this booklet contains 21 printed pages. test pattern : jee … · 2018. 10. 31. · 6. write the...

This booklet contains 21 printed pages.

A. General: INSTRUCTIONS 1. This Question Paper contains 21 pages having questions.60 2. No additional sheets will be provided for rough work. 3. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets

in any form are not allowed. 4. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately. 5. Do not Tamper/mutilate the ORS or this booklet.B. Filling the bottom-half of the ORS: 6. Write the Code on the ORS same as that given on this question booklet 7. Write your N , Name and Name of centre and sign with pen in appropriate boxes. Do not

write these anywhere else.Enrollment umber

8. Darken the appropriate bubbles below your with HB Pencil.Enrollment numberC. Question paper format and Marking scheme : 9. Th question paper consists of 3 parts P , Chemistry and Mathematicsis hysics (80 Marks) (80 Marks)

(80 Marks). Each part consists of three Sections. 10. For each question in you will be award arks if you darken only the bubbles corresponding

to the correct answer and zero mark if no bubbles are darkened. In all other cases, min k willbe awarded.

ed mSection-I, 4us two mar (-2)

11. For each question in tyou will be award arks if you darken only the bubbles correspondingto the correct answer and zero mark if no bubbles are darkened. In all other cases, min k willbe awarded.

Section II, 4ed mus two mar (-2)

12. For each question in you will be awarded marks if you darken only the bubbles correspondingto the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded in thisSection.

Section-III, 4

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Test Pattern : JEE AdvancePaper-2 Syllabus

Test ID : 81113002D-NM

Time : 3 HoursM.M : 240

Rotation

Gaseous State, Thermodynamics 1st law & Thermochemistry

Quadratic Equations & Straight Lines ( System of Coordinates,,Distance and SectionFormula, Section Formula Problems,Shifting of Origin, Centroid,Incentre, Circumcentre,Orthocentre , Relation, Area and Locus, Slope and Angle between lines)

Physics

Chemistry

Mathematics

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Space for rough work

Patiala Centre : TEL. 0175-5012029, 5012030Chandigarh Centre : TEL. 0172-4612029, 4622029 LAKSHYA EDUCARE PVT. LTD.Panchkula Centre : TEL. 0172-4004028, 4005028 www.lakshyainstitute.comMohali Centre : TEL. 9888590180, 9988850467 Forum for Competitions

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Section --- I : Multiple Correct Choice TypeThis Section contains 8 multiple choice questions. Each question has four choices a), b) c) and d) out of

which ONE OR MORE may be correct.

1. A child is standing with folded hands at the centre of a platform rotating about its central axis.The kinetic energy of the system is K. The child now stretches his arms so that the moment ofinertia of the system doubles. The kinetic energy of the system now is :

(a) 2K (b)K

2(c)

K

4(d) 4K

2. A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing throughits end. Its maximum angular speed is . Its centre of mass rises to a maximum height of

(a)2 21

3

l

g

(b)

1

6

l

g

(c)

2 21

2

l

g

(d)

2 21

6

l

g

3. A rod AB is 1 m long. It is hinged at A so as to rotate in a vertical plane. Initially the rod ishorizontally placed and then it is released from rest .Obtain the angular speed of the rod and thelinear speed of its free end as it passes through the position shown in the diagram

(a) 5.05rad/s, v 5.05m/s (b) 1rad/s, 1m/s

(c) 4.04rad/s, mv 2.02m/s (d) 5.05rad/s, 1.01m/sv

PART --- I : PHYSICS

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4. A circular disc rotates in a vertical plane about a fixed horizontal axis which passes through a point

X on the circumference of the disc. When the center of the disc moves with speed v, the speed of

the opposite end of the diameter through X is

(a) 2v (b) 2v (c) V (d)1

2v

5. A ball moves over a fixed track as shown in the figure. From A and B the ball rolls without slipping.

If surface BC is frictionless and KA, KB and KC are kinetic energies of the ball at A, B and C

respectively, then :

