FIITJEE Ltd. 9A Edmonston Road Opp. NIP Civil Line Allahabad–211001 (UP), Ph. 2400674, 9792712323 1 PHYSICS, CHEMISTRY & MATHEMATICS JEE - MAINS 2015 PHASE – I SET - A Time Allotted: 3 Hours Maximum Marks: 360 Do not open this Test Booklet until you are asked to do so. Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. Important Instructions : 1. Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is strictly prohibited. 2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully. 3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are 360. 5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response. 6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. ¼ (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 7. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side-1 and Side-2 of the Answer Sheet. Use of pencil is strictly prohibited. 9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination hall / room. 10. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room / Hall. However, the candidates are allowed to take away this Test Booklet with them. 11. Do not fold or make any stray marks on the Answer Sheet. Name of the Candidate (in Capital Letters) :_____________________________________ Enrolment Number :_________________________________________________________ Batch :________________________ Date of Examination : ________________________ FIITJEE - JEE (Mains)
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Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
You are not allowed to leave the Examination Hall before the end of the test.
INSTRUCTIONS
Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.
A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Parts.
3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
4. Each part is further divided into two sections: Section-A & Section-C
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.
B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR
sheet. 2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No.
and write in ink your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers.
C. Marking Scheme For All Three Parts. (i) Section-A (01 – 10) contains 10 multiple choice questions which have only one correct answer. Each
question carries +3 marks for correct answer and – 1 mark for wrong answer. Section-A (11 – 15) contains 5 multiple choice questions which have one or more than one correct
answer. Each question carries +4 marks for correct answer. There is no negative marking. (ii) Section-C (01 – 05) contains 5 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.
Name of the Candidate :__________________________________________
Batch :___________________ Date of Examination :___________________
Enrolment Number :______________________________________________
PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS SECTION – A
(Single Correct Choice Type)
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. Which of the following is a unit vector
(A) ji (B) cos i - sin j (C) sin jcos2i (D) ji3
1
2. A force ˆ ˆ ˆF 5i 3j 2k N
is applied over a particle which displaces it from its origin to the
point ˆ ˆr 2i j m.
The work done (in J) on the particle is :
(A) + 13 (B) + 10 (C) + 7 (D) – 7
3. A uniform chain of length 2m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table ?
(A) 3.6 J (B) 7.2 J (C) 1200 J (D) 120 J
4. A projectile is thrown with velocity u at an angle above the horizontal. Find the average velocity during the time of ascent
(A) u cos (B) usin
2 (C) 2u
1 3cos2
(D) None of these
5. A block of mass m is attached with a spring in its natural length, of spring constant k. The other end A of spring is moved with a constant acceleration ‗a‘ away from the block as
mAa
shown in the figure. Find the maximum extension in the spring. Assume that initially block and spring is at rest w.r.t ground frame
(A) ma
k (B)
1 ma
2 k (C)
2ma
k (D)
4ma
k.
6. A balloon B is moving vertically upward and viewed by a
telescope T. At a particular angular position = 53° measured
parameters are r = 1 km, dr
3m / sdt
and d
0.02 rad / s.dt
The
magnitude of the linear velocity of the balloon at this instant is
cross the river such that he reaches from A to B directly. Point B is 45 m ahead of line AC (perpendicular to river) Assume speed of river and speed of swimmer as equal. Swimmer must
try to swim at angle with line AC. Value of is A
BC
River Flow
(A) 37º (B) 53º (C) 30º (D) 16º
8. Find minimum value of the angle so that block of mass m does not move on rough surface, whatever may be the value of applied force F.
The coefficient of state friction between the block and surface is .
F m
() Rough Surface
(A) tan1() (B) 11tan ( )
2
(C) cot1() (D) 11cot ( )
2
9. At time t = 0, a bullet is fired vertically upwards with a speed of 98 ms1. At time t = 5 s (i.e., 5 seconds later) a second bullet is fired vertically upwards with the same speed. If the air resistance is neglected, which of the following statements will be true ?
(A) The two bullets will be at the same height above the ground at t = 12.5 s (B) The two bullets will reach back their starting points at the same time (C) The two bullets will have the same speed at t = 20 s (D) The two bullets will attain the different maximum height 10. Figure shows the changes in speed of a marble as it rolls down
an inclined plane P1, travels on a flat horizontal surface and then up another inclined plane P2. What can you say about the steepness of P1 and P2 from the information given in the figure ?
(A) P1 is steeper than P2 (B) P2 is steeper than P1 (C) P1 and P2 are equally steep (D) Nothing can be said about the relative steepness of P1 and P2
as the information given is insufficient
C
P2
BA20
0
10
ED
P1
20 50 100
Time (s)
Sp
eed
(m
s)
-1
(Multi Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.
11. A spring and block is placed on a fixed smooth wedge as shown. Following conclusion can be drawn about block.
(i) magnitude of its momentum will be max when Fnet on block is zero
(ii) its kinetic energy will be max when Fnet on block is zero (iii) KE of block is max when block just touches the spring. (iv) net force on block is maximum when KE = 0
12. In the figure, if F = 4 N, m = 2kg, M = 4 kg then
(A) The acceleration of m w.r.t. ground is 22m / s
3
(B) The acceleration of m w.r.t. ground is 1.2 m/s2 (C) Acceleration of M is 0.4 m/s2
F
s=0.1=0m
M
k = 0.08
Ground
z
(D) Acceleration of m w.r.t. ground is 22m / s
3
13. A particle moves along positive branch of the curve x
y2
where 3t
x ,3
x and y are
measured in metres and t in seconds, then :
(A) The velocity of particle at t = 1 s is 1ˆ ˆi j2
(B) The velocity of particle at t = 1 s is 1 ˆ ˆi j2
(C) The acceleration of particle at t = 1 s is ˆ ˆ2i j
(D) The acceleration of particle at t = 2 s is ˆ ˆi 2 j
14. Two blocks of masses m1 and m2 are connected through a massless inextensible string. Block of mass m1 is placed at the fixed rigid inclined surface while the block of mass m2 hanging at the other end of the string, which is passing through a fixed massless frictionless pulley shown in figure. The coefficient of static friction between the block and the inclined plane is 0.8. The system of masses m1 and m2 is released from rest.
m=4kg1m=2kg2
30º Fixed
g=10m/s2
=0.8
(A) The tension in the string is 20 N after releasing the system (B) The contact force by the inclined surface on the block is along normal to the inclined
surface
(C) The magnitude of contact force by the inclined surface on the block m1 is 20 3N
(D) None of these
15. A particle ‗P‘ of mass ‗m‘ is rotating in horizontal circle about vertical axis AB with the help of two strings each of length ‗L‘ as shown in
figure. The separation AB = L, and ‗P‘ rotates with angular velocity ‗‘ about axis AB. Tension in the upper and lower strings are T1 and T2
This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.
1. A particle of mass 10 kg is in equilibrium with the help of two ideal
and identical strings. Now one string is cut then, find the ratio of tension in the other string just before cutting and just after cutting.
30°30°
10 kg 2. In a car race, car A takes 4 seconds less than car B to reach the finish line and passes the
finishing line with velocity v more than car B. Assume cars start from rest and travel with constant acceleration aA = 4 m/s2 and aB = 1 m/s2. Find the value of v in m/s.
3. In the figure, find the velocity of m1 in ms–1 when m2 falls by 9m. Given m1 = m m2 = 2m (take g = 10 ms–2)
m1=0.1
m2 4. A ball is projected from some height with initial horizontal speed
20 m/s. There is a wall at a horizontal separation of 100 m from
the building. If collision is perfectly elastic find the time in sec
after which it will hit the wall. (t = 0 is taken when ball is thrown).
