Mock Advanced Test-3 Paper-2

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VMC/Paper-2 1 MOCK JEE ADVANCED - 3

Mock Advanced Test-3 Paper-2

TIME : 3 hrs M.M. : 180

Read the following Instructions very carefully before you proceed.

A. General

1. This booklet is your Question Paper. Do not break the seals of this booklet before being instructed to do so by the invigilators.

2. Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers, and electronic gadgets are NOT allowed inside the examination hall.

3. Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficient pressure so that the impression is created on the bottom sheet.

4. DO NOT TAMPER WITH/MUTILATE THE OMR OR THE BOOKLET.

5. Read carefully the Instructions printed at the beginning of each section.

B. Filling the Right Part of the OMR

6. For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your Test Code, Roll No. and Group properly in the space given in the ANSWER SHEET.

C. Question Paper Format

The question paper consists of 3 SUBJECTS (Physics, Chemistry and Mathematics). Each SUBJECT consists of one section only. Each section contains three types (1, 2 & 3).

12. TYPE-1 contains 10 Multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE CHOICE is correct.

13. TYPE-2 contains 3 Paragraphs each describing theory, experiment, data etc. There are 6 multiple choice questions relating to three paragraphs with 2 questions on each paragraph. Each question of a particular paragraph has four choices (A), (B), (C) and (D) out of which ONLY ONE CHOICE is correct.

14. TYPE-3 contains 4 Match the following Objective type Questions. Each question contains statements given in 2 columns. Statements in the column I have to be matched with statements in column II and then option with the appropriate code is to be marked in the answer sheet. The options for the correct match are provided as (A), (B), (C) and (D) out of which ONLY ONE CHOICE is Correct.

D. Marking Scheme

15. For each question of TYPE-1, TYPE-2 and TYPE-3, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer ONLY and zero (0) marks if no bubbles are darkened. In all other cases, minus one (−1) mark will be awarded in these sections.

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PART - I (PHYSICS) 60 MARKS

TYPE-1 SINGLE CORRECT ANSWER

This section contains 10 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of which ONLY ONE Choice is Correct:

1. A soap bubble of radius R is surrounded by another soap bubble of radius 2R, as shown in figure. Take surface tension = S. Then, the pressure inside the smaller soap bubble, in excess of the atmospheric pressure, will be :

(A) 4S/R (B) 3S/R (C) 6S/R (D) None of these

2. A solid sphere of uniform density and mass M has radius 4 m. Its centre is at the origin of the coordinate system. Two spheres of radii 1 m are taken out so that their centres are at P(0, –2, 0) and Q (0, 2, 0), respectively. This leaves two spherical cavities. What is the gravitational field at the origin of the coordinate axes?

(A) 311024

GM (B) 1024Gm

(C) 31G/M (D) Zero

3. Five point charges, +q each, are placed at the five vertices of a regular hexagon. The distance of centre of the hexagon from any of the vertices is a. The electric field at the centre of the hexagon is :

(A) 2

04q

a (B)

208

qa

(C) 2

016q

a (D) Zero

4. Three separate segments of equal area A1, A2 and A3 are shown in the energy distribution curve of a blackbody radiation. If n1, n2 and n3 are number of photons emitted per unit time corresponding to each area segment respectively then:

(A) 2 1 3n n n (B) 3 1 2n n n

(C) 1 2 3n n n (D) 3 2 1n n n

SPACE FOR ROUGH WORK

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5. Uniform rod AB is hinged at the end A in a horizontal position as shown in the figure. The other end is connected to a block through a massless string as shown. The pulley is smooth and massless. Masses of the block and the rod are same and are equal to ‘m’. Then acceleration of the block just after release from this position is:

(A) 6g/13 (B) g/4 (C) 3g/8 (D) None of these

6. The energy that should be added to an electron, to reduce its de-Broglie wavelength from 92 10 m to 90.5 10 m will be:

(A) 1.1 MeV (B) 40.56 MeV (C) 0.56 KeV (D) 5.6 eV

7. A bead can slide on a smooth straight wire and a particle of mass m is attached to the bead by a light string of length L. The particle is held in contact with the wire with the string taut and is then let fall. The bead has mass 2m. When the string makes an angle θ with the wire the bead will have slipped a distance equal to :

(A) (1 cos )L (B) (1 cos )2L

(C) (1 cos )3L

(D) (1 cos )6L


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8. A potentiometer arrangement is shown in the figure. Driving cell has e.m.f. e and internal resistance r.

