FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com FULL TEST – IV Time Allotted: 3 Hours Maximum Marks: 432 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 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 has only one section: Section-A. 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 black pen for each character of your Enrolment No. and write 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 to 03 and 10 to 12) contains 6 multiple choice questions which have only one correct answer. Each question carries +8 marks for correct answer and – 2 mark for wrong answer. Section-A (04 to 09 and 13 to 30) contains 24 multiple choice questions which have only one correct answer. Each question carries +4 marks for correct answer and – 1 mark for wrong answer. Name of the Candidate Enrolment No. ALL INDIA TEST SERIES FIITJEE JEE (Main)-2016 FIITJEE Students From Classroom / Integrated School Programs have secured to 2 Zonal, 6 State & 18 City Topper Ranks. 33 in Top 100, 78 in Top 200 and 205 in Top 500 All India Ranks bagged by FIITJEE Students from All Programs have qualified in JEE (Advanced), 2015.
Time Allotted: 3 Hours Maximum Marks: 432 Please r ead the inst ruct ions carefu l l y. You are a l lot ted 5 m inutes
speci f i ca l l y for th is purpose. You are not a l lowed to leave the Exam inat ion Hal l before the end of
the test .
INSTRUCTIONS
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 has only one section: Section-A. 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 black pen for each character of your
Enrolment No. and write 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 to 03 and 10 to 12) contains 6 multiple choice questions which have only one correct answer. Each question carries +8 marks for correct answer and – 2 mark for wrong answer.
Section-A (04 to 09 and 13 to 30) contains 24 multiple choice questions which have only one
correct answer. Each question carries +4 marks for correct answer and – 1 mark for wrong answer.
This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. Four particles each of mass M, are orbiting in a circle of radius r in the same sense of rotation
due to their mutual gravitational force of attraction. The time period of revolution is
(A)
3rT 2GM 1 2 2
(B)
3rT 4GM 1 2 2
(C)
32rTGM 1 2 2
(D)
32rT 2GM 1 2
2. For a silver atom, energy corresponding to K transition is 21.75 KeV. Also minimum energy of a
striking electron so as to produce L X-rays is 3.56 KeV. Now, if electron with an energy of 23 KeV strike a silver target the characteristic X-rays spectrum will have : (A) Only K and L X-rays (B) Only L X-rays
(C) K and L X-rays (D) Only K X-rays 3. In n, 2n, 3n are the fundamental frequencies of the three segments into which a string is divided
by placing required number of bridges below it. If n0 is the fundamental frequency of the string, then (A) n0 = 3n (B) n0 = 6n
(C) 03nn5
(D) 06nn11
4. Two SHMs are represented by equations 1 2y 6cos 6 t / 6 , y 3 3 sin3 t cos3 t
(A) Ratio of their amplitudes is 1 (B) Ratio of their amplitudes is 1/2 (C) Ratio of their maximum velocities is 1 (D) Ratio of their maximum velocities is 1/2
5. From the following transistor characteristics, what can be inferred? (A)
1 2 3CE CE CEV V V
(B) 1 3
2
CE CECE
V VV
2
(C) 2 1 2CE CE CEV V V
(D) 3 2 1CE CE CEV V V
(mA)
1CEV 2CEV
3CEV
BEV (V)
IB
6. A particle is dropped to move along the axis of a concave mirror of focal
length f from a height f/2 as shown in the figure. The acceleration due to gravity is g. Find the maximum speed of the image.
(A) 3fg16
(B) 27fg16
(C) 3 fg4
(D) fg16
f
f2
7. A spherical metal ball of radius ‘r’ is lying at the bottom of
a stationary container containing liquid of density as shown in the figure. Find the force exerted on the upper hemispherical portion of the sphere due to gauge pressure ( 0P atmospheric pressure)
r 4r
(A) 2
0r 3P 7r g3
(B) 2
0r 3P 7r g2
(C) 20r 3P 7r g (D) 2
02 r 3P 7r g 8. A spring mass system executes damped harmonic oscillations given by the equation
bt2my Ae sin ' t
where
2
2k b'm 4m
where the symbols have their usual meanings. If a 2 kg mass (m) is attached to a spring of force constant (K) 1250 N/m, the period of the
oscillation is / 12 s . The damping constant ‘b’ has the value. (A) 9.8 kg/s (B) 2.8 kg/s (C) 98 kg/s (D) 28 kg/s
9. White light (wavelength 4000-7000 Ao) is incident normally on a glass plate of thickness one micron and refractive index 1.5. Number of strongly reflected wavelengths by the plate is (A) 1 (B) 2
(C) 3 (D) 4 10. Electromagnetic radiations fall on a metallic body whose work function is 2eV. For a particular
radiation of frequency v, the maximum kinetic energy of the photoelectrons is found to be 4 eV.