All surfaces one smooth.
100 m
20 m/s
5. Figure shows a smooth cylindrical pulley of radius R with centre at origin
of co-ordinates. An ideal thread is thrown over it on the two parts of ideal
thread two identical masses are tied initially at rest with co-ordinates (R, 0)
and (-R, -R) respectively. If mass at x-axis is given a slight upward jerk, it
leaves contact with pulley at (R cos, Rsin). Then find /sin.
This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is
1. The distance between 3rd and 2nd orbit of hydrogen atom is
(A) 2.646108 cm (B) 2.116108 cm (C) 2.646 cm (D) 0.529 cm
2. H–B–H bond angle in 4BH is:
(A) 180° (B) 120° (C) 109° (D) 90° 3. Which of the following has maximum lattice energy? (A) CaO (B) Na2O (C) MgO (D) BaO 4. The atomic radii of F and Ne in angstrom unit are respectively given by (A) 0.72, 1.60 (B) 1.60, 1.60 (C) 0.72, 0.72 (D) 1.60, 0.72 5. The K.E. of N molecule of O2 is x Joules at –123°C. Another sample of O2 at 27°C has a KE of
2x Joules. The latter sample contains. (A) N molecules of O2 (B) 2N molecules of O2
(C) N/2 molecules of O2 (D) N/4 molecule of O2
6. Out of the following, which does not have zero dipole moment is (A) CO2 (B) CCl4 (C) BCl3 (D) NH3 7. The wave function for 1s orbital of hydrogen atom is given by
r /a01s e
2
a0 = radius of Bohr orbit r = distance from nucleus What will be ratio of probability density of finding the electron at the nucleus to the first Bohr‘s
orbit (a0)? (A) e (B) e2 (C) 1/e (D) 0 8. The IP1, IP2, IP3, IP4 and IP5 of an element are 7.1, 14.3, 34.5, 46.8, 162.2 eV respectively.
The element is likely to be (IP ionization potential) (A) Na (B) Si (C) K (D) Ca
9. 12.25 g KClO3 on heating gives enough O2 to react completely with H2 produced by the action of the Zn on dilute H2SO4.
3 2
2KClO 2KCl 3O , 2 4 4 2
H SO Zn ZnSO H , 2 2 2
2H O 2H O
The weight of Zn required for this is: [At.wt of Zn = 65.5] (A) 9.825 g (B) 19.65 g (C) 39.3 g (D) 8.5 g
10. 2 moles of 4
FeSO in acid medium are oxidised by x moles of 4
KMnO , whereas 2 moles of
2 4FeC O in acid medium are oxidised by y moles of
4KMnO . The ratio of x and y is:
(A) 1
3 (B)
1
2 (C)
1
4 (D)
1
5
Multiple Correct Answer(s) Type
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONE or MORE are correct.
11. Which of the following statement is correct regarding H2O2?
(A) it has open booklike structure (B) it is both an oxidizing as well as reducing agent (C) it is a bleaching agent (D) it acts as only oxidizing agent 12. Which of the following will represent Boyle‘s law correctly?
(A) PV
P
(B) V
PV
(C) PV
1/P
(D) P
V 13. Which of the following pairs will not diffuse at the same rate through porous plug at same
conditions of temperature and pressure? (A) CO & NO2 (B) NO2 & CO2 (C) NH3 & PH3 (D) CO2 & N2O 14. A gas obeys the equation P(V-b) = RT. Which of the following is/are correct about the graphs
15. Highly pure dilute solution of sodium in liquid ammonia: (A) Shows blue colour (B) Exhibits electrical conductivity (C) Shows reducing properties (D) Shows oxidizing properties
SECTIONC Integer Answer Type
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).
1. 1 g of an acid (Molar mass = 150 g/mol) is completely neutralized by 1.5 g KOH. Calculate the number of neutralizable protons in acid.
2. Find out the number of angular nodes in the orbital to which the last electron of Cr enter. 3. According to molecular orbital theory, the number of electrons present in the antibonding
molecular orbitals of N2 is (are)
4. A 17 gm sample of H2O2 contains a% H2O2 by weight and requires a mL of KMnO4 in acidic
medium for comlete oxidation. Thus what is the molarity of KMnO4? 5. The value of x+y+z in following redox reaction
(Single Correct Choice Type) This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
1. In a triangle ABC, A(2, 4) and internal angular bisector of B & C are y = x & 2x + y = 3, then find the equation of BC
(A) x = 2 (B) y = 2 (C) x + y = 2 (D) none of these 2. Find the equation of minimum radius of that circle which contain all free circles S1, S2 & S3
(A) (−, −1) (2, ) (B) (2, ) (C) (−1, 2) (D) none of these
9. In the equilateral ABC the side length is 8 unit, inscribe this another triangle is form through the
midpoints of vertices A,B and C is DEF. Inside
DEF another triangle is also form through the
midpoints of vertices D,E & F is PQR Find the
area of PQR.
(A) 2 3 (B) 3
(C) 3
2 (D) none of these
A B
C
D E
F
P
Q R
10. Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement ―Suman is brilliant and dishonest if and only if Suman is rich‖
This Section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.
1. A(0, 0), B(2, 1) and C(3, 0) are the vertices of a triangle ABC, and BD is its altitude. The line
through D parallel to the side AB intersects the side BC at a point K. If the product of the areas of the triangle ABC and BDK is k, then the value of 2k is
2. If 2sinx sin x 1 then the value of 2 4 4 2cos x cos x cot x cot x is equal to
3. If 1 2 3cos 2cos 3cos 6 then 1 2 3tan tan tan equals to
4. If 2 2 2log x log y log z
4 6 3k and x3y2z = 1
Then |k| is 5. Let the co-ordinates of the circumcentre of the triangle whose vertices are A(5, – 1), B(–1, 5)
and C(6, 6) is (a, b) then [a + b] is (where [.] denotes the greatest integer function)
MATHEMATICS 1. B Take the reflection of A about internal angular bisector of B & C lie on the line BC. 2. C For centre - find the circumcentre of the centres S1, S2 & S3, For radius - find the circum radius from the centres S1, S2 & S3 and add the maximum radius
of the circles S1, S2 & S3 in the circum radius. 3. A Use the log properties 4. A
2x – y + 4 = ( x – 2y 1) For acute angle bisector use + sign 5. B 33cos2x+4sin2x Then maximum value is 35 6. D Use the homogenization 7. A Lines are x = 2 and x = 6, y = 5, and y = 9 Then centre is (4, 7) 8. A 9. B
Area = 232
4
10. A (Multi Correct Choice Type)
11. A,B,C,D
2 2 2 2 2 21 1sin A sin B sin C (1 cos A) (1 cos B) sin C
Points can be calculated by the internal and external section formula using centres of both the circles and slope can be calculated by using the condition of tangency.
14. A,B,C Use the internal and external touching condition of two circles. 15. A,C
x 1
2 x 1
9 7log 2
3 1
32x2 + 7 = 4(3x1 + 1)
x 1 x 1(3 1)(3 3) 0
x 1 = 0 or x 1 = 1 x = 1, 2.
