FFIIIITTJJEEEE JJEEEE AADDVVAANNCCEEDD ...3. 50 gm ice at –10 C is mixed with 10 gm steam at 100...

INSTRUCTIONS A. General:

1. This booklet is your Question paper. Do not open the booklet before being instructed to do so by the invigilators.

2. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be provided for rough work.

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

4. Use a black ball point pen; darken the bubbles on the OMR sheet. B. Question paper format and Marking scheme: (i) Part-A (01 – 10) contains 10 multiple choice questions which have one or more than one

option is/are correct. Each question carries +4 marks for correct answer and no negative for wrong answer.

(ii) Part-C (01 – 10) contains 10 Numerical based questions with single digit integer as

answer, ranging from 0 to 9 and each question carries +4 marks for correct answer. There is no negative marking.

FFIIIITTJJEEEE JJEEEE AADDVVAANNCCEEDD FFUULLLL TTEESSTT

Full Test-1

(Paper-1)

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2 JEE Advanced Full Test–1_Paper-1_ 12/04/2018

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PHYSICS

PART-A

SECTION–1

Multiple Correct Questions This Section contains 10 Multiple Correct Questions which have one or more than one option is/are correct

1. A particle of mass m is projected with speed u inside a fixed uniform spherical shell of radius R as

shown in the figure from point P which lies on the circumference of shell. The collisions of the particle with the surface of the shell are perfectly elastic. Point P & A lie in the plane of paper. Choose the CORRECT option(s) from the following :

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

(B) The particle will come back to A after a time of 3 3 R

u after its projection from A.

(C) The particle will come back to A after a time of 6 3 R


(D) The particle will come back to A after a time of 9 3


2. A small object of mass m and of charge q slides down frictionlessly along a slope of angle of elevation

from a height of h. From the midpoint of the slope, it enters a region of uniform horizontal electric field, and it decelerates and stops at the bottom of the slope.

(A) The magnitude of E is mg

tanq

(B) The normal reaction on block before dotted line and after dotted line remains the same. (C) The magnitude of acceleration before and after dotted line remains the same.

(D) The speed at height h/4 from bottom is gh

2 .

Space for rough work



3. 50 gm ice at –10°C is mixed with 10 gm steam at 100°C. When the mixture finally reaches its steady

state inside a calorimeter of water equivalent 1.5 gm then : [Assume calorimeter was initially at 0°C, Take latent heat of vaporization of water = 540 cal/gm, Latent heat of fusion of water = 80 cal/gm and specific heat capacity of water = 1 cal/gm-°C, specific heat of ice = 0.5 cal/gm°C]

(A) Mass of water remaining is 60 gm (B) Mass of ice remaining is 3 gm (C) Mass of steam remaining is 1.20 gm (D) Final temperature is between 0°C and 100°C 4. Two spheres having masses m1 and m2 are kept on a inclined plane as shown. Both of them are in

equilibrium. What is a necessary condition for this? (μ1 is coefficient of friction between m1 and inclined plane and μ2 is coefficient of friction between m2 and inclined plane).

(A) m1 > m2 (B) m1 < m2 (C) μ1 > μ2 (D) μ1 < μ2 5. The primary winding of step-down transformer with a turn ratio 10 has a source voltage of 120 V

connected to it. The resistance of the secondary and primary winding is negligible, the current in secondary is I = 5 A.

(A) The current in primary is 0.5 A (B) The power delivered to the load is 60 W (C) The load resistance is 24 ohms (D) The voltage across the load is 1200 V. 6. Structure-A is a half-circle infinite sheet carrying uniform electric current I flowing out of the paper plane.

Structure-B is a quarter-circle infinite sheet carrying same uniform electric current I flowing out of the paper plane

(A) At the centre, on the axis of circular sheet point-O the total magnetic field is pointing to right in both

cases (B) At the center, on the axis of circular sheet point-O the total magnetic field is pointing to left in both

cases (C) The field strength of structure-A is larger than that of structure-B at point O. (D) The field strength of structure-A is smaller than that of structure-B at point O.