(a) ; Kh h K A c B c (b) ;h h K KA C C A (c) ;h h K K A C C A (d) ;h h K K A C B C

6. A disc is rolling (with slipping) on a horizontal surface. C is its centre and Q & P are two

points equidistant from C. Let , , be the magnitude ofP Q C velocities of Points P, Q, & C

respectively, then :

(a) Q C P (b) Q C P (c)1

,2Q P C P (d) Q C P

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7. A particle moves in a circular path with decreasing speed. Choose the correct statement :

(a) Angular momentum remains constant

(b) Acceleration is towards the centrea

(c) Particle moves in a spiral path with decreasing radius

(d) The direction of angular momentum remains constant.

8. A solid sphere of mass M and radius R is placed on a rough horizontal surface. It is struck by a

horizontal cuestick at a height h above the surface. The value of h so that the sphere performs pure

rolling motion immediately after it has been struck is

(a)2R

5(b)

5R

2(c)

7R

5(d)

9R

5

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Section---II : Paragraph TypeThis Section contains 2 paragraphs. Based upon the first paragraph 2 multiple choice questions and

based upon the second paragraph 2 multiple choice questions have to be answered. Each of these

questions has four choices (a), (b), (c) and (d) out of which ONLY ONE is correct.

Paragraph for Questions 9 & 10A rod AB of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m

travelling along the surface hits the end A of the rod with a velocity v0 in a direction perpendicular to

AB. The collision is elastic. After collision, the particle comes to test.

9. Find the ratiom

M.

(a)2

3(b)

1

5

(c)1

4(d)

2

5

10. A point P on the rod is at rest immediately after collision. Find the distance AP.

(a)6

L(b)

5

6

L

(c)2

3

L(d)

3

L

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Paragraph for Questions 11 & 12

A thin uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m

and 2m moving in the same horizontal plane with speeds 2v and v respectively strike the bas as

shown in the figure and stick to it after collision.

11. After collision, the velocity of centre of mass is

(a) Zero (b)5

v

(c)2

v(d)

2 2

v

12. After collision, the angular velocity of the rod about centre of mass is

(a)3

v

a(b)

5

v

a

(c)v

a(d)

2 2

v

a

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Section --- III : Integer Type Answer

This section contains 8 Questions. The answer should be written in four digits. For example : If your

answer is 692, please mark it as 0692 as shown below (in the separate section on the ORS). Answers

should be rounded off to the nearest whole number or as directed in the question.

1. A car of mass m travelling at speed v moves on a horizontal track. The centre of mass of the cardescribes a circle of radius r. If 2a is the separation between the inner wheels and outer wheels andh is the height of the centre of mass above the ground.

Then calculate the speed limit beyond which the car will overturn if a = 1 m, r = 5 m, h = 2 m2. A solid sphere is released from a height of 49 m from horizontal on an inclined plane as shown in

the figure. All the surfaces are smooth except AB which has2

3 and length of AB is 49 m. After

passing over the rough surface, the sphere climbs to the right portion BD of incline.(Given, g = 10 ms-2)

If height from horizontal to which it climbs on BD is h = xy. Then calculate x + y.

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3. A solid cylinder of mass m and radius R is set in rotation about its axis with an angular velocity 0 ,

then lowered with its lateral surface onto a horizontal plane and released. The coefficient of friction

between the cylinder and the plane is . If the time taken by the cylinder to start performing pure

rolling isR

tx g

0 . Then find x.

4. A small solid ball (mass = 0.1 kg) rolls without slipping along the track shown in the figure. The

radius of the circular track is R. If the ball starts from rest at a height 8R above the bottom, the

horizontal force acting on it at point P is 5x newton. Find the value of x. (Given, g = 10 ms-2)

5. A man of mass m = 80 kg runs at a speed u = 4 ms-1 along the tangent to a disc shaped platform of

mass M = 160 kg and radius R = 2 m. The platform is initially at rest and can rotate freely about an

axis through its centre. Find the angular velocity of the man after the man jumps on to the disc and

sticks on the edge of the disc. Dimension of man are negligible comparison to the dimension of

platform.