SECTION–C (Integer Type)
1. 1 Calculate the area of ABC and BDK then multiply these two 2. 2 Given sin x + cos x + tan x + cot x + sec x + cosec x = 7
1 sinx cosx
sinx cosx 7sinx cosx sinx cosx
1 1
sinx cosx 1 7sinx cosx sinxcosx
2 2
2 21 sin2x 1 7
sin2x sinx
2 2
1 t t 2 7t 2 , where t = sin 2x
3 2t 44t 36t 0
2t 44t 36 0 [sin 2x 0]
244 44 4 36
t 22 8 72
sin2x 22 8 7
3. 0
Given 1 2 3cos 2cos 3cos 6
1 2 3cos cos cos 1
1 2 3 0
1 2 3tan tan tan 0
4. 8 Use the log property. 5. 5 Circum centre can be calculated by using the perpendicular bisectors of vertices of the
1. From a uniform circular plate of radius R, a small circular plate of radius R/4 is cut off as shown. If O is the center of the complete plate, then the x-coordinate of the new center of mass of the remaining plate will be:
(A) – R/20 (B) – R/16 (C) – R/15 (D) – 4
3 R
Y
O
X
2. The ratio of excess pressure in two soap bubbles is 3 : 1. The ratio of their volumes will be:
(A) 3
1 (B)
9
1 (C)
1
27 (D)
27
1
3. A mass M is supported by a massless string wound round a uniform cylinder of mass M and radius R. On releasing the mass from rest, it will fall with acceleration :
(A) g (B) g2
1 (C) g
3
1 (D) g
3
2
R M
M
4. A 3 kg ball strikes a heavy rigid wall with a speed of 10 m/s at an angle of 60° with the wall. It gets reflected with the same speed at 60° with the wall. If the ball is in contact with the wall for 0.2 s, the average force exerted on the ball by the wall is:
(A) 300 N (B) zero
(C) 150 3 N (D) 150 N
60°
60°
Wall
N
5. A wide vessel is filled with water of density 1 and kerosene of
density 2. The thickness of water layer is h1 and that of kerosene layer is h2. The gauge pressure at the bottom of the vessel will be:
(A) h11g (B) h22g
(C) h11g + h22g (D) h12g + h21g
h2
h1 Water
Kerosene
6. A ball hits a floor and rebounds after an inelastic collision. In this case:
(A) the momentum of the ball just after the collision is the same as that just before the collision
(B) the mechanical energy of the ball remains the same in the collision
(C) the total momentum of the ball and the earth is conserved
(D) the total energy of the ball and the earth is conserved
7. Two balls of masses m1 = 3 kg and m2 = 2 kg are moving towards each other with speeds u1 and u2. The ball m1 stops after collision and m2 starts moving with speed u1. The co-efficient of restitution for the balls is:
(A) zero (B) 1 (C) 3
2 (D)
2
1
8. A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity . Two objects, each of mass m, are attached gently to the opposite ends of a diameter
of the ring. The ring rotates now with an angular velocity:
(A) mM
M
(B)
mM
mM
2
)2(
(C)
mM
M
2
(D)
M
mM )(
9. An isolated particle of mass m is moving in horizontal plane (x-y), along the x-axis, at a certain height above ground. It suddenly explodes into two fragments of masses m/4 and 3m/4. An instant later, the smaller fragment is at y = +15cm. The larger fragment at this instant is at:
(A) y = –5 cm (B) y = -15 cm (C) y = +5 cm (D) y = +15 cm
10. A cylindrical vessel contains a liquid of density upto a height h. The liquid is closed by a piston of mass m and area of cross-section A. There is a small hole at the bottom of the vessel. The speed v with which the liquid comes out of the hole is: (neglect presence of atmosphere)
v
m, A
h
(A) gh2 (B)
A
mggh2 (C)
A
mggh2 (D)
A
mggh 2
11. The magnitude of the force (in N) acting on a body varies with
time t (in s) as shown. AB, BC and CD are straight line segments. The magnitude of the total impulse of the force on
the body from t = 4 s to t = 16 s is:
(A) 5 × 10–3 Ns (B) 5.8 × 10–3 Ns
(C) 5.8 × 103 Ns (D) 5 × 103 Ns
2 4 6 8 10 12 14 16
200
400
600
800
B
A
D
C
F
Fo
rce (
N)
Time (s)
12. Two equal drops of water each of radius r are falling through air with a steady velocity 8 cm/s. The two drops combine to form a big drop. The terminal velocity of big drop will be:
13. The height of water in a vessel is h. The vessel wall of width b is at
an angle to the vertical. The net force exerted by the water on the wall is:
(A) 21cos
3 bh g (B) gbh 2
(C) 21sec
2 bh g (D) zero
h
B
A
14. The acceleration of centre of mass of the system shown in figure will be:
(A) 10 m/s2 (B) 3
10 m/s2
(C) 3
5m/s2 (D) –5 m/s2
5kg
40kg
15. A block Q of mass M is placed on a horizontal frictionless surface AB and a body P of mass m is released on its frictionless slope.
As P slides by a length L on this slope of inclination , the block Q would slide by a distance:
C
A B
Q
M P
(A) cosLM
m (B) L
mM
m
(C)
cosmL
mM (D)
Mm
mL
cos
16. A disc is rolling without slipping with angular velocity . P and Q are two points equidistant from the centre C as shown. The order of magnitude of velocity is:
C
P
Q
(A) VQ > VC > VP (B) VP > VC > VQ
(C) VP > VC, VQ = VC / 2 (D) VP < VC > VQ
17. Moment of inertia of a ring about a diameters is I0. The moment of inertia of the ring about a
tangent perpendicular to the plane of the ring will be: (A) I0 (B) 2I0 (C) 3I0 (D) 4I0
18. An equilateral triangle ABC has its centre at O as shown in figure. Three forces 10 N, 5N and F are acting along the sides AB, BC and AC. Magnitude of force F so that the net torque about ‗O‘ is zero, will be:
(A) 15 N (B) 5 N (C) 50 N (D) 2 N
O
A
B C 5N
F 10N
19. A disc is rotating with an angular velocity 0. A constant retarding torque is applied on it to
stop the disc. Its angular velocity becomes 0/2 after n rotations. How many more rotations will it make before coming to rest?
(A) n (B) 2n (C) 2
n (D)
3
n
20. When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total
kinetic energy is: (A) 1 : 7 (B) 1 : 2 (C) 1 : 1 (D) 5 : 7
21. One end of a glass U-tube contains oil and the other end contains water as shown. The INCORRECT statement is:
(A) the oil is less dense than water
(B) the pressure at D and E is same
(C) the pressure at B and C is same
(D) the pressure due to column AB of the oil is the same as
that due to column EC of water
E
C B
D
A
Water
Oil
22. An inclined plane makes an angle of 30° with the horizontal. A solid cylinder rolling down this
inclined plane from rest without slipping has a linear acceleration equal to:
(A) 3
g (B)
7
5g (C)
3
2g (D)
14
5g
23. Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line one after another. The velocity of flow of water in the pipe of 2 cm diameter is:
(A) 4 times that in the other pipe (B) 4
1 times that in the other pipe
(C) 2 times that in the other pipe (D) 2
1 times that in the other pipe
24. A concentric hole of radius R/2 is cut from a thin circular plate of mass M and radius R. The
moment of inertia of the remaining plate about its axis will be:
25. A liquid film is formed over a frame ABCD as shown in figure. Wire CD (massless) can slide without friction. The mass to be hung from CD to keep it in equilibrium is: (Surface tension of liquid is T)
(A) Tl
g (B)
g
Tl2
(C) 2
3
Tl
g (D)