7. The potential difference between the target and the cathode of an X-ray tube is 50 kV. The current in

the tube is 20 mA. Only 1% of the total energy is emitted as X-rays. (Take: hc = 1240 eV nm) (A) The maximum frequency of the emitted x-rays is approx 1.2 × 10

19 Hz.

(B) The heat should be removed at 900W to keep the target at constant temperature (C) A wavelength of 0.2 nm can be emitted by this tube (D) Electrons are being emitted at the rate of 1.25 × 10

17/sec by the cathode

8. The electric field in space is ˆ ˆ4i 3 j N / C . Choose the correct statement(s) :-

(A) The Potential at (4,3,0) is 7V if the potential at the origin is taken to be zero. (B) The field exert a net force on a dipole placed at origin with dipole moment along y-axis. (C) The potential at (4, 3, 0) is –7V if potential at origin is taken to be zero (D) The field exerts no net force on a dipole placed at origin with dipole moment along x-axis. 9. 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 v0 perpendicular to its length on a smooth horizontal surface. If the maximum

elongation in spring is 0l

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

(A) velocity at maximum elongation, 04vv

5 (B) velocity at maximum elongation, 03v

v4

(C) 00

5 l kv

12 m (D) 0

0

l kv

12 m

10. A particle executes SHM about a point other than x = 0 as shown in the graph. Then :

(A) amplitude is equal to 4m (B) equilibrium position is at x = 0

(C) equilibrium position is at x = 2m (D) angular frequency = 2

3

rad/s.




PART-C Single Digit Integer Questions

This Section contains 10 Single Digit Integer Answer type Questions ranging from 0 to 9.

1. A tank of area 7 m

2 containing water at 0°C has a depth of 1m. There is a coin at the bottom which is

being viewed by an observer in air vertically above the coin. 374.4 × 106 cal of heat is extracted from

water so that a part of the water freezes. If the apparent depth of the coin as seen by the observer before freezing is d1 and the apparent depth of the coin as seen by the observer after freezing is d2, find d2 – d1 (in cm). (Take : Specific gravity of ice = 0.9, refractive index of ice = 1.3, refractive index of water = 4/3, Latent heat of fusion of ice = 80 cal/g)

2. A large cube of glass has a metal reflector on one face and water on an adjoining face as shown figure.

A light beam strikes the reflector as shown. You observe that as you gradually increase the angle, for

60° no light enters the water. (nwater = 4/3). How much time (in 10–9

sec) does light take to travel

9 3

10 m in this glass?

3. There is a sample of diatomic gas in a container (whose volume is constant). The temperature of this

gas was increased greatly so some molecules fell into atoms (dissociated). The pressure of the gas increased by a factor of 6 and the internal energy of the gas increased to a value of 4.4 times the original internal energy. By what factor did the temperature of the gas (measured in Kelvins) increased?

4. Four packages each having a mass of 4 kg are attached on the belt at equal distances d = 200 mm as

shown in the figure. Initially belt is at rest. If a constant force of magnitude 840 N is applied to the belt, determine the velocity of package 2 as it falls off the belt at point A. Assume that the mass of the belt and pulleys is small compared with the mass of the packages. Assume that the radius of pulley is negligible in comparison to width d.




5. A rod is arranged at an angle of 30° from the horizontal. Attached to the rod with two strings is the mass

m, as shown in figure. The rod is rotated, maintaining its direction in space, so that m rotates in a circular path. The strings are of equal length and make angles of 60° with the rod as shown. Take the length of the strings as 2.4 m. Calculate the minimum value of the tangential speed (in m/s) of the mass such that the string with tension T2 does not become slack when the mass is directly above the rod : (g = 10 m/s

2)

6. A ice hockey player shoots a puck towards the centre of the goal from a position 32 ft directly in front of the goal as shown in figure-1. The initial speed of the puck is 12 ft/s and the puck has a mass 150g. Half way to the goal the puck explodes into two fragments. One piece of mass m1 = 90 g comes back with a speed of v1 = 5 ft/s and passes 12 ft to the side of the spot it was initially shot from as shown in the figure-2. The other piece of the puck with mass m2 = 60 g continues on with a speed v2. Assume that there is no friction as the puck slides along the surface. Find the distance (in ft) by which the piece that continues towards the goal miss the centre of the goal.

7. A semicircular loop of mass per unit length 10

kg / m is placed on a horizontal surface with its plane

parallel to the surface in a uniform magnetic field of magnitude 1 tesla as shown in figure. Find the minimum amount of current (in Amp) that should be passed in the loop so that loop can be rotated about side XY.