What would be the maximum kinetic energy of photoelectrons for the radiation of frequency 5v3
?
(A) 6 eV (B) 14 eV3
(C) 8 eV (D) 10 eV3
11. In the figure shown A and B are two thin
transparent slabs of refractive indices 1 and
2 2 1 and there is no gap between A and B. A beam of light of wavelength falls on A normally. A part of it reflects at upper face and a part reflect at the interface of A and B and then come back to the previous medium. The phase difference between two reflected waves at a particular point at any time t is
12. A capacitor is connected across an inductor. At time t = 0 charge on the capacitor is equal to 12
qmax, where qmax is the maximum charge on the capacitor. The time t, at which the energy stored in the capacitor is equal to the energy stored in the inductor is
(The inductance of the inductor is L and capacitance of the capacitor is C. Resistance of the circuit is zero)
(A) 2 LC (B) 1 LC2
(C) LC2
(D) 12 LC
13. A long horizontal rod has a bead which can slide along its length, the bead initially at a distance L
from end A of the rod. The rod is set in angular motion in the horizontal plane about end A with constant angular acceleration . If the coefficient of friction between rod and the bead is , and gravity is neglected then graph between frictional force acting on bead and the time is
14. A block of mass 4 m and a conducting square loop of mass m (with a cell of emf E and resistance R) are connected by a light insulating string passing over a frictionless pulley as shown in the figure. The plane of the loop (initially at rest) is perpendicular to magnetic field. As the system is released
x x x x x x x x
x x x x x x x x x x x
E
4m 0
R g
x
y
z
(A) the block does not move (B) the loop starts rotating about y-axis.
(C) the loop moves down with constant velocity (D) the acceleration of the block is constant but not zero
15. A conductor of (area A) having charge density is placed
perpendicularly to a uniform electric field E and is connected to a spring (of spring constant k) whose other end is fixed. Now the spring is replaced by similar spring having length one third of the original spring. The extension of spring in this position is
E
k
E
(A) 2E Ak (B) 2E A
3k
(C) E A3k (D) 2E A
4k
16. A uniform rope of mass m and length L hangs from the ceiling. A small wave
pulse is created at bottom, then which of following is correct regarding wave pulse.
(1) Rate of change of speed with respect to time varies (2) Rate of change of speed with respect to time is constant (3) Rate of change of speed with respect to time is zero (4) Wave speed varies (A) 1, 3 (B) 1, 4 (C) 2, 4 (D) 3, 4
17. A conducting rod of length l is rotating with constant angular velocity about point O in a uniform magnetic field B as shown in the figure. The emf induced between ends P and Q will be
(A) 21B4
l (B) 25 B10
l
(C) zero (D) 21B2
l
3l/4 l/4 P O
Q
x x x x x
x
x
x x x x x
x
18. A solid sphere of mass M and radius R is placed vertically on a
rough horizontal surface. If a horizontal force F is applied at a distance R/6 below the centre line parallel to the diameter of the sphere, the direction of frictional force will be
(A) forward (B) backward (C) depends upon value of F (D) insufficient information
R/6 F
R M
19. In a potentiometer experiment, two cells connected in series get balanced at 9 cm length on the
wire. Now the connections of terminals of the cell of lower emf are reversed, then the balancing length is obtained at 3 cm. The ratio of emf’s of two cells will be (A) 1 : 2 (B) 2 : 1
(C) 1 : 4 (D) 4 : 1 20. One mole of a monoatomic ideal gas undergoes the process A
B as indicated in the given P-V diagram. The molar heat capacity for the process is (A) 3R/2 (B) 13 R/6
21. If l1 and l2 (> l1) are the lengths of an air column for the first and second resonance when a tuning fork of frequency n is sounded on a resonance tube, then the minimum distance of the anti-node from the top end of the resonance tube is
(A) 2 12 l l (B) 1 21 22
l l
(C) 2 132l l
(D) 2 1
2l l
22. A thin convex lens is split into two halves. One of the
halves is shifted along the optical axis. The separation between fixed luminous point object O and fixed screen is D = 180 cm. The magnification of image formed by one of the half lens is m = 2. It follows that (A) The separation between the lens is 90 cm (B) The separation between the lens is 60 cm
(C) The focal length of the lens is 45 cm (D) The focal length of the lens is 60 cm
180 cm
O screen
23. A block of mass 1 kg is placed on a smooth horizontal surface as
shown. Its center is tied to a string of length l = 10 m and other end of the string is connected of ball of same mass. Ball B is released from the position shown. It falls under gravity and the string becomes taut. The kinetic energy of block and ball of the bodies just after string is
24. Calculate the moment of inertia of uniform thin hemispherical shell of mass M and radius R about axis X - X' shown in figure.