2
Tl
g
A B
D C Liquid
Film X Y
l
26. A raft of wood (density 600 kg/m3) of mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?
(A) 120 kg (B) 200 kg (C) 40 kg (D) 80 kg
27. The angular velocity of a wheel increases from 1200 rpm to 4500 rpm in 10 s. The number of revolutions made during this time is
(A) 950 (B) 475 (C) 237.5 (D) 118.75
28. A T shaped object, having uniform linear mass density, with
dimensions shown in the figure is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only translational motion without rotation. The distance of P with respect to C is:
(A) 3
4l (B) l (C)
3
2l (D)
2
3l
l
P
C
F
B A
2l
29. Four particles each of mass m are placed at the corners of a square of side length l. The
radius of gyration of the system about an axis perpendicular to the square and passing through centre is
(A) 2
l (B)
2
l (C) l (D) l)2(
30. A particle of mass m moving eastward with a speed v collides with another particle of same mass moving northward with same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-east direction with a velocity of
1. If n n 1 2 1x x ......... x x 1 , then the value of .....x1
n 1
1 2 3 n
xx x x x nlog log log .........log x
(A) 1 (B) 0 (C) 2 (D) none of these 2. If cosxlog sinx 2 , then sin x lies in the interval
(A) 5 1
,12
(B) 5 1
0,2
(C) 1
0,2
(D) none of these
3. If |z + 1| = z + 1, where z is a complex number, then the locus of z is
(A) a straight line (B) a ray (B) a circle (D) an arc of a circle
4. If the roots of the equation 24 2 0 are of the form k
k 1 and
k 1
k 2
then the value of
is
(A) 2k (B) 7 (C) 2 (D) k+1 5. The length of the chord of the parabola x2 = 4y passing through the vertex and having slope
cot is
(A) 4 cos . cosec2 (B) 4 tan sec
(C) 4 sin. sec2 (D) none of these
6. If the normals at the end points of a variable chord PQ of the parabola y2 – 4y – 2x = 0 are
perpendicular, then the tangents at P and Q will intersect at (A) x + y = 3 (B) 3x – 7 = 0 (C) y + 3 = 0 (D) 2x + 5 = 0
7. The point P on the parabola y2 = 4ax for which |PR – PQ| is maximum, where R (– a, 0),
Q (0, a), is (A) (a, 2a) (B) ( a, -2a) (C) (4a, 4a) (D) (4a, -4a) 8. If tangents at A and B on the parabola y2 = 4ax intersect at the point C, then ordinates of
A, C and B are (A) always in A.P. (B) always in G.P. (C) always in H.P. (D) none of these
9. If z 25i 15 , then find the least positive value of arg z is
(A) 1 4tan
3
(B) 1 3tan
4
(C) 1 5tan
12
(D) 1 12tan
5
10. if |z – i| 2 and z0 = 5 + 3i then the maximum value of |iz + z0| is
, where z is a non real, can be the angle of a triangle if
(A) Re(Z) =1 , Im(Z) = 2 (B) Re(Z) =1 , -1 Im(Z) 1 (C) Re(Z) + Im (Z) = 0 (D) None of these
12. If z1 and z2 are two complex numbers satisfying the equation 1zz
zz
21
21
, then
2
1
z
z is a
number which is (A) Positive real (B) Negative real
(C) Zero or purely imaginary (D) None of these 13. If w is a complex cube root of unity and (a + bw + cw2)3 + (a + bw2 + cw)3 = 0, then b, a, c are
in (A)A.P. (B)G.P. (C)H.P. (D) None of these
14. Number of distinct solution for equation 2 2 2
x x 2 x 3 0 , if is a real no. is
(A) 0 (B) 1 (C) 2 (D) none of these
15. If the numbers a, b, c, d, e form an A.P. then the value of a 4b + 6c 4d + e is (A) 1 (B) 2 (C) 0 (D) none of these 16. If a, b, c are positive real numbers then the number of real roots of the equation
2ax b | x | c 0 is (|x| is always positive)
(A) 2 (B) 4 (C) 0 (D) none of these
17. If a b2 3 43 and a 3 a 12 3 47, then the respectively value of ‗a‘ and ‗b‘ are
(A) 3, 4 (B) 4, 3 (C) 16, 27 (D) 8, 9
18. The number of solutions of the equation 02xlogx2xlog2
1 2 is
(A) 2 (B) 0 (C) 1 (D) 3
19. If both the roots of 2 0x ax a are greater then 2, then
(A) , 4a (B) 0,2a
(C) 4,a (D) none of these
20. Let a,b,c are positive real numbers forming an A.P. If 2 0ax bx c has real roots then
(A) 2 3a c
c a (B) 2 3
a c
c a
(C) 2 3a c
c a (D) 2 3
a c
c a
21. If 1 2 3tan , tan , tan are the real roots of 3 21 0x a x b a x b , where
5. (A) Let A Vertex, AP chord of x2 = 4y such that slope of AP is cot.
Let P ( 2t, t2)
Slope of AP = 2
t cot =
2
t t = 2cot
Now, AP = 42 tt4 = t 2t4 = 4cot cosec = 4cos . cosec2α
6. (D) Since normals at P and Q are perpendicular, the tangents at P and Q will also be
perpendicular but any two perpendicular tangents of a parabola always intersect on its directrix. The parabola is (y – 2)2 = 2( x +2). So its directrix is 2x + 5 = 0
7. (A) We know any side of the triangle is more than the difference of the remaining two sides so
that |PR – PQ| RQ
The required point P will be the point of intersection of the line RQ with parabola which is (a, 2a) as PQ is a tangent to the parabola.
8. (A) A (at12, 2at1)
B (at22, 2at2)
Tangents at A and B will intersect at the point C, whose coordinate is given by ( at1t2, a(t1+t2)) clearly ordinate of A , C and B are always in A.P.
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
You are not allowed to leave the Examination Hall before the end of t he test.
INSTRUCTIONS
Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.
E. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Parts.
3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
4. Each part is further divided into two sections: Section-A & Section-C
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.
F. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR
sheet. 2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No.
and write in ink your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers.
C. Marking Scheme For All Three Parts. (i) Section-A (01 – 10) contains 10 multiple choice questions which have only one correct answer. Each
question carries +3 marks for correct answer and – 1 mark for wrong answer. Section-A (11 – 15) contains 5 multiple choice questions which have one or more than one correct
answer. Each question carries +4 marks for correct answer. There is no negative marking. (ii) Section-C (01 – 05) contains 5 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.
Name of the Candidate :__________________________________________
Batch :___________________ Date of Examination :___________________
Enrolment Number :______________________________________________
PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS SECTION – A
(Single Correct Choice Type)
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. Which of the following is a unit vector
(A) ji (B) cos i - sin j (C) sin jcos2i (D) ji3
1
2. A force ˆ ˆ ˆF 5i 3j 2k N
is applied over a particle which displaces it from its origin to the
point ˆ ˆr 2i j m.
The work done (in J) on the particle is :
(A) + 13 (B) + 10 (C) + 7 (D) – 7
3. A uniform chain of length 2m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table ?
(A) 3.6 J (B) 7.2 J (C) 1200 J (D) 120 J
4. A projectile is thrown with velocity u at an angle above the horizontal. Find the average velocity during the time of ascent
(A) u cos (B) usin
2 (C) 2u
1 3cos2
(D) None of these
5. A block of mass m is attached with a spring in its natural length, of spring constant k. The other end A of spring is moved with a constant acceleration ‗a‘ away from the block as
mAa
shown in the figure. Find the maximum extension in the spring. Assume that initially block and spring is at rest w.r.t ground frame
(A) ma
k (B)
1 ma
2 k (C)
2ma
k (D)
4ma
k.
6. A balloon B is moving vertically upward and viewed by a
telescope T. At a particular angular position = 53° measured
parameters are r = 1 km, dr
3m / sdt
and d
0.02 rad / s.dt
The
magnitude of the linear velocity of the balloon at this instant is
cross the river such that he reaches from A to B directly. Point B is 45 m ahead of line AC (perpendicular to river) Assume speed of river and speed of swimmer as equal. Swimmer must
try to swim at angle with line AC. Value of is A
BC
River Flow
(A) 37º (B) 53º (C) 30º (D) 16º
8. Find minimum value of the angle so that block of mass m does not move on rough surface, whatever may be the value of applied force F.
