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FIITJEE
JEE (Main), 2016

HALF COURSE TEST V
Time Allotted: 3 Hours
Maximum Marks: 432
Pl ea s e r ea d t h e i n s t r u c t i o n s c a r ef u l l y. Yo u a r e a l l o t t ed 5 m i n ut es
s p ec i f i c a ll y f o r t h i s p u r p o s e.
Yo u a r e n o t a ll o wed t o l ea v e t h e E xa m i n at i o n Ha ll b ef o r e t h e en d o f
t h e t es t .
INSTRUCTIONS
A. General Instructions
1.
2.
3.
4.
5.
Attempt ALL the questions. Answers have to be marked on the OMR sheets.
This question paper contains Three Parts.
Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
Each part has only one section: Section-A.
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 02 and 09 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.
Section-A (03 to 08) contains 6 multiple choice questions which have only one correct answer.
Each question carries +8 marks for correct answer and 2 marks for wrong answer.
Name of the Candidate
Enrolment No.
FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
AIITS-HCT-V-PCM-JEE (Main)/16
Useful Data
PHYSICS
2
Acceleration due to gravity
g = 10 m/s
Planck constant
h = 6.6 1034 J-s
Charge of electron
e = 1.6 1019 C
Mass of electron
me = 9.1 1031 kg
Permittivity of free space
0 = 8.85 1012 C2/N-m2
Density of water
water = 103 kg/m3
Atmospheric pressure
Pa = 105 N/m2
Gas constant
R = 8.314 J K1 mol1
CHEMISTRY
Gas Constant
Avogadro's Number Na
Plancks constant h
1 Faraday
1 calorie
1 amu
1 eV
=
=
=
=
=
=
=
=
=
=
8.314 J K1 mol1
0.0821 Lit atm K1 mol1
1.987 2 Cal K1 mol1
6.023 1023
6.625 1034 Js
6.625 1027 ergs
96500 coulomb
4.2 joule
1.66 1027 kg
1.6 1019 J
Atomic No:
H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,

N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16,
Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25,
Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33,
Br=35,
Ag=47, Sn=50, I=53, Xe=54, Ba=56,
Pb=82, U=92.
Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16,
F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32,
Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59,
Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108,
Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.
Physics
PART I
SECTION A
Single Correct Choice Type
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.
When the temperature of a gas, filled in a closed vessel, is increased by 10C its pressure
increases by 0.4 %. The initial temperature of the gas is,
(A) 250 K
(B) 2500 K
0
0
(C) 250 C
(D) 25 C
2.
A string of linear mass density 0.8 kg/m is stretched to a tension 500 N. The mean power
required to maintain a travelling wave of amplitude of 10 mm and wavelength 0.5 m is
(A) 70 W
(B) 85.3 W
(C) 98.7W
(D) 110 W
3.
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 (P0 = atmospheric pressure).
(C) r 2 3P0 7rg

4.
4r
r 2
(B)
3P0 7rg
2
(D) 2r 2 3P0 7rg
r 2
(A)
3P0 7rg
3
A spring mass system executes damped harmonic oscillations given by the equation
bt
2m
k
b2
,
m 4m2
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
y Ae
sin( ' t ) where '
Space for rough work
5.
6.
A small section of area A is removed from a uniform spherical

shell with surface mass density and radius R as shown in the
figure. Find the magnitude of gravitational field intensity at point P
P
due to the remaining mass.
O
A
4AG
4AG
R
(A)
(B)
R/2
9R2
R2
AG
(C)
(D) zero
R2
A horizontal spring mass system is executing SHM with time period of 4 sec. At time t = 0, it is at
mean position. Find the minimum time after which its potential energy becomes three times of
kinetic energy.
(A) 1 sec
(B) 1/2 sec
(C) 1/3 sec
(D) 2/3 sec
7.
3 m/s
Two blocks connected with the spring of force constant
4 m/s
100 N/m are given velocities 4i m/s and 3i m/s when