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6. Two uniform rods A and B length 0.6 m each and of masses 0.01 kg and 0.02 kg, respectively are

rigidly joined end to end. The combination is pivoted at the higher end P shown in figure, such that

it can freely rotate about point P in a vertical plane. A small object to mass 0.05 kg moving

horizontally hits the lower end of the combination and sticks to it. If the velocity of the object so that

the system could just be raised to the horizontal position is xy. Find x + y.

7. A thin rod of mass m and length L is pivoted at one end. Initially, the rod makes an angle of 600

with the vertical and is then released. Calculate the magnitude of the force on the pivot, when the

rod is horizontal.

If2

10m kg .

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8. A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. the stick

applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m/s2. The

coefficient of friction between the ground and the ring is large enough that rolling always occurs and

the coefficient of friction between the stick and the ring is10

P

. Find ([ ] 1)P where [ ] means the

greatest integer value.

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1. If enthalpy of hydrogenation of C6H6(l) (benzene) into C6H12(l) (cyclohexene) is -205 kJ and resonance

energy of C6H6(l) (benzene) is -152 kJ/mol. (Consider H vap of all the required hydrocarbons to be

equal). Then

(a) Enthalpy of hydrogenation of is -535.5 kJ/mol

(b) Enthalpy of hydrogenation of is -238 kJ/mol

(c) Enthalpy of hydrogenation of is -238 kJ/mol

(d) Enthalpy of hydrogenation of is -119 kJ/mol

PART --- II : CHEMISTRY

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2. Following compound named Buta-1, 3-diene can undergo resonance.

( )CH CH CH CH C H 2 2 4 6

Given that Bond energy (BE) for C = C, C --- C , and C --- H bonds are +a, +b and +c calories.

H for following reaction of resonance hybrid of C4H6 is calories is shown under :

4 6 ,C H g C g H g H calories 4 6 .

Then, which among the following is/are correct statement(s)?

(a) Dissociation of C4H6 (Resonance hybrid) and C4H6 (most stable resonating structure) to 6C(g) +

4H(g) would require some amount of heat i.e. (2a + b + 6c).

(b) 4 6 ,C H g C g H g H 4 6 for this reaction would be (2a + b + 6c) had C4H6(g) be most

stable resonating structure of Buta-1, 3-diene.

(c) Resonance energy of Buta-1, 3-diene is 2 6a b c

(d) Resonance energy of Buta-1, 3-diene is 2 6a b c

3. Identify the intensive quantities from the following

(a) Enthalpy (b) Temperature

(c) Volume (d) Refractive index

4. The internal energy change when a system goes from state A to B is 40 kJ/mol.

If the system goes from A to B by a reversible path and returns to state A by an

irreversible path, what would be not the net change in internal energy ?

(a) 40 kJ (b) 40kJ

(c) 40kJ (d) zero

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5. Which among the following statement is/are correct?

(a) Ratio of diffusion of rate of oxygen gas to hydrogen gas at identical conditions is1

4.

(b) According to law of equipartition of energy, Kinetic energy associated with each gas molecule at T

Kelvin with each degree of freedom is.

.2

K TB

(c) With increase in temperature, fraction of molecules having most probable speed decreases but

most probable speed increases.

(d) Real gases tend to behave ideally when pressure is high and temperature is low.

6. The enthalpy of neutralization of a strong acid by a strong base is -57.32 kJ mol-1.

The enthalpy of formation of water is -285.84 kJ mol-1 . The enthalpy of formation of hydroxyl ion is

(a) +228.52 kJ mol-1 (b) -114.26 kJ mol-1

(c) -228.52 kJ mol-1 (d) +114.26 kJ mol-1

7. Which among the following statement is/are correct?

(a) An ideal gas obeying PV = Constant equation would have to absorb heat when it is expanding.