The coefficient of state friction between the block and surface is .
F m
() Rough Surface
(A) tan1() (B) 11tan ( )
2
(C) cot1() (D) 11cot ( )
2
9. At time t = 0, a bullet is fired vertically upwards with a speed of 98 ms1. At time t = 5 s (i.e., 5 seconds later) a second bullet is fired vertically upwards with the same speed. If the air resistance is neglected, which of the following statements will be true ?
(A) The two bullets will be at the same height above the ground at t = 12.5 s (B) The two bullets will reach back their starting points at the same time (C) The two bullets will have the same speed at t = 20 s (D) The two bullets will attain the different maximum height 10. Figure shows the changes in speed of a marble as it rolls down
an inclined plane P1, travels on a flat horizontal surface and then up another inclined plane P2. What can you say about the steepness of P1 and P2 from the information given in the figure ?
(A) P1 is steeper than P2 (B) P2 is steeper than P1 (C) P1 and P2 are equally steep (D) Nothing can be said about the relative steepness of P1 and P2
as the information given is insufficient
C
P2
BA20
0
10
ED
P1
20 50 100
Time (s)
Sp
eed
(m
s)
-1
(Multi Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.
11. A spring and block is placed on a fixed smooth wedge as shown. Following conclusion can be drawn about block.
(i) magnitude of its momentum will be max when Fnet on block is zero
(ii) its kinetic energy will be max when Fnet on block is zero (iii) KE of block is max when block just touches the spring. (iv) net force on block is maximum when KE = 0
12. In the figure, if F = 4 N, m = 2kg, M = 4 kg then
(A) The acceleration of m w.r.t. ground is 22m / s
3
(B) The acceleration of m w.r.t. ground is 1.2 m/s2 (C) Acceleration of M is 0.4 m/s2
F
s=0.1=0m
M
k = 0.08
Ground
z
(D) Acceleration of m w.r.t. ground is 22m / s
3
13. A particle moves along positive branch of the curve x
y2
where 3t
x ,3
x and y are
measured in metres and t in seconds, then :
(A) The velocity of particle at t = 1 s is 1ˆ ˆi j2
(B) The velocity of particle at t = 1 s is 1 ˆ ˆi j2
(C) The acceleration of particle at t = 1 s is ˆ ˆ2i j
(D) The acceleration of particle at t = 2 s is ˆ ˆi 2 j
14. Two blocks of masses m1 and m2 are connected through a massless inextensible string. Block of mass m1 is placed at the fixed rigid inclined surface while the block of mass m2 hanging at the other end of the string, which is passing through a fixed massless frictionless pulley shown in figure. The coefficient of static friction between the block and the inclined plane is 0.8. The system of masses m1 and m2 is released from rest.
m=4kg1m=2kg2
30º Fixed
g=10m/s2
=0.8
(A) The tension in the string is 20 N after releasing the system (B) The contact force by the inclined surface on the block is along normal to the inclined
surface
(C) The magnitude of contact force by the inclined surface on the block m1 is 20 3N
(D) None of these
15. A particle ‗P‘ of mass ‗m‘ is rotating in horizontal circle about vertical axis AB with the help of two strings each of length ‗L‘ as shown in
figure. The separation AB = L, and ‗P‘ rotates with angular velocity ‗‘ about axis AB. Tension in the upper and lower strings are T1 and T2
This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.
1. A particle of mass 10 kg is in equilibrium with the help of two ideal
and identical strings. Now one string is cut then, find the ratio of tension in the other string just before cutting and just after cutting.
30°30°
10 kg 2. In a car race, car A takes 4 seconds less than car B to reach the finish line and passes the
finishing line with velocity v more than car B. Assume cars start from rest and travel with constant acceleration aA = 4 m/s2 and aB = 1 m/s2. Find the value of v in m/s.
3. In the figure, find the velocity of m1 in ms–1 when m2 falls by 9m. Given m1 = m m2 = 2m (take g = 10 ms–2)
m1=0.1
m2 4. A ball is projected from some height with initial horizontal speed
20 m/s. There is a wall at a horizontal separation of 100 m from
the building. If collision is perfectly elastic find the time in sec
after which it will hit the wall. (t = 0 is taken when ball is thrown).
All surfaces one smooth.
100 m
20 m/s
5. Figure shows a smooth cylindrical pulley of radius R with centre at origin
of co-ordinates. An ideal thread is thrown over it on the two parts of ideal
thread two identical masses are tied initially at rest with co-ordinates (R, 0)
and (-R, -R) respectively. If mass at x-axis is given a slight upward jerk, it
leaves contact with pulley at (R cos, Rsin). Then find /sin.
This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is
1. The distance between 3rd and 2nd orbit of hydrogen atom is
(A) 2.646108 cm (B) 2.116108 cm (C) 2.646 cm (D) 0.529 cm
2. H–B–H bond angle in 4BH is:
(A) 180° (B) 120° (C) 109° (D) 90° 3. Which of the following has maximum lattice energy? (A) CaO (B) Na2O (C) MgO (D) BaO 4. The atomic radii of F and Ne in angstrom unit are respectively given by (A) 0.72, 1.60 (B) 1.60, 1.60 (C) 0.72, 0.72 (D) 1.60, 0.72 5. The K.E. of N molecule of O2 is x Joules at –123°C. Another sample of O2 at 27°C has a KE of
2x Joules. The latter sample contains. (A) N molecules of O2 (B) 2N molecules of O2
(C) N/2 molecules of O2 (D) N/4 molecule of O2
6. Out of the following, which does not have zero dipole moment is (A) CO2 (B) CCl4 (C) BCl3 (D) NH3 7. The wave function for 1s orbital of hydrogen atom is given by
r /a01s e
2
a0 = radius of Bohr orbit r = distance from nucleus What will be ratio of probability density of finding the electron at the nucleus to the first Bohr‘s
orbit (a0)? (A) e (B) e2 (C) 1/e (D) 0 8. The IP1, IP2, IP3, IP4 and IP5 of an element are 7.1, 14.3, 34.5, 46.8, 162.2 eV respectively.
The element is likely to be (IP ionization potential) (A) Na (B) Si (C) K (D) Ca
9. 12.25 g KClO3 on heating gives enough O2 to react completely with H2 produced by the action of the Zn on dilute H2SO4.
3 2
2KClO 2KCl 3O , 2 4 4 2
H SO Zn ZnSO H , 2 2 2
2H O 2H O
The weight of Zn required for this is: [At.wt of Zn = 65.5] (A) 9.825 g (B) 19.65 g (C) 39.3 g (D) 8.5 g
10. 2 moles of 4
FeSO in acid medium are oxidised by x moles of 4
KMnO , whereas 2 moles of
2 4FeC O in acid medium are oxidised by y moles of
4KMnO . The ratio of x and y is:
(A) 1
3 (B)
1
2 (C)
1
4 (D)
1
5
Multiple Correct Answer(s) Type
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONE or MORE are correct.
11. Which of the following statement is correct regarding H2O2?
(A) it has open booklike structure (B) it is both an oxidizing as well as reducing agent (C) it is a bleaching agent (D) it acts as only oxidizing agent 12. Which of the following will represent Boyle‘s law correctly?
(A) PV
P
(B) V
PV
(C) PV
1/P
(D) P
V 13. Which of the following pairs will not diffuse at the same rate through porous plug at same
conditions of temperature and pressure? (A) CO & NO2 (B) NO2 & CO2 (C) NH3 & PH3 (D) CO2 & N2O 14. A gas obeys the equation P(V-b) = RT. Which of the following is/are correct about the graphs
15. Highly pure dilute solution of sodium in liquid ammonia: (A) Shows blue colour (B) Exhibits electrical conductivity (C) Shows reducing properties (D) Shows oxidizing properties
SECTIONC Integer Answer Type
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).