8. Two identical point charges (q = 2 coulomb) are placed such that one lies at the centre of the sphere of

radius 2 cm and other at a distance 2 2 cm from the centre of sphere as shown in figure. Total flux

through the surface of sphere enclosed by all the tangents to the sphere drwan from the outer charged

as shown in figure is 0

xq

2 find the value of x.

9. The voltage measured between points A and B in the circuit consisting of eight resistors, each having a

resistance of 119 , is 5 V. What is the power dissipated (in W) in the system of eight resistors?

10. Many stars collapse under gravitational pull into a neutron star when most of the hydrogen is used up

The entire star is then a tightly packed ball of neutrons with the density of nucleus. Assume that a star of mass 2 × 10

32 kg, radius 5.5 × 10

8 m collapses into a neutron star. It has a time period of rotation of

108 sec about its axis initially. What is its rotation period (in sec.) after collapse.

(Take : R0 = 1.1 fm, 1 amu = 1.6 × 10–27

kg)




CHEMISTRY

PART-A

SECTION–1


1. COOH

COOH and

COOK

COOH behave as acid as well as reducing agent. Then which of the following are the

correct statements regarding COOH

COOH and

COOK

COOH ?

(A) When COOH

COOH and

COOK

COOH behaves as reducing agent with KMnO4, then its equivalent weights are

equal to half of its molecular weight respectively . (B) 1000 mL of 1 N solution of each is neutralised by 1000 mL 1 N Ca(OH)2. (C) 1000 mL of 1 M solution of each is neutralised by 1000 mL 1 M Ca(OH)2. (D) 1000 mL of 1 M solution of each is neutralised by 200 mL 2 M KMnO4 in acidic medium. 2. Which of the following graph is correctly plotted for an ideal gas having constant moles and fixed

temperature.

(A) (B) (C) (D)

3. Equal volumes of following solutions are mixed, in which case the pH of resulting solution will be

average value of pH of two solutions - (A) Aqueous HCl of pH = 2, aqueous HCl of pH = 4 (B) Aqueous HCl of pH = 2, aqueous NaOH of pH = 12 (C) Aqueous NaOH of pH = 12, aqueous NaOH of pH = 10 (D) Aqueous CH3COOH of pH = 5, aqueous NH3 of pH = 9

[Given : Ka(CH3COOH) = Kb (NH3)]

4. Which of the following speices(s) having bond order equal or less than one.

(A) 2H (B) C2 (C)

2O

(D) B2




5. Which of the following anion gives CO2 gas with dil. HCl.

(A) 23CO (B) 2

3SO (C) 22 3S O (D) 2S

6. Self reduction is possible for metal extraction (metal in given ores) (A) HgS (B) ZnO (C) PbS (D) Cu2S 7. Which of the following molecules are polar as well as planar.

(A) BFClBr (B) 3 3 6B N H (C) ClF3 (D) 2 2CH C =C =CF

8. Product obtained in following reaction is/are :

(A) (B) (C) (D)

9. Consider the following process:

Which one of the following is/are correct? (A) Optical activity of the solution will decline to near zero i.e. near about racemisation will occur (B) The observed rate of racemisation will thus be twice the rate of inversion (C) The optical activity of the solution will remain same (D) The observed rate of inversion will thus be twice the rate of racemisation




10. In which of the following reaction(s) achiral product(s) is/are formed –

(A) (B)

(C) (D)



1. Milli moles of sucrose which should be dissolved in 500 gm of water so as to get a solution which has a

difference of 102.3°C between boiling and freezing point is. (Kf = 1.8 K kg mole

–1 and Kb = 0.5 K kg mole

–1)

Fill your answer as sum of digits (excluding decimal places) till you get the single digit answer. 2. A 250.0 ml sample of a 0.20 M Cr

3+ is electrolyzed with a current of 96.5 A , so as to deposit Cr. If the

remaining [Cr3+

] is 0.1M, the time taken (in sec.) in the process. Fill your answer as sum of digits (excluding decimal places) till you get the single digit answer.

3. Two radioactive elements P and Q have decay constant hr–1

and 6 hr–1

respectively. If decay

begins with same number of atoms of them, and if ratio of atoms of P to those of Q after 1

5hrs is 'e

x ' ,

then value of 'x' will be : 4. To a 1 litre solution containing 0.2 M Al

3+ and 0.2 M Zn

2+, NaOH is added slowly, if concentration of

[Al3+

] is 16 × 10–x

at the time when Zn(OH)2 is just begins to precipitate, then find 'x'. Ksp [Al(OH)3] = 16 × 10

–25 ; Ksp [Zn(OH)2] = 2 × 10

–13

Fill your answer as sum of digits (excluding decimal places) till you get the single digit answer.