5kg
2kg
the spring is in natural length as shown in figure
(A) The velocity of 2kg block is maximum when 5 kg
block is at instantaneous rest.
(B) The maximum and minimum velocities of 2kg block is 7i m/s and 3i m/s respectively.
(C) The maximum and minimum velocities of 5kg block is 4 m/s and zero respectively.
(D) All of the above
8.
Two blocks of masses 2kg and 3kg are connected by string

of length 1m. At any instant the velocities of block of mass
2kg and 3kg is 5 m/s in opposite direction and perpendicular
to the length of string and is also parallel to horizontal table.
(A) Tension in the string is 110 N
(B) Tension in the string is 120 N
(C) Velocity of centre of mass is 2 m/s
(D) Velocity of centre of mass is 5 m/s
9.
5 m/s
3kg
2kg
1m
5 m/s
F
A block of mass 2kg starts moving at t = 0
with speed 2m/s on a smooth horizontal
2N
surface. A horizontal force F is applied in
the direction of velocity which varies with
2kg
2m/s
O
time shown in figure (b) the speed of
2
(a)
particle at t = 3 seconds (g = 10 m/s )
(A) 2.5 m/s
(B) 3.5 m/s
(C) 4.5 m/s
(D) none of these
(b)
10.
11.
12.
13.
Two objects of mass 3kg and 2kg move along x and y axis with speed 4 m/s and 3 m/s
respectively on the horizontal smooth table. After collision the bodies stick together. Then
(A) Heat generated in the process is 15 J
(B) Heat generated in the process is 18 J
(C) Direction of motion with x-axis after collision is 60.
1
(D) Direction of motion with x-axis after collision is tan1 .
3
In the shown figure the linear mass density of the rod is and
dimension are shown in figure. The moment of inertia about

the dashed axis is
4
(A) 3
3
8
(B) 3
10 3
(C)
3
(D) 4 3
A block of mass 3kg is connected with two identical massless
springs A and B and a block of mass 2kg is hanging with a third
identical spring C as shown in figure then the magnitude of
acceleration of 3kg and 2kg block just after cutting the spring A
25
(A)
m/s2 and zero
3
50
(B)
m/s2and zero
3
50
(C)
m/s2, 10 m/s2
3
(D) 20 m/s2, zero m/s2
30
30
A
3kg
C
2kg
and 5m/s (i)
Two particles of masses 1kg and 2kg are moving with constant velocities 2m/s (i)
respectively and crosses the y-axis simultaneously at t = 0 sec and are moving on a smooth
horizontal xy-plane. The separation between the two particles is 10 meter at t =0. The angular
momentum of 2kg particle with respect to 1kg particle at t = 5 sec is
(A) 20 N-m-sec
(B) 40 N-m-sec
(C) 60 N-m-sec
(D) 80 N-m-sec
14.
15.
16.
17.
18.
A particle moves along an arbitrary path. If v and a are the instantaneous velocity and
acceleration vectors of the particle, then the ratio of magnitude of tangential and centripetal
acceleration is

|av |
| a v |
(A)
(B)
| a v |
|av |
dv / dt
(C)
(D) None of these
dlv / dt
A ball is released from rest at a height of 10m on an inclined plane

of inclination 53. If collision is in elastic then find the horizontal
velocity of the ball
(A) 10 2
(B) 6 2
(C) 12 2
(D) 14 2
A wedge whose curved surface is parabolic in shape and has
equation x2 = 4y starts accelerating with acceleration g m/s2
when a block is at the bottom of wedge and is located at (0, 0).
The maximum height attained by the block (assume the curved
surface is sufficiently long)
(A) 1m
(B) 2m
(C) 4m
(D) 8m
O
10m
53
a= g m/s
(0, 0)
The ratio of magnitude of work done in moving slowly a block of mass m on a rough inclined
surface of inclination 45(tan ) from bottom to top and from top to bottom is 5. The
coefficient of friction between the block and surface is
1
2
(A)
(B)
2
3
2
4
(C)
(D)
5
5
Four identical particles of mass m are projected along the plane towards the centre of a square
from the corners of the square simultaneously with constant speed V0. Then
(A) If the two spheres comes to rest after collision then the other two must also come to rest after
collision.
(B) If the three spheres comes to rest after collision then the fourth one must also stop after
collision.
(C) If all comes to rest after collision then loss of energy is 4m V02 .
(D) If all comes to rest after collision then it will violate the law of conservation of momentum.
19.
Figure shows the pressure P versus volume V graphs for a

certain mass of an ideal gas at two constant temperatures T1
and T2.
Which of the following option is correct?
(A) T1 = T2
(B) T1 > T2
(C) T1 < T2
(D) no inference can be drawn due to insufficient information.
T2
T1
V
20.
Two identical vessels A and B contain mass m and 2m of same gas respectively. The gases in
the vessels are heated keeping their volumes constant and equal. The Temperature-Pressure
curve for mass 2m makes angle with T-axis and that for mass m makes an angle with T-axis
then
(A) tan = tan
(B) tan = 2 tan
(C) tan = 2 tan
(D) None of these
21.
If the moment of inertia of a isosceles right angle plate is I about an axis

shown in figure. Then moment of inertia of a square plate of same
material and thickness shown in figure about the given axis is
(A) 30I
(B) 32I
(C) 64I
(D) 90I
a
a
22a
22.
22a
Two simple pendulum of length and 16 are released from the same phase together. They will
be at the same phase after a minimum time.
8
3 g
(C) 2s
(A)

