)

(A) 2.667 108 (B) 2.667 105 (C) 2.667 104 (D) 2.667 109

13. The energy of activation for reaction (kcal/mol) is (log 2 = 0.3)-

(A) 1.68 (B) 3.36 (C) 6.72 (D) 1.12

SECTION II & SECTION IIIMatrix Match Type Integer Answer Type



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SECTIONIV

Integer Answer Type


0 to 9.

1. A gaseous mixture of N2& O

2containing 60% by mole N

2is allowed to react with each other according

to the following equaion.

N2

+ O2 NO

2

If 92 gm of NO2

is formed, find the mole of N2

present in the mixture.

2. Find the number of d-block elements from the following

La, Th, Ac, Pd, Pb, Pm , Pt

3. Find the number of S-S linkage in hexathionate ion.


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4.

14

14

Na

Na

D O2

Product(s)

+12

H2

How many organic product(s) are obtained.

5.OH

major product

conc.H SO2 4

Number of 1, 2 shifts involved in above reaction.


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6. HO CCH CHCNHCHCOMe2 2

NH2 O CH2

Number of functional group = x excluding (C = C)

Number of amino acids formed on hydrolysis = y

Then find out the value of (x + y).

7. How many of the following compounds will show Tautomerism.

(a) Ph CH = NH (b) C

O

(c) Me C C CMe3 3

O

(d) C

O

CHMe2

(e) Me3C N = O (f)

PhO

(g) Ph C Me

O

(h)

NO2

(i)

Ph

O

(j) O


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PART-3 : MATHEMATICS

SECTIONI


This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and(D), out of which ONLY ONE is correct.

1. If y = cos1(cos (|2x| (x)), where

2 x 0

(x) 0 x 0

2 x 0

, then 58

dy

dx is -

(A) 2 (B) 0 (C) 2 (D) Not defined

2. If (x) x 1 2 x , then the domain of ([x] x2 + 4), is

(where [.] denotes the greatest integer function) -

(A) 5, 1 3, 7 (B) 3, 1 3, 7

(C) 3, 1 3, 5 (D) 5, 1 5, 7

3. If (x) is differentiable and '(x) is continuous with '(2) = 14, then x 0 (2 sin x) (2 x cos x)lim x sin x

is

equal to-

(A) 14 (B) 7 (C) 28 (D) 56


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4.4 4

dx

x 1 is equal to-

(A)2 41 log x x 1 C

2 (B)

44 41

4

1 x x 1 1 x 1n tan C4 2 xx x 1

(C)2 41 log x x 1 C

2 (D)

44 41

4

1 x x 1 1 x 1n tan C

4 2 xx x 1

5. Possible value of a2, for which equation

2 2 2

2

a sin x a 2

1 tan x cos 2x

has no solution, is (tan x 1)

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

6. If x and y are independent variables and x

x y 2 x

0

(x) e '(y)dy x x 1 e

, where (x) is a

differentiable function, then (x) is-

(A) (x2 + x 1)ex (B) (2x + 1)ex (C) (2x 1)ex (D) (x2 + x 1)ex


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7. If 21(x)

x 1

, then identify the correct option(s) (where n(x) represent

nd (x)dx

)

(A) 2013(x) is an odd function (B) 2014(x) is an even function

(C) n(x) is always an odd function (D)

n n 1 n 1

n

n 12

1 n! x 1 x 1 (x)

2 x 1

8. If x and y are independent variables and 1

2 2

0

(x) 1 x y x (y)dy be a continuous and differentiable

function, then identify the correct option(s)-

(A) 164

' 057

(B) 25

' 019

(C)

1

0

164(x)dx

57 (D)

1

0

25(x)dx

19


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9. Let /3

sinx

/3

I cos x dx

, then I is greater than -

(A)2 (B) 2

3 (C) 4

3 (D) 2

10. Let : , a ( , b]2

be an invertible function with longest domain defined as

(x) = tanx + cotx2 then -

(A) Ordered pair (a,b) is

4 2 3,3 3

(B) Ordered pair (a,b) is, 4

4

(C)2

1 1 x 2 x 4x (x) tan2

(D)2

1 1 x 2 x 4x (x) tan2


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This section contains 3 multiple choice questions relating to one paragraph with three questions


correct.


Let

n 2

2nn

| x 1| xlim 6 x 0

| x | x(x)

sin x 0 x 6

, where {.} denotes fractional part function.

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

11. Number of points at which (x) is not differentiable in [6,6] -

(A) 6 (B) 5 (C) 4 (D) 3

12. Number of solutions of the equationx

(x)6

in [6,6]

(A) 2 (B) 3 (C) 4 (D) 5

13. Value of/ 2

/ 2

(x)dx

is-

(A)7

2(B)

5

2(C)

3

2(D)

1

2

SECTION II & SECTION III

Matrix Match Type Integer Answer Type



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SECTIONIV

Integer Answer Type


0 to 9.

1. If the period of

x x x x x x

(x) sin cos tan cot sec cosecn 2 ! n 1 ! n! n 1 ! n 2 ! n 3 !

is

10080, then the value of n is

2. If '' is a solution of1 1 1tan x cot

x 4

, then1

is equal to (where [.] denotes greatest integer

function)


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3. If x sin y cos = 0 & x sin3 + y cos3 = sin. cos (x,y 0), then the value of (x2 + y2) is

equal to

4. If11 4

tan tan3 3

&11 4 2

sin sin2 9

, then the value of3 2

1

4 3 is


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5. If xy 2 2 2n e 1 e x x y , then 1,0

dy

dx

is equal to

6. Let (x) = min(tan1x, cot1x) & h(x) = (x + 2) /3. Let x1,x

2(where x

1< x

2) be the integers in the

range of h(x), then the value of (cos1(cosx1) + sin1(sin x2)) is equal to

7. Let : A 1

,02

is such that 3(x) 3x(x) + x3 + 1 = 0 and (x) is an invertible function, then

number of solution(s) of the equation (((x)))2 =3

21(x) + 1 is


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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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