5. In how many of the following species, percentage ‘s’ character of all bonds is not identical

7 4 4 3 2 2 3 2I F , CH , SF , XeF , OCl , ICl , BF , SO , 5PCl

6. Among the following how many are tetrahedral in shape

63 24 4 4 44 4

34 4 4XeO , XeF , SF , , ,PO AlH , BH , NH SO SiH , , [Cu(CN) ]

7. Find the number of sulphurized ores. Copper glance, Pitch blende, Azurite, Horn Silver, Sphalerite

8.

1 2 3pKa 2; pKa 4; pKa 10

Find isoelectric point of the above amino acid. 9. Total number of atoms / groups, when attached on benzene are ortho/para directing & activating in

nature towards electrophilic substitution are.

(a) – Me (b) – F (c) C– NH R

O

(d) C NH

O

R

(f) C H

O

(g) – NO2 (h) – Br (i) CF3

(j) C CH3

O

O (k) C OCH3

O

10. Reaction – I : 5 3 3PCl x moles of NaNH CH I(A) (B)

Reaction – II : 2y moles of NaNH

3 3CH C C CH

Reaction – III : 32 CH Iz moles of NaNH

3(A) Et C C CH

Value of x + y + z is




MATHEMATICS

PART-A

SECTION–1


1. Let N be the number of values of x for which

tan3x tan 2x

1,x 0,41 tan3x tan2x

,then

(A) N > 3 (B) N < 6 (C) N > 4 (D) N < 4

2. Let ƒ(x) be a continuous odd function in x R, such that 5

0

f x dx 5 , if A is area bounded by y = ƒ(x),

x-axis, x = –5 and x = 5, then A cannot be equal to - (A) 5 (B) 8 (C) 10 (D) 14 3. Let S be the set of positive value(s) of r such that the area enclosed by the tangents drawn from the

point P(6,8) to the circle x2 + y2 = r2 and the chord of contact is 75 3

4sq. units. Then the correct

option(s) is/are - (A) S is singleton set

(B) Equation of chord of contact is 6x + 8y = 2, S

(C) Let A and B are point of contact of tangents then the equation of circumcircle of ABP is x2 + y2 – 6x – 8y = 0

(D) Number of elements in set S is 2

4. Let ƒ : R R, x + |ƒ(x)| = 2ƒ(x), then (A) ƒ(x) is an one-one function (B) ƒ(x) is a many one function (C) ƒ(x) is an onto function (D) ƒ(x) is an into function




5. Let

2

1

2 x

x 02

2x x sinx cosx

lim 1 6 8sin 0 L

12sin 16sin 1 4sin

, if L is finite and [0,2], then which of the following

statement is(are) true? (A) L can be 1 (B) L can be e

24

(C) Sum of all possible value(s) of is 6 (D) Sum of all possible value(s) of sin is 1

2

6. A continuous function ƒ : R R is defined as

1/ 2

2

sin p q x sin2x, x 0

x

f x q, x 0

x rx x, x 0

rx x

, then which of the

following is(are) correct ?

(A) 1

q2

(B) p = -2

(C) p + q + r = 3

2 (D) Complete set of values of r is R -{0}

7. Let

17 sin

A 5

5 cos

, [0,2] and |A3| = 8k

3, then which of the following statements is(are) true –

[Note : |A| denotes determinant value of matrix A] (A) Number of possible integral values of k is less than equal to 7 (B) Number of possible integral values of k is greater than equal to 8

(C) If k = 1

212

, then number of possible value of is 1.

(D) If k = 6 1 , then number of possible values of is 2.




8. Let ƒ(x) satisfy the differential equation

d f x 6

dx x f x

and ƒ(1) = 0, then select the correct

statement(s) (A) If ƒ(a) = 6, a > 0, then a = 7e – 12 (B) If ƒ(a) = 6, a > 0, then a = 5e – 9 (C) Curve y = ƒ(x) intersects line x + y = 8 at y = 4 ln2 (D) Curve y = ƒ(x) intersects line x + y = 8 at y = 6 ln2 9. Let N be the number of arrangements of the letters of the word 'LOVE IS LIFE' in which no two alike

letters are together and containing the word LOVE. Then select the correct statement(s) (A) N > 1200

(B) N 1200 (C) Remainder when N is divided by 11 is 3. (D) Remainder when N is divided by 9 is 6. 10. Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} one by one without replacement.