1. 1 g of an acid (Molar mass = 150 g/mol) is completely neutralized by 1.5 g KOH. Calculate the number of neutralizable protons in acid.
2. Find out the number of angular nodes in the orbital to which the last electron of Cr enter. 3. According to molecular orbital theory, the number of electrons present in the antibonding
molecular orbitals of N2 is (are)
4. A 17 gm sample of H2O2 contains a% H2O2 by weight and requires a mL of KMnO4 in acidic
medium for comlete oxidation. Thus what is the molarity of KMnO4? 5. The value of x+y+z in following redox reaction
(Single Correct Choice Type) This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
1. In a triangle ABC, A(2, 4) and internal angular bisector of B & C are y = x & 2x + y = 3, then find the equation of BC
(A) x = 2 (B) y = 2 (C) x + y = 2 (D) none of these 2. Find the equation of minimum radius of that circle which contain all free circles S1, S2 & S3
(A) (−, −1) (2, ) (B) (2, ) (C) (−1, 2) (D) none of these
9. In the equilateral ABC the side length is 8 unit, inscribe this another triangle is form through the
midpoints of vertices A,B and C is DEF. Inside
DEF another triangle is also form through the
midpoints of vertices D,E & F is PQR Find the
area of PQR.
(A) 2 3 (B) 3
(C) 3
2 (D) none of these
A B
C
D E
F
P
Q R
10. Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement ―Suman is brilliant and dishonest if and only if Suman is rich‖
This Section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.
1. A(0, 0), B(2, 1) and C(3, 0) are the vertices of a triangle ABC, and BD is its altitude. The line
through D parallel to the side AB intersects the side BC at a point K. If the product of the areas of the triangle ABC and BDK is k, then the value of 2k is
2. If 2sinx sin x 1 then the value of 2 4 4 2cos x cos x cot x cot x is equal to
3. If 1 2 3cos 2cos 3cos 6 then 1 2 3tan tan tan equals to
4. If 2 2 2log x log y log z
4 6 3k and x3y2z = 1
Then |k| is 5. Let the co-ordinates of the circumcentre of the triangle whose vertices are A(5, – 1), B(–1, 5)
and C(6, 6) is (a, b) then [a + b] is (where [.] denotes the greatest integer function)
MATHEMATICS 1. B Take the reflection of A about internal angular bisector of B & C lie on the line BC. 2. C For centre - find the circumcentre of the centres S1, S2 & S3, For radius - find the circum radius from the centres S1, S2 & S3 and add the maximum radius
of the circles S1, S2 & S3 in the circum radius. 3. A Use the log properties 4. A
2x – y + 4 = ( x – 2y 1) For acute angle bisector use + sign 5. B 33cos2x+4sin2x Then maximum value is 35 6. D Use the homogenization 7. A Lines are x = 2 and x = 6, y = 5, and y = 9 Then centre is (4, 7) 8. A 9. B
Area = 232
4
10. A (Multi Correct Choice Type)
11. A,B,C,D
2 2 2 2 2 21 1sin A sin B sin C (1 cos A) (1 cos B) sin C
Points can be calculated by the internal and external section formula using centres of both the circles and slope can be calculated by using the condition of tangency.
14. A,B,C Use the internal and external touching condition of two circles. 15. A,C
x 1
2 x 1
9 7log 2
3 1
32x2 + 7 = 4(3x1 + 1)
x 1 x 1(3 1)(3 3) 0
x 1 = 0 or x 1 = 1 x = 1, 2.
SECTION–C (Integer Type)
1. 1 Calculate the area of ABC and BDK then multiply these two 2. 2 Given sin x + cos x + tan x + cot x + sec x + cosec x = 7
1 sinx cosx
sinx cosx 7sinx cosx sinx cosx
1 1
sinx cosx 1 7sinx cosx sinxcosx
2 2
2 21 sin2x 1 7
sin2x sinx
2 2
1 t t 2 7t 2 , where t = sin 2x
3 2t 44t 36t 0
2t 44t 36 0 [sin 2x 0]
244 44 4 36
t 22 8 72
sin2x 22 8 7
3. 0
Given 1 2 3cos 2cos 3cos 6
1 2 3cos cos cos 1
1 2 3 0
1 2 3tan tan tan 0
4. 8 Use the log property. 5. 5 Circum centre can be calculated by using the perpendicular bisectors of vertices of the
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
You are not allowed to leave the Examination Hall before the end of the test.
INSTRUCTIONS
Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.
G. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Parts.
3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
4. Each part is further divided into two sections: Section-A & Section-C
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.
H. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet. 2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and write in ink
your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers.
C. Marking Scheme For All Three Parts. (i) Section-A (01 – 8) contains 10 multiple choice questions which have only one correct answer. Each question carries +3
marks for correct answer and – 1 mark for wrong answer. Section-A (09 – 12) contains 4 multiple choice questions which have one or more than one correct
answer. Each question carries +4 marks for correct answer. There is no negative marking.
(ii) Section-B (01 – 02) contains 2 Matrix Match Type questions containing statements given in 2 columns. Statements in the first column have to be matched with statements in the second column. Each question carries +8 marks for all correct answer. For each correct row +2 marks will be awarded. There may be one or more than one correct choice. No marks will be given for any wrong match in any question. There is no negative marking.
(iii) Section-C (01 – 06) contains 6 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.
Name of the Candidate :__________________________________________
Batch :___________________ Date of Examination :___________________
Enrolment Number :______________________________________________
PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS SECTION – A
(Single Correct Choice Type)
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. A cubical box of wine has a small spout located in one of the bottom
corners. When the box is full and placed on a level surface, opening
the spout results in a flow of wine with a initial speed of v0 (see
figure). When the box is half empty, someone tilts it at 45° so that the
spout is at the lowest point (see figure). When the spout is opened
the wine will flow out with a speed of
(A) v0 (B) v0/2
(C) 0v 2 (D) 4
0v 2
2. A vertical tank, open at the top, is filled with a liquid and rests on a smooth horizontal surface. A small
hole is opened at the centre of one side of the tank. The area of cross-section of the tank is N times the
area of the hole, where N is a large number. Neglect mass of the tank itself. The initial acceleration of the tank
is
(A) g
2N (B)
g
2N
(C) g
N (D)
g
2 N
3. The figure shows an isosceles triangular plate of mass M and base L.
The angle at the apex is 90°. The apex lies at the origin and the base
is parallel to X–axis. The moment of inertia of the plate about the y-
axis is
(A) 2ML
6 (B)
2ML
8
(C) 2ML
24 (D) none of these
4. A cone of radius r and height h rests on a rough horizontal surface, the coefficient of friction between
the cone and the surface being µ. A gradually increasing horizontal force F is applied to the vertex of
the cone. The largest value of µ for which the cone will slide before it topples is
PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY SECTION – A
(Single Correct Choice Type)
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and
(D) out of which ONLY ONE is correct.
1. B2O3 + CaF2 + conc. H2SO4 A + B +C Where ‗A‘ is Boron containing compound, A is (A) B2H6 (B) H3BO3 (C) Ca2B6O11 (D) BF3 2. Inorgnaic Benzene (Borozine) is more reactive than that of Benzene is due to: (A) Electronegativity difference in B and N (B) Non-aromatic character of inorganic benzene (C) due to non planar structure of inorganic benzene (D) all of these 3. At 25°C, a saturated solution of BaSO4 is 3.9 × 10
–5 M. What is its solubility in 0.1 M Na2SO4 solution?