Resistance of potentiometer wire AB is R, F is the cell of e.m.f. e/3 and interval resistance r/3. Balance point (J)

can be obtained for all finite values of : (A) R > r/2 (B) R < r/2 (C) R > r/3 (D) R < r/3

9. When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from 0.26 μm to 0.13 μm. The ratio of the emissive powers of the body at the respective temperatures is :

(A) 161

(B) 41

(C) 14

(D) 116

10. In displacement method distance of object from a convex lens of focal length 20 cm in one position is 60 cm. Then

(A) In the other position distance of object form the convex lens will be 30 cm (B) Distance between object and screen is 90 cm (C) Both (A) and (B) are correct (D) Both (A) and (B) are wrong


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TYPE-2 LINK COMPREHENSION TYPE

This section contains 6 multiple choice questions relating to three paragraphs with two questions on each paragraph. Each question has four choices A, B, C and D out of which ONLY ONE is correct.

Paragraph for Questions 11 - 12

A container of volume 4V0 made of a perfectly non-conducting material is divided into two equal parts by a fixed rigid wall whose lower half is non-conducting and upper half is purely conducting. The right side of the wall is divided into equal parts (initially) by means of a massless non-conducting piston free to move as shown. Section A contains 2 mol of a gas while the section B and C contain 1 mol each of the same gas (γ = 1.5) at pressure P0. The heater in left part is switched on till the final pressure in section C becomes 125/27 P0. Calculate :

11. Final temperature in part C.

(A) 0 0P VR

(B) 0 053P V

R (C) 0 0

3P V

R (D) 0 05P V

R

12. The heat supplied by the heater :

(A) 0 03689

P V (B) 0 0113

5P V (C) 0 0

3169

P V (D) 0 04058

P V


A cylindrical object of cork of mass 15 g and cross-sectional area A1 = 10 cm2 floats in a pan of water as shown in the figure. An aluminium cylinder of mass 25 g and cross-sectional area A2 = 2 cm2 is attached with a string, 4 cm below the cork and slides through a watertight frictionless hole in the bottom of the pan. Take density of the cork, ρ = 0.2 g/cm3, ρaluminium = 2.7 g/cm3, g = 10 m/s2, Based on the above information, answer the following question. [Density of water = 1 g/cm3]

13. The length of the cork cylinder inside the water in equilibrium is : (A) 6 cm (B) 4 cm (C) 8 cm (D) 3 cm

14. The tension in the string joining the cork and aluminium cylinder is : (A) 2 N (B) 1 N (C) 0.45 N (D) 0.6 N


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A thin, uniform rod with negligible mass and length 0.200 m is attached to the floor by a frictionless hinge at point P (as shown in the figure). A horizontal spring with force constant k = 4.80 Nm–1 connects the other end of the rod to a vertical wall. The rod is in a uniform magnetic field B = 0.340T directed into the plane of the figure. There is current I = 6.50 A in the rod, in the direction shown.

15. Calculate the torque due to the magnetic force on the rod, for an axis at P. (A) 0.0442 Nm–1, into the plane (B) 0.0442 Nm–1, out of the plane (C) 0.022 Nm–1, into the plane (D) 0.022 Nm–1, out of the plane

16. When the rod is in equilibrium it makes an angle of 53.0° with the floor as shown in the figure, how much is the spring stretched or compressed?

(A) 0.05765 m, stretched (B) 0.05765 m, compressed (C) 0.0242 m, stretched (D) 0.0242 m, compressed


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TYPE-3 MATCH MATRIX TYPE


17. Three identical metal plates with large surface areas are kept

parallel to each other as shown in figure. The leftmost plate is

given charge Q, the rightmost given charge –2Q and the

middle one remains neutral. Then :

Column-1 Column-2

(P) The charge appearing on outer surface of the rightmost plate 1. 2Q

(Q) The charge appearing on outer surface of the leftmost plate 2. 2Q

(R) The charge appearing on left surface of the middle plate 3. 3 2Q

(S) The charge appearing on right surface of the middle plate 4. 3 2Q

Codes : P Q R S P Q R S

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

18. For a concave mirror of focal length 20 cm, match the following: (Column-1 gives object distance for a real object).

Column-1 Column-2

(P) 10 cm 1. Magnified, inverted and real

(Q) 30 cm 2. Equal size, inverted and real

(R) 40 cm 3. Smaller, inverted and real

(S) 50 cm 4. Magnified, erect and virtual


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


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19. A block of mass m is put on a rough inclined plane of inclination θ, and is tied with a light thread shown. Inclination θ is increased gradually from θ = 0° to θ = 90°. Match the column according to corresponding curve.

Column-1 Column-2

(P) Tension in the thread versus θ 1.