3 g
(D) none of these
(B)
23.
Two springs, each of spring constant k = 100 N/m are attached

to a block of mass 2 kg as shown in figure. The block can slide
smoothly along horizontal platform clamped to the opposite walls
of trolley of mass 5 kg. The block is slightly displaced and then
released. The period of oscillation is (in seconds). (all surfaces
are smooth).
7
1
(A) T 2
(B) T 2
1000
140
(C) T 2
1
20
(D) T 2
2kg
5kg
=0
49
100
24.
Two particles are executing SHM of equal amplitude along parallel lines with same time period.
Their velocity vectors are always oppositely directed to each other. The minimum phase
difference between the two particles is
(A) 0
(B) 90
(C) 180
(D) 270
25.
Which of the following statements is incorrect?

(A) Work done is zero if the point of application of force does not move.
(B) Total work done by static friction is zero in rolling without slipping for the complete system.
(C) Work done by friction must be zero in pure rolling for the rolling body.
(D) For an isolated system momentum of the system is conserved for any type of collision.
26.
Three small spheres A, B and C of masses 1kg, 2kg and

3kg are rotating with a circular disc with angular velocity 3
radian/sec and are connected with strings to O as shown in
figure. Coefficient of friction between spheres A, B, C and
disc is 0.4, 0.3 and 0.2 respectively.
(A) Friction force acting on sphere B is 6 N.
(B) Tension in the string connecting sphere A and B is 9 N
(C) Tension in the string connecting sphere C and O is 8 N
(D) Data insufficient
27.
=3 rad/sec
A
B
O
50cm
50cm
C
100cm
A block of mass 2kg is kept gently on a moving tape of a machine in

which the rotating cylinders have angular speed of 20 rad/sec and
there radius is 20cm. If coefficient of friction between the tape and
block is 0.5 and there is no slipping between tape and cylinder. Then
(take g = 10 m/s2)
(A) The distance travelled by the block before relative motion with tape ceases is 1.6 m
(B) Work done by friction on the block is 8 N
(C) Work done by friction on the block is 16 N
(D) Linear velocity of tape is 40 m/s
28.
A rod of mass m kg and length meter is hinged about its end A and is vertical
initially. Now the end A is accelerated horizontally with acceleration a0 = g m/s2.
The hinge reaction when the rod becomes horizontal is
4mg
mg
mg
mg
(A) R x
N, R y
N
(B) R x
N, R y
N
3
3
3
4
mg
mg
mg
(C) R x
N, R y
N
(D) R x 4mgN, R y
N
4
3
4
a0
29.
The temperature at which the speed of sound wave in helium gas is same as that in hydrogen
gas at 27C, is
(A) 504C
(B) 45C
(C) 327C
(D) 231C
30.
A triangular wave pulse on a taut string travels in positive x-direction with speed v. The tension in
the string is F, and linear mass density of string is . At t = 0, the shape of pulse is given by
if
x L
0
h(L x)
for L x 0
L
y(x,0)
h(L x) for
0 x L
L
0
for
x L
choose the correct statement.

(A) Magnitude of instantaneous power is zero for L < (x vt) < 0
2
h
(B) Magnitude of instantaneous power is Fv for (x vt) < L
L
2
h
(C) Magnitude of instantaneous power is Fv for (x vt) > L
L
2
h
(D) Magnitude of instantaneous power is Fv for 0 < (x vt) < L
L
10
Chemistry
PART - 1
SECTION A
Straight Objective Type
This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices (A),
(B), (C) and (D), out of which only one is correct.
1.
The velocity of electron in the second orbit of He+ will be

(A) 2.18 10 6 m / s
(B) 1.09 10 6 m / s
(C) 3.8 106 m / s
2.
(D) 6.8 106 m / s
A mixture of (CH3)3C CHOand HCHO on heating with aqueous KOH solution will give
(A) HCOONa + (CH3)3C CH2 OH
(B)
CH3
CH3
(C)
HCOONa
H3C