(A) 1.5 × 10–9
M (B) 1.5 × 10–8
M (C) 2.4 × 10
–7 M (D) 2.5 × 10
–9 M
4. Calculate the pH of 0.1 M solution of NaHCO3; K1 = 4 × 10
5. Which of the following does not work as a Buffer solution? (A) Na2B4O7 Solution (B) NaHCO3 / NaOH (C) NH4Cl (0.1M, 500 ml) + NaOH (0.01M, 500 ml) (D) All of them
6. What can be concluded about the values of H and S from this graph?
(A) H > 0, S > 0 (B) H > 0, S < 0
(C) H < 0, S > 0 (D) H < 0, S < 0
7. The rate constant for the reaction 2N2O5 4NO2 + O2 is 3 × 10
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.
9. Which of the following option is true? If o 1
Ioniz(HCN) 45.2kJmol and
o 1
ioniz 3H (CH COOH) 2.1kJ mol
(A) pKa(HCN) =pKa(CH3COOH) (B) pKa(HCN) > pKa(CH3COOH) (C) Ka(HCN) < Ka(CH3COOH) (D) Ka(HCN) > Ka(CH3COOH) 10. For which of the following reactions, the degree of dissociation cannot be calculated from the vapour
density data
(A) 2 22HI(g) H (g) I (g)
(B) 3 2 22NH (g) N (g) 3H (g)
(C) 2 22NO(g) N (g) O (g) (D)
5 3 2PCl (g) PCl (g) Cl (g)
11. Which of the following statement(s) is/are true? (A) Work is a state function (B) Temperature is a state function (C) Change of state is completely defined when initial and final states are specified (D) Work appears at the boundary of the system 12. Which of the following is/are endothermic reaction (s)? (A) Combustion of methane (B) Decomposition of water (C) Dehydrogenation of ethane to ethylene (D) Conservation of graphite to diamond
This section contains 6 questions. The answer to each question is a single-digit integer, ranging from 0 to 9.
The correct digit below the question number in the ORS is to be bubbled.
1. No. of B–OH bonds in Borax (Na2B4O7.10H2O) are 2. Amongst the following the total numbers of compounds whose aqueous solution turns red litmus paper
blue is KCN, K2SO4, (NH4)2C2O4, NaCl, Zn(NO3)2, FeCl3, K2CO3, NH4NO3, HCN 3. The pressure necessary to obtain 50% dissociation of PCl5 at 400 K is numerically equal to ‗x‘ times of
Kp, x is 4. Total number of extensive properties among the following is heat capacity, Molar heat capacity, Molar Volume, Resistance, Emf. density, volume, enthalpy, entropy. 5. Ratio of the rate of diffusion of He and CH4 under identical condition of P and T will be. 6. Which of the following elements form amphoteric oxide? Na, Be, Mg, B, Al, Ca, Si.
PPPAAARRRTTT ––– IIIIIIIII ::: MMMAAATTTHHHEEEMMMAAATTTIIICCCSSS SECTION – A
(Single Correct Choice Type) SECTION – A
1. C
pq
1a d t 1
pq (For A.P).
2. A
a
.a.ar 1 a 1r
is a root.
b c
3. D For z = x + iy, we get x
2 = y
2.
4. C z will lie on AB (line segment), A(–3, 0) and B(1, 0). Then 3 ≤│z – 4│≤ 7. 5. B If tangents at P and Q meet at R, and S is focus then SP . SQ = SR
2.
6. B The centroid always lie on the axis of the parabola, and parabola is,
2
2 2 3x 4y 12(x 5) (y 6)
5
Hence, S ≡ (5, 6) and Axis ≡ 4x – 3y – 2 = 0 7. C Total number of oranges = (1) + (1 + 2) + (1 + 2 + 3) + …… + (1 + 2 + ….. + 10)
=10
n
n(n 1)220
2
8. B (15x – 5y
2)2 + (5y – 3z)
2 + (3z – 15x)
2 = 0
x y z x y z
21 3 5 9
y 6 .
9. A, B (a – c)(b – c)(a + d)(b + d) = q
2 – p
2.
10. C
If the reflection of z1 in the line az az c is z2, then 2 1az az c , and so in our case 2
SECTION-B 1. A → (r, s), B → (p, q), C → ((r, s), D → (p, q) a < b < c < d, let λ be +ve. Let f(x) = (x – a)(x – c) + λ(x – b)(x – d) = 0 f(a) = +ve and f(b) = –ve, f(c) = –ve and f(d) = +ve. All other parts can also be done in the same manner. 2. A → (q), B → (s), C → ((q), D → (p, q)
SECTION–C
1. 2 2. 1
Let the parabola be y2 = 4ax and coordinates of P and Q on this parabola are 2
1 1P at ,2at and
2
2 2Q at ,2at ; T is the point of intersection of tangents at t1 and t2,
Coordinates of T ≡ {at1, t2, a(t1 + t2)} Similarly P‘ ≡ {at3t1, a(t3 + t1)} Q‘ ≡ {at2t3, a(t2 + t3)} Let TP‘ : TP = λ : 1
30. Three moles of an ideal monatomic gas performs a cycle
1 2 3 4 1 as shown. The gas temperatures in different states are T1 = 400 K, T2 = 800 K, T3 = 2400 K and T4 = 1200 K. The work done by the gas during the cycle is
(a) 1200 R (b) 3600 R (c) 2400 R (d) 2000 R
Section – 1I Chemistry
(1) In the following carbocations, the stability order is:
It is true that (A) Only II and IV are chiral compounds (B) All four are chiral compounds (C) Only I and II are chiral compounds (D) Only III is a chiral compound
(4) An alkene on oxidation ozonolysis gives adipic acid. The alkene is (A) cyclohexene (B) 1-methylcyclopentene (C) 1, 2 – dimethylcyclobutene (D) 3-hexene (C) 1, 2 – dimethylcyclobutene (D) 3-hexene
(5) But-1-ene may be concerted to butane by reaction with (A) Pd/H2 (B) Zn/HCl (C) Sn/HCl (D) Zn-Hg
(6) Acetone will be formed by the ozonolysis of (A) but-1-ene (B) but-2-ene (C) iso butene (D) but-2-yne
(7) How many 1°carbon atom will be present in a simplest hydrocarbon having two 3° and one 2° carbon atom?
(A) 3 (B) 4 (C) 5 (D) 6
(8) IUPAC name of is: (A) 5-methyl hexanol (B) 2-methyl hexanol (C) 2-methyl hex-3-enol (D) 4-methyl pent-2-en-1-ol
(9) Which of the following compounds is optically active? (a) CH3CH2COOH (b) CH3CHOHCOOH (c) HOOC.CH2.COOH (d) CH3.CO.COOH
(10) Which of the following does not possess any element of symmetry? (a) ethane (b) (+) tartaric acid (c) carbon tetrachloride (d) meso tartaric acid
(11) Which of the following new man projection formula for 1, 2 - dichloro ethane represents the stable staggered from ?
(a)
Cl Cl
H
HH
H
(b)
ClCl H
H
H
H
(c)
ClClH
H
H
H
(d)
ClH
H
H
HCl
(12) Which of the following structure are super imposable?
(1)
H
Br
HO
Me
Me
Et
(2)
H
Br
OH
Me
Me
Et
(3)
H
Br
OH
Me
Me
Et
(4)
HBr
HO
Me
Et
Me (a) 3 and 4 (b) 1 and 3 (c) 2 and 4 (d) 2 and 3
(13) Which of the following structures are non superimpossable (Mirror Image)?