(b) An ideal gas obeying tanV

Cons tT , equation would have to absorb heat when it is expanding.

(c) An ideal monatomic gas obeying PV constant (whereC

C P

v

) have to release heat when

compressed in insulated conditions.

(d) Potential energy for ideal gas is zero.

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8. At 5 10 5 bar pressure, density of diamond and graphite are 3 g/cc and 2 g/cc respectively, at

certain temperature ‘T’. find value of U H for the conversion of 1 mole of graphite to 1 mole of

diamond at temperature ‘T’ : (Take 1 L atm 100 J if required)

(a) 100 kJ/mol (b) 10 . /m atm mole6 3 (c) -100 kJ/mol (d) 10 . /cm bar mole6 3





Consider the adjacent diagram to answer these questions :Initially, flask A contained oxygen gas at

270C and 950 mm of Hg, and flask B contained neon gas at 270C and 900 mm. Finally, the two flasks

were joined by means of a narrow tube of negligible volume equipped with a stopcork and gases were

allowed to mix up freely. The final pressure in the combined system was found to be 910 mm of Hg.

9. If volume of flask B was measured to be 10L, mass of oxygen gas present initially in flask A was

(a) 2.00 g (b) 4.00 g (c) 8.00 g (d) 16.00 g

10. How many moles of gas are present in flask A in the final condition?

(a) 0.155 (b) 0.122 (c) 0.022 (d) 0.222

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Observe the following graphic representation of four basic thermodynamic processes.

11. If the ratio 1.30C

Cp

V

, the atomicity of gas is

(a) 1 (b) 2

(c) 3 (d) Any of the above can be correct.

12. 2 mole of an ideal monoatomic gas undergoes a reversible process for which PV2 = C.The gas is

expanded from initial volume of 1 L to final volume of 3L starting from initial temperature of 300 K.

Find H for the process :

(a) -600R (b) -100R

(c) -3000R (d) None of these

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1. One mole each of two ideal gas 'A'3

2C R

v and 'B'5

2C R

v are mixed then average molar

heat capacity at constant pressure for gaseous mixture is xR. What is the value of x?

2. A gas is found to have the formula (C3O2)n. Its vapour density is 34. The value of n will be …..?

3. What would be the value of compressibility factor (Z) for 1 mole of CO2 gas at a high pressure of 800

atm and 300 K when value of 'b' is 0.03 L mol-1?

(Take R = 0.08 L atm K-1 mol-1)

4. The stop cock containing two bulbs of volume 5 litre and 10 litre containing an ideal gas at 9 atm

and 6 atm respectively are opened. What is the final pressure in atm if the temperature remains the

same?

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5. 3.2 g of oxygen and 0.2 g of hydrogen are placed in 1.12 litre flask at 00C. The total pressure in atm

of the gas mixture will be …....

6. 4.48 L of ideal gas at STP require 12 cal to raise the temperature by 150C at constant volume. The CP

of the gas is ………. cal.

7.

In the present graph, the area of circle A and B are 25 unit and 20 unit respectively work done will

be …….. unit.

8. For the reaction, 3 2N g H g NH g 2 2 3 . Heat of reaction at constant volume exceeds theheat of reaction at constant pressure by the value of xRT. The value of x is ………..

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1. For which of the following graphs of the quadratic expression, y = ax2 + bx + c, the product a b c is

negative.