(Q) Normal reaction between the block and the incline versus θ 2.

(R) Friction force between the block and the incline versus θ 3.

(S) Net interaction force between the block and the incline versus θ 4.


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


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20. In the table shown, Column II shows the possible outcomes to the water level of a swimming pool when a person standing on a boat in it does any one of the actions shown in Column I match the possible outcomes.

Column-1 Column-2

(P) He throws a 20 kg iron anchor from the boat into the water, which then settles at the bottom ( ).iron water

1. The water level of swimming pool becomes lower

(Q) He throws a 20 kg log of wood from the boat. The log floats on water ( ). wood water

2. The water level of swimming pool becomes higher

(R) He empties 20 kg of water from the boat into the pool. 3. The water level of swimming pool stays the same

(S) He drinks some water from the pool. 4. The water level of swimming pool cannot be predicted from the information given


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


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PART - II (CHEMISTRY) 60 MARKS


This section contains 10 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of which

ONLY ONE Choice is Correct:

1. Which of the following is an incorrect IUPAC name: (A) 5-ethyl-3-methylheptane (B) 3-(2,2-Di-methylpropyl) pentane (C) 2-ethylpentane (D) All of the above

2. Which of the following reactions would give pentan-2-ol? (A) (B) (C) (D) All of the above 3. There are two path (I and II) for the preparation of

phenyl-2, 4-dinitro phenyl ether (X).

Path 1 : Path 2 :

Which of the following statements is true? I. Path I is feasible, whereas Path II is not. II. Path II is feasible, whereas Path I is not. III. The Cl of (A) undergoes SN reaction because it is activated by the two electron withdrawing (–NO2)

groups.

IV. The nitration of (B) does not give (X) but it gives because the first

nitro group is deactivating, so the second nitro group enters the other ring.

The correct choice is : (A) I (B) II (C) I, III, IV (D) I and IV


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4. In which of the following cases, the oxidation state of N atom is wrongly calculated? Compound Oxidation state (A) NH4Cl –3 (B) (N2H5)2SO4 +2 (C) Mg3N2 –3 (D) NH2OH –1

5. Red phosphorous reacts with alkali to give salt of hypo-phosphoric acid. The sum of number of P – OH and number of P – P bonds in the hypo phosphoric acid is:

(A) 4 (B) 5 (C) 6 (D) 7

6. Consider the following reactions:

I. n2 xAg S NaCN [Ag(CN) ] II. 2H O n

2 yAu NaCN O [Au(CN) ]

III. n n mx y z[Ag(CN) ] /[Au(CN) ] Zn Ag / Au [Zn(CN) ]

Find the value of x, y and z and report your answer as the sum of x, y and z. (A) 4 (B) 5 (C) 8 (D) 9

7. Which of the following order is correct order of stability of resonating structure of diazomethane (CH2N2) ?

I. 2CH N N

II. 2CH N N

III. 2CH N N IV. 2C H N N

The correct choice is : (A) I > II > IV > III (B) I > II > III > IV (C) I > IV > II > III (D) I > III > IV > II


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8. For the following parallel reaction :

Initially concentration of A is a0 and concentrations of B & C are zero. Calculate time at which the concentration

of all three components becomes equal.

(A) 1 2

ln 2 / 3k k

(B) 1 2

ln3k k

(C) lln3

2k (D)

2

l ln 32k

9.

The product R is : (A) NaOCl (B) NaClO3 (C) HCl (D) Cl2 10. Consider the following reactions :

I. KOH4NH Cl Product (Containing nitrogen)

II. KOH4PH I Product (Containing phosphorous)

III. NaOH4P

Product (Containing phosphorous in negative oxidation state)

The order of change in bond angle (For reactant-specified product) is : (A) I > II > III (B) II > III > I (C) III > II > I (D) II > I > III


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Catalytic hydrogenation is a best way to convert unsaturated hydrocarbons, alkenes and alkynes into alkanes. Reactants passed over surface of the metals like Pd, Pt, Ni and a transition state develops between the reactants from same side and that is why it is a syn addition.

Mechanism in case of other metals, 2H molecule will be adsorbed on the surface of metal

To compare rate : I. More the stable alkene less will be the rate of hydrogenation. II. Steric factor will also affect rate of hydrogenation.

If 4Pd/BaSO is used alkenes are not reduced to alkanes and major product of alkyne reduction is cis alkene.

11. Number of isomers of C5H12 that can be prepared by catalytic hydrogenation of any alkene is : (A) 1 (B) 2 (C) 3 (D) None

12. Correct statement(s) is(are): I. Methane cannot be prepared by catalytic hydrogenation of alkene II. Only 3 isomeric alkenes on catalytic hydrogenation can give iso-pentane as product III. Solution of product(s) obtained shows no optical rotation.