(1)
H
Br
HO
Me
Et
Me (2)
H
Br
OH
Me
Et
Me (3)
H
Br
OH
Me
Et Me
(4)
HBr
HO
Me
Et
Me (a) 1 and 2 (b) 2 and 4 (c) 1 and 4 (d) 1 and 3
(14) Among the following compounds, the decreasing order of reactivity towards electrophilic substitution is
Mathematics 1. A 2. B 3. A 4. D 5. A 6. A 7. C 8. A 9. C 10. C 11. C 12. A 13. B 14. A 15. A 16. A 17. D 18. D 19. A 20.A 21. C 22. D 23. C 24. B 25. A 26. B 27. B 28. D 29. C 30. D
8. A wave disturbance in a medium is described by(select incorrect option)
y(x, t) = 0.02 cos (50 t + /2) cos (10 x), where ‗x‘ and ‗y‘ are in metre and ‗t‘ in seconds. (A) A node occurs at x = 0.15 m (B) An antinode occurs at x = 0.3 m (C) The speed of the component wave is 5.0 m/s (D) The wavelength is 0.1 m. 9. An organ pipe filled with oxygen gas at 47ºC resonates in its fundamental mode at a frequency of 300
Hz. If it is now filled with nitrogen gas, at which temperature will it resonate at the same frequency, in the fundamental mode ?
(A) 7ºC (B) 41.1°C
(C) 280ºC (D) 92.7°C
Reasoning Type
This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D),
out of which ONLY ONE is correct.
10. STATEMENT-1 : Compression and rarefaction involve changes is density and pressure.
STATEMENT-2 : When particles are compressed, density of medium increases and when they
are rarefied, density of medium decreases.
(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for
Statement – 1.
(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation
for Statement – 1.
(C) Statement – 1 is True, Statement – 2 is False.
(D) Statement – 1 is False, Statement – 2 is True.
11. STATEMENT-1 : Coefficient of adiabatic elasticity of air is greater than the coefficient of
isothermal elasticity.
STATEMENT-2 : Heat is exchanged freely in an isothermal change, but not in an adiabatic
change.
(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for
Statement – 1.
(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation
for Statement – 1.
(C) Statement – 1 is True, Statement – 2 is False.
(D) Statement – 1 is False, Statement – 2 is True.
Paragraph for Questions 17 and 19 One end of an ideal spring is fixed to a wall at origin O and axis of spring is parallel to x–axis. A block of mass m = 1 kg is attached to free end of the spring and it is performing SHM. Equation of position of the block in co–ordinate system shown in figure is x = 10 + 3 sin (10 t) where t is in second and x in cm. Another block of mass M = 3 kg, moving towards the origin with velocity 30 cm/s collides with the block performing SHM at t = 0 and gets stuck to it.
Om M
x
17. Angular frequency of oscillation after collision is
(A) 20 rad/s (B) 5 rad/s (C) 100 rad/s (D) 50 rad/s 18. New Amplitude of oscillation is (A) 3 cm (B) 20 cm
(C) 10 cm (D) 100 cm
19. New equation for position of the combined body is
(A) (10 + 3 sin 5 t) cm (B) (10 + 3 sin 5 t + π) cm
(C) (10 + 3 cos 10 t) cm (D) (10 – 3 cos 10 t) cm
SECTION–B
MatrixMatch Type This Section contains 3 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or 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.
p q r s
p q r s
p q r s
p q r s
A B C
D
p q r s t
t
t
t
t
1.
Column I Column II
(A) Temperature of a gas (P) Internal energy increases
(B) Work done by the gas (Q) Intermolecular force decreases
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and
(D), out of which ONLY ONE is correct.
1. A large number of liquid drops each of radius r coalesce to form a single drop of radius R. The
energy released in the process is converted into the kinetic energy of the big drop so formed.
Assuming that all the particles of the big drop move with the same speed v, this speed is given
by (given surface tension of liquid is T, density of liquid is )
(A) 6 1 1T
r R
(B)
4 1 1T
r R
(C)
6 1 1T
r R
(D)
4 1 1T
r R
2. Which of the following will have a different time period, if taken to the moon ?
(A) A simple pendulum.
(B) A spring mass system oscillating vertically in the gravitational field.
(C) A torsion pendulum.
(D) None of these 3. A wave is represented by the equation :
1 1y (1mm)sin 50s t (2.0m )x
+ 1 1(1mm)cos 50s t (2.0m )x
(A) The wave–velocity is zero, since it is a standing wave.
(B) A node is formed at 3
8x m
.
(C) The amplitude of the oscillation at the antinode is 3 mm.
(D) Energy transfer occurs along the positive x–axis.
4. A solid sphere of mass m is lying at rest on a rough horizontal
surface. The coefficient of friction between ground and sphere is
. The maximum value of F, so that sphere will not slip, is equal to
(A) 7
mg5 (B)
4mg
7 (C)
5mg
7 (D)
7mg
2
F
5. Two constant forces 21 FandF
acts on a body of mass 8 kg. These forces displaces the body
from point P(1, –2, 3) to Q(2, 3, 7) in 2s starting from rest. Force 1F
is of magnitude 9 N and is
acting along vector )ˆˆ2ˆ2( kji . Work done by the force 2F
is
(A) 80 J (B) –80 J (C) –180 J (D) None of these
Space for rough work
6. A particle is dropped from a height equal to the radius of the earth
above the tunnel dug through the earth as shown in the figure. R : Radius of earth. M : Mass of earth. (A) Particle will oscillate through the earth to a height R on both
sides (B) Particle will execute simple harmonic motion (C) Motion of the particle is non periodic
(D) Particle passes the centre of earth with a speed = 2R
GM2
R
C
7. A point moves such that its displacement as a function of time is given by x
8. The moment of inertia of a rod about an axis through its centre and perpendicular to it is
2
12
ML (where
M is the mass and L, the length of the rod). The rod is bent in the middle so that the each halves make an angle of 30º with that axis. The moment of inertia of the bent rod about the same axis would be (The axis lies in the plane of structure)
(A)
2ML
96 (B)
2ML
48
(C)
2ML
12 (D)
2ML
8 3
Multiple Correct Answer(s) Type
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONE or MORE are correct.
9. A sound wave is traveling along positive x-direction.
Displacement (y) of particles from their mean positions at any time t is shown in the figure. (A) Particle located at S has zero velocity. (B) Particle located at T has its velocity in the negative direction. (C) Change in pressure at S is zero
Q R S T xP
Y
(D) Particles located near R are under compression.
13. If a maxima is formed at a detector then, the magnitude of wavelength of the wave produced
is given by : (Select wrong option)
(A) R (B) R
2
(C) R
4
(D)
R
3
14. If a minima is formed at the detector then, the magnitude of wavelength of the wave
produced is given by
(A) R2 (B) R2
3
(C) 2 R
3 (D)
2 R
5
15. The maximum intensity produced at D is given by
(A) 4I0 (B) 2I0
(C) I0 (D) 3I0
Paragraph for Question Nos. 16 to 17
The figure shows the variation of internal energy (U) of a
2 moles of Argon gas with its density in a cyclic process
ABCA. The gas was initially in the state A whose pressure
and temperature are PA = 2 atm TA = 300 K respectively. It
is also stated that the path AB is a rectangular hyperbola
and the internal energy of the gas at state C is 3000 R.
Based on the above information answer the following
questions.
BC
A
3000 R
U(Joule)
kg/m-3
16. Select the best option (A) The process AB is isobaric, BC is adiabatic and CA is isochoric. (B) The process AB is adiabatic, BC is isothermal and CA is isochoric. (C) The process AB is isochoric, BC is isothermal and CA is isobaric (D) The process AB is isobaric, BC is isothermal and CA is isochoric. 17. The Heat supplied to the gas in the process AB is (A) 700 R (B) 3500 R (C) 4400 R (D) 1600 R