Let P1 denotes the probability that maximum of the two numbers is greater than 4 and P2 denotes the probability that minimum of the two numbers is 3, then

(A) P1 + P2 = 1 (B) 2 2

1 2

2P P

5 (C)

1 2P 2P (D) 2P1 > 5P2



1. Let a,b,c are distinct positive numbers in arithmetic progression and , , are distinct negative

numbers in increasing arithmetic progression. Let ƒ : R R be a twice differential function and a + ƒ()

= b + ƒ() = c + ƒ(), then minimum number of solution(s) of equation 2

2

d f x0

dx in x (,) is

2. Suppose z1, z2, z3 are vertices of an equilateral triangle in argand plane inscribed in |z| = 2. If z1 =

1 i 3 , z2 = a + ib, z3 = c + id, where a,b,c,d R and a > c, then the value of |3a + d – c| is

[Note : i = 1 ]

3. Let k be smallest integral value of a for which equation 4x

3 – 4x

2 + ax – a = 0 has exactly one real root,

then the value of k is




4. Let system of linear equations in x, y, z,

xsin2 ycos2 zcos2 ,

x 2sin2 2cos2sin2 0,

yz z y

xsin2 y sin2 cos2 2zcos2 0

has a non-trivial solution, then number of value(s) of in the interval [0, ] is 5. If P(x, y) be any point on 16x2 – 9y2 = 144 and A(5, 0), B(–5, 0), then the value of |PA – PB| is

6. In a triangle ABC, the position vectors of the points A,B and C are ˆ ˆ ˆ2i j,5i j and ˆ ˆ2i 7j respectively.

Let AD,AB,AC are non-coplanar vectors. If M is minimum integral value of 2 2 2

AD BD CD , then

sum of digits of M is 7. In a triangle PQR, let a,b and c be lengths of the sides opposite to the angles P,Q and R respectively

2 2a bcosP

2bc

and

sinR

sin P Q

. If distance between two parallel lines 2x + y – 2 = 0 and x + y + 3

= 0 is d, then the value of d2 is

8. Consider lines 1

x 2 y 1 z 1L :

1 3 2

& 2

x 2 y 2 z 3L :

1 1 3

. If

a

b 3is the shortest distance

between lines L1 and L2, then the value of (a – 2b) is (where a and b are coprime numbers)

9. The curve y = 2 3 nx x x xe e e ... e ,n N have equation of tangent y – b = 45ex + c at x = 1, then the

value of n is

10. Number of solutions of equation tan-1

(tan(x)) + cos-1

(cos(x)) = 3

,x ,22 2

is




FFIIIITTJJEEEE JJEEEE AADDVVAANNCCEEDD FFUULLLL TTEESSTT ANSWER KEY

Full Test-1

(Paper-1)

PHYSICS CHEMISTRY MATHEMATICS

PART-A PART-A PART-A

1. BCD 1. ABD 1. BD

2. CD 2. ABCD 2. AB

3. AD 3. BD 3. ABC

4. B 4. AD 4. AC

5. AB 5. A 5. ABC

6. AD 6. ACD 6. AB

7. ACD 7. ABCD 7. BD

8. CD 8. AB 8. AD

9. AC 9. AB 9. ACD

10. ACD 10. D 10. BCD

PART-C PART-C PART-C

1. 7 1. 5 1. 0

2. 8 2. 3 2. 5

3. 4 3. 1 3. 1

4. 7 4. 7 4. 2

5. 6 5. 4 5. 6

6. 2 6. 8 6. 4

7. 4 7. 2 7. 8

8. 0 8. 3 8. 7

9. 6 9. 3 9. 9

10. 1 10. 8 10. 3



HINTS AND SOLUTION PHYSICS

PART - A



PART - C



MATHEMATICS PART-A



PART-C

FFIIIITTJJEEEE JJEEEE AADDVVAANNCCEEDD ...3. 50 gm ice at –10 C is mixed with 10 gm steam at 100...

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