IV. Solution of product(s) obtained shows no optical rotation

The correct choice is : (A) I, III, IV (B) I, II, III (C) I, II, IV (D) I, II, III, IV


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A, B and C are three complex of chromium (III) with molecular formula. H12O6Cl3Cr. All the three have water and chloride ion as ligands. Complex A does not react with H2SO4, whereas complex B and C losses 6.75% and 13.5% of the original weight, respectively on treatment with concentrated H2SO4. Aqueous solution of A, B and C are prepared independently,

Answer the following questions with respect to solution of A, B and C

13. Which of the following complex shows geometrical isomerism ? (A) Only A (B) Only C (C) Both B and C (D) None

14. Which of the following is correct for equimolar solution of A, B and C with respect to ionic conductance ? (A) B > A > C (B) C > B > A (C) A > B > C (D) C > A > B


For two gases A and B, P v/s V isotherms are drawn at T K as shown in figure. TA and TB are critical temperature of A and B respectively.

15. Which of the following is true? (A) TA < T < TB (B) TA > T > TB (C) TA > TB > T (D) None of above

16. The correct statement(s) is(are) : I. Pressure correction term will be more negligible for gas B at T K II. The curve for gas ‘B’ will be of similar shape as for gas A if T > TB III. Gas ‘A’ will show similar P v/s V curve as of gas ‘B’ if T > TA The correct choice is : (A) III only (B) II and III (C) II only (D) All


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17. Match the set of reaction in Column 1 with total number of products formed including stereoisomers in Column 2 and select the correct answer using code given below :

Column 1 Column 2

(P)

1. 1

(Q)

2. 2

(R)

3. 3

(S) 2 4Br / CCl3 2 3

(Cis and Trans form)CH CH CH CH CH 4. 4


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


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18. MATCH THE COLUMN :

Column 1 Column 2

(P)

1. Orange dye

(Q)

2. White precipitate

(R)

3. Yellow dye

(S)

4. Aspirin


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


Column 1 Column 2

(P) 3 3K [Fe(OX) ] 1. Geometrical isomerism

(Q) 3 4 2K [CoF Cl ] 2. Optical isomerism

(R) 3 6K [Fe(CN) ] 3. Linkage isomerism

(S) 2 5[Fe(H O) Br]Cl 4. Ionization isomerism


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


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20. Match the orbital overlap figures in Column 1 with the resulting overlap diagram in Column 2 and select the correct answer.

Column 1 Column 2

(P)

1.

(Q)

2.

(R)

3.

(S)

4.


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


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PART - III (MATHEMATICS) 60 MARKS




1. 300

2 3 100

0

(1 ) .rr

r

a x x x x

If 300

0

,rr

a a

then 300

1

. rr

r a is equal to :

(A) 300 a (B) 100 a (C) 150 a (D) 75 a

2. If g(x) is a differentiable real valued function satisfying g(x) – 3g(x) 3 x 0 and g(0) = –1 then g(x) + x for x 0 is :

(A) Increasing function of x (B) Decreasing function of x (C) Data insufficient (D) None of these

3. If 1

0

( ) ( ) ,dy f x f x dxdx

then the equation of the curve y = f (x) passing through (0, 1) is :

(A) 2 1( )3

xe ef xe

(B) 3 2 1( )

2(2 )

xe ef xe

(C) 2 1( )1

xe ef xe

(D) None of these

4. The value of / 4

2 20

(cos sin )

(cos sin ) sin cos sin cos

d

is equal to :

(A) 3 (B)

6 (C)

4 (D)

2

5. The equation 3 3 3 3( 3 4) 3( 3 4) 4 2( 4 3 2)x x x x x x has :

(A) all its solutions real but not all positive (B) only three of its solutions real (C) three of its solutions positive, two negative and all other imaginary (D) only one real solution

6. For 0 < < 2, sin–1 (sin ) > cos–1 (sin ) is true when ' ' lies in the interval :

(A) ,4

(B) 3,

2

(C) 3,

4 4

(D) 3 , 24


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7. If in a right angled triangle ABC, 4sin cos 1 0A B and tan A is finite, then : (A) Angles are in A. P. (B) Angles are in G. P. (C) Angles are in H. P. (D) None of these

8. If A and B are two events such that, ( ) 0.3, ( ) 0.25, ( ) 0.2,P A P B P A B then cc

cAPB

is equal to :