(A) 25 MR3
(B) 27 MR6
(C) 22 MR3
(D) None of these
3
X
X'
25. A small particle of mass M is released from rest from
point A inside a frictionless fixed hemispherical bowl as shown. The graph between the ratio(r) of magnitude of centripetal force and normal reaction on the particle at any point on the bowl as a function of cos is
R
r
1 +1 cos
r
r r 1
1 1
+1
+1 +1
cos
cos cos
(A) (B)
(C) (D)
26. In a certain region of space there exists a constant and uniform magnetic
field of induction B. The width of the magnetic field is a. A charge particle having charge q is projected perpendicular to B
and along the width of the
field. If deflection produced by the field perpendicular to width is d, the magnetic of the momentum of the particle is
27. If two uniform spherical drops of a liquid same mass, radius, and falling freely with a terminal velocity of 3 16 m/s. Coalesce to form bigger drop, then the terminal velocity with which the bigger drop fall is
(A) 8 m/s (B) 4 m/s (C) 10 m/s (D) None of these 28. Binding energy of A = X MeV, B = Y MeV, C = Z MeV [X > Y > Z]. A person in a lab tries to break
each nucleus into its constituents with the help of energy S MeV [y < S < x], then which of the following nuclei may break?
(A) B and C (B) C and A (C) A and B (D) Only C 29. A mono chromatic light is used in Young’s double slit experiment when one of slits is covered by
a transparent sheet of thickness 51.8 10 m, made of material of refractive index 1 no. of fringes
which shift is 18. When another sheet of thickness 53.6 10 m made of material of refractive index 2 is used; no. of fringes which shift is 9. Relation between 1 2 and is given by (A) 2 14 3 (B) 1 14 3
(C) 2 13 4 (D) 1 22 4 30. In the circuit shown in the figure, K1 is open. The charge
on capacitor C in steady state is q1. Now key is closed and at steady state charge on C is q2. The ratio of charges q1 and q2 is (A) 5/3 (B) 3/5
This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. Picric acid is
3. The heats of neutralization of four acids A, B, C and D are –13.7, –9.4, –11.2 and –12.4 kcal respectively, when they are neutralized by a common base. The acidic character obeys the order:
(A) A > B > C > D (B) A > D > C > B (C) D > C > B > A (D) D > B > C > A 4. At constant volume and at 27oC, the heat of combustion of 7.8 g of benzene is 327 kJ. What will
be the heat of combustion of benzene at constant pressure (R = 8.3 J/mol-K) (A) 3273 kJ (B) 3278 J (C) 327.3 kJ (D) 32.73 kJ 5.
10. A compound D (C8H10O) upon treatment with alkaline solution of iodine gives a yellow ppt. The filtrate on acidification gives a white solid E (C7H6O2). The structure of ‘D’ is
CH CH3
OHCH2 CH2 OH
COOH CH2CH3
(A) (B)
(C) (D)
11. In which of the following reaction the final product is neither acid nor an acid salt?
Ph CHO Tollen's reagent CH3 CH2 CH3KMnO4/OH
Ph CHO Fehling solution Ph CH2 OH K2Cr2O7/H+
(A) (B)
(C) (D)
12. Which optically active compound on reaction with LiAlH4 will give optically inactive compound?
14. If the electronic velocity is 61.09 10 m/s, then electron may be revolving in the (A) 1st orbit of hydrogen (B) 1st orbit of helium
(C) 2nd orbit of hydrogen (D) 2nd orbit of helium 15. The amount of current which produces hydrogen gas at the rate of 1 cc. per second under
standard conditions - (A) 17.22 ampere (B) 8.61 ampere
(C) 25.83 ampere (D) 4.30 ampere 16. If the density of a mixture of O2 & N2 at NTP is 1.3 g/l, then (A) partial pressure of O2 will be 0.28 atm (B) partial pressure of O2 will be 29.12 atm (C) partial pressure of O2 will be 1 atm (D) partial pressure of O2 will be 0.72 atm 17. The rms speed of oxygen molecule is 24.92 10 m/sec. then
(A) the temperature of the oxygen molecule is 310oC (B) the temperature of the oxygen molecule is 37oC (C) the temperature of the oxygen molecule is 37 K (D) the temperature of the oxygen molecule is 370 K 18. What is the density of Na2O having antifluorite-type crystal structure, if the edge lengh of cube is
100 pm and what is the effect on density by 0.05% Frankel defect? (A) 823.5 g/cm3, density decreases (B) 414.16 g/cm3, density decreases (C) 823.5 g/cm3, density remains same (D) 414.16 g/cm3, density remains same 19. Mole fraction of component A in vapour phase is 1 and that of A in liquid phase is 1 , then
o oA BP vapour pressure of A, P vapour pressure of pure B . The total pressure of liquid is
20. The vapour pressure of 1 molal glucose solution at 100oC will be (A) 760 mmHg (B) 76.0 mmHg
(C) 1 atm (D) 746.32 mmHg 21. The standard free energy of formation of AgCl (s) at 25oC is 109.7 kJ/mol and H Cl (aq)
is 131.2 kJ/mol. Find oE of a cell made up with standard hydrogen electrode, and Cl / Ag / AgCl s