(a) (b)

(c) (d)

PART --- III : MATHEMATICS

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2. For 0,a the roots of the equation log log log 0,ax x a xa a a 2

2 3 are given by

(a) a43 (b) a

34

(c) a12 (d) a-1

3. The roots of the equation (b + c) x2 - (a + b + c) x + a = 0 are ( , , , Q)a b c

(a) Real (b) Real and Rational

(c) Non real and different (d) Real and equal

4. If both the roots of the equation x2 - 2ax + a2 + a - 3 = 0 in the variable x are less than 3 then a can

be

(a) 2 (b)5

2

(c) 3 (d) -7

5. The Quadratic polynomials defined on real coefficients

2 ; 2 ;P x a x b x c Q x a x b x c 2 21 1 1 2 2 2 where 0, 0 and and Qa a P x x 1 2 both take

positive values x R . g x a a x b b x c c 21 2 1 2 1 2 then

(a) g x takes +ve values only (b) g x takes negative values only

(c) g x takes both +ve and -ve values (d) nothing can be said about g x

6. If 2 0x x 2 for all real values of 'x', then value of may be:

(a) -1 (b) 1

(c) -3 (d) -5

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7. Let . .f x A x B x C 2 when A,B, C R If x is an integer then f(x) is an integer then

(a) C is an integer (b) A+B is an integer

(c) B is an integer (d) 2A is an integer

8. The triangle formed by the lines x + y = 0, 3x + y - 4 = 0 and x + 3y - 4 = 0

(a) isosceles (b) scalene

(c) acute angled (d) obtuse angled





If , are roots of ax2 + bx + c = 0 then ax2 + bx + c = a (x - a) (x - )

9. If the difference of the roots of the equation x2 - bx + c = 0 is equal to the difference of the roots of

the equation x2 - cx + b = 0 and b c , then b + c =

(a) 0 (b) 2

(c) 4 (d) -4

10. If each root of the equation 3x2 - 7x + 4 = 0 is increased by 2, then the resulting equation is

(a) 3x2 - 19x + 30 = 0 (b) 3x2 + 5x + 2 = 0

(c) 3x2 - 19x + 2 = 0 (d) 3x2 - 19x + 20 = 0

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Let , , be three numbers such that 2 2 2+ 2, 6and 1 1 1 1

.2

11. 3 3 3The value of ( ) is equal to:

(a) -2 (b) -1 (c) 6 (d) 8

12. If roots of the quadratic equation 4 12 lies on either side ofx ax 2 ( ), then the largest

integral value of a equals:

(a) 2 (b) 3 (c) 4 (d) 5





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1. A triangle ABC is given with A(1,-2), B(-4,3), C(3,2). Find sum of both the coordinates of 'P' in the

plane of the ABC such that area of PAB = PBC = PAC.

2. If the orthocenter and circumcentre of a triangle are (0, 0) and (3, 6) respectively then the sum of the

coordinates of centroid of the triangle is

3. A(3x1, 3y1), B(3x2, 3y2), C(3x3, 3y3) are vertices of a triangle with orthocentre H at

(x1 + x2 + x3, y1 + y2 + y3) then the ABC in degrees is

4. P(3, 1), Q(6, 5) and R(x, y) are three points such that the angle PRQ is a right angle and the area of

7RPQ . Then the number of such points R is

5. The area of the pentagon whose vertices are (4, 1), (3, 6), (-5, 1), (-3, -3) and (-3, 0) is

6. If P(2, 1), Q(4, -1), R(3, 2) are the vertices of a triangle and if through P and R lines parallel to the

opposite sides are drawn to intersect at S, then the area of PQRS in square units is

7. Two vertices of an equilateral triangle are (0, 0) and (0, 2 3) . If the third vertex is ( , )x y3 3 in first

quadrant, then evaluate x y 23 3 .

8. If tan , tan , tan are the roots of the equation 12 15 1 0t t t 3 2 ; then the centroid of triangle

having vertices (tan ,cot );(tan ,cot );(tan ,cot ) is given by G(h, k); then evaluate

(h + k)/(k - h).

Dream on !!

this booklet contains 21 printed pages. test pattern : jee … · 2018. 10. 31. · 6. write the...

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