(A) 215

(B) 1115

(C) 1315

(D) 1415

9. If the eccentric angle of a point lying in the first quadrant on the ellipse 2 2

2 2x ya b

= 1 (a > b) be and the line

joining centre to point makes angle with x-axis then will be maximum when is equal to :

(A) tan1 ab

(B) tan1 ba

(C) 4 (D) None of these

10. If the number of radical axes of a system of circles is same as number of radical centres then number of circles in that particular system is :

(A) 4 (B) 5 (C) 6 (D) 10


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If a circle Co, with radius 1 unit touches both the axes and as well as line (L1) through P(0,4), L1 cuts the x-axis at 1( , 0)x . Again a circle C1 of unit radius is drawn touching x-axis, line L1 and another line L2 through point P. L2 intersects x-axis at

2 , 0x and this process is repeated n times.

11. The value of x2 is : (A) 3 (B) 4 (C) 15/2

(D) 17/2

12. The centre of circle C2 is :

(A) (3, 1) (B) 15 , 12

(C) 31, 14

(D) None of these

Paragraph for Question 13 - 14

If ( ) ( ) ( ), 2nf x x g x n and 1( ) '( ) ''( ) .......... ( ) 0nf f f f where, f (x) and g(x) are polynomials.

For polynomials f (x) and g(x) with rational coefficients, answer the following questions.

13. If ( )y f x touches the x-axis at only one point, then the point of contact (A) is always a point with rational co-ordinates (B) may or may not be a rational co-ordinates (C) will have irrational co-ordinates (D) None of these

14. If f (x) is of degree 3 and touches x-axis, then : (A) All the roots of f (x) are rational (B) Only one root is rational (C) Both (A) and (B) may be possible (D) None of these


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Paragraph for Question 15 - 16

Using three basic colours (Red, Blue, Green) different colours are made by mixing these two or more colours in equal proportion. The n vertical stripes are painted by all colours available, such that no two consecutive stripes have the same colour.

15. The number of ways of painting the n stripes be nt ( 1)n then :

(A) 1 6n nt t (B) 1 7n nt t (C) 1 3n nt t (D) 1 2n nt t

16. The number of ways of painting n stripes such that only alternate stripes are painted by a basic colour (n is odd) is:

(A) 1 1

2 23 . 4n n

(B) 1

27.12n

(C) 1 1

2 23 . 4n n

(D) 1

27.12n


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17. If an equilateral triangle ABC with vertices at 1 2 3, andz z z be inscribed in the circle 2z and again a circle is

inscribed in the triangle ABC touching the sides AB, BC and CA at D(z4), E(z5) and F(z6) respectively.

Column 1 Column 2

(P) Then value of Re 1 2 2 3 3 1z z z z z z is equal to 1. 2

(Q) If 1

3

4zz

is equal to 1 3a i , then a is 2. –6

(R) The value of 2 2 21 2 2 3 3 1z z z z z z is 3. 12

(S) If P is any point on incircle the value of 2 2 2DP EP FP is 4. 6


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

18. If , ,x y z are unit vectors such that 3 7 ˆ, , , . , . , 22 4

x y z a x y z b x y z c a x a y a a , then

match the following column 1 with column 2 :

Column 1 Column 2

(P) x 1. 4c

(Q) y 2. 43

c b

(R) z 3. 1 3 4 83

a b c

(S) 3 2 3x y z 4. 3 4a c


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


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Column 1 Column 2

(P) The last digit of 1021! 2! .................. 2010 ! will be _______ 1. 3

(Q) If

1 2 23 2 1 2

2A

a b

and A is an orthogonal matrix then value of (|a| + |b|) is

equal to ______

2. 9

(R) If 20 1 2 0 1 21 1 ........., 1, 10a bx x a a x a x a a a , then value

of (a + b) is equal to ______ ,a b N

3. 80

(S) Let

20102 1

2 11

5 rr

rf x a x

and f (–1) = 4 then f (1) is equal to_______ 4. 6


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


Column 1 Column 2

(P) Number of points in the plane of three different coplanar non-concurrent lines which are equidistant from them, may be

1. 1

(Q) Let A, B, C, D be four non-coplanar points. Then the number of planes which are equidistant from all the four points can be

2. 2

(R) For the points A(0,0), B(1,0), C(0,2), D(3,4), there exist a point P such that PA + PB + PC + PD is minimum. The number of such point P may be

3. 7

(S) P is a point on the plane of the square ABCD such that each of , , andPAB PBC PCD PDA is an isosceles triangle. The number of

such point P can be

4. 9


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


End of Mock JEE Advanced-3/PAPER-2

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Mock Advanced Test-3 Paper-2