(A) 0.446 V (B) 0.669 V (C) 0.1115 V (D) 0.223 V
22. For the elimentary reaction 1
2
K
K2A B , the rate of disappearance of A is equal to
(A) 21
2
2KA
K (B) 2
1 22K A 2K B
(C) 21 22K A 2K B (D) 1 22K K A
23. In an experiment, 200 ml of 0.5 m oxalic acid is shaken with 10 g of activated charcoal & filtered.
The concentration of the filtrate is reduced to 0.4 m. The amount of adsorption is (A) 0.9 (B) 1.8 (C) 0.18 (D) 0.09 24. a fA B, H 10 kJ/mol, E 50 kJ/mol, then Ea of B A will be
(A) 40 kJ/mol (B) 50 kJ/mol (C) 50 kJ/mol (D) 60 kJ/mol 25. In the reaction, 3 2 22Cu NO CuO NO O . On balancing
(A) 1 mole Cu (NO3)2 gives 1 mole of O2 (B) 1 mole Cu (NO3)2 gives 2 moles of O2 (C) 1 mole Cu (NO3)2 gives 1/2 moles of O2 (D) 1 mole Cu (NO3)2 gives 3 moles of O2
26. If the pH of the half-equivalence point of an amino acid is 2.286 with HCl & 9.719 with NaOH then, the pH of isoelectric point will be
(A) 6.003 (B) 7.002 (C) 5. 004 (D) 6.010 27. Which of the following match is incorrect? (I) XeOF2 T-shaped (II) XeO2F2 Square planar (III) XeO3 Pyramidal (IV) XeF6 Distorted octahedron
(A) (I) (B) (II) (C) (III) (D) (IV) 28. The structure of glycine at isoelectric point is
(A) 2 2H N CH COOH (B) 2 2H N CH COO
(C) 3 2H N CH COOH (D) 3 2H N CH COO
29. Correct statement is (A) [Co(NH3)6]3+ has hybridization d2sp3 & octahedral shape (B) [Ni(CN)4] 2 has hybridization dsp2 & square planar shape (C) [Ni(CO)4] has hybridization sp3 & tetrahedral shape
(D) All are correct 30. Correct statement is :
(A) During extraction of Mg, MgCl2 + NaCl is electrolysed (B) During extraction of Pb, NaCN removes ZnS & PbS during floatation (C) During electrolytic refining of Zn, electrolyte is ZnSO4 + H2SO4 (D) All are correct
This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. Px 2y 1 is normal to parabola 2y 4ax for:
(A) no value of P (B) exactly one value of P (C) exactly two values of P (D) exactly three values of P
2. The number of solutions of the matrix equation 2 1 1X
2 3
is
(A) more than 2 (B) 2 (C) 0 (D) 1
3. If 2
x2
d xy sin x e ,then dy
(A) x 1( sinx e ) (B) x
x 2
sinx e(cos x e )
(C) x
x 3
sinx e(cos x e )
(D) x
x 3
sin x e(cos x e )
4. The line 2x y 1 0 is tangent to the circle at the point (2,5) and the centre of the circles lies on
10. The area bounded by the two branches of curve 2 3(y x) x and straight line x=1 is (A) 1/5 sq. units (B) 3/5 sq. units (C) 4/5 sq. units (D) 8/4 sq. units
11. The population of a country increases at a rate proportional to the number of inhabitants. If the
population doubles in 30 years, then the population will triple in approximately (A) 30 years (B) 45 years (C) 48 years (D) 54 years
12. If z1 is a root of the equation n n 1
o 1 n 1 n ia z a z .......a z a 3,where a 2for i=0,1,......,n. Then
(A) 11z3
(B) 11z4
(C) 11z4
(D) 1z3
13. The ratio of the area of a regular polygon of n sides inscribed in a circle to that of the polygon of
same number of sides circumscribing the same circle is 3:4. Then the value of n is (A) 6 (B) 4 (C) 8 (D) 12
14. Differential equation of the family of circles touching the line y= 2 at (0,2) is
(A) 2 2 dyx (y 2) (y 2) 0dx
(B) 2 dxx (y 2) 2 2x y 0dy
(C) 2 2 dxx (y 2) y 2 y 2 0dy
(D) None of these
15. Two vertices of a triangle are (5,-1) and (-2,3). If orthocentre of the triangle is origin, then the co-
ordinates of third vertex is (A) (4,7) (B) (3,7) (C) (-4,-7) (D) (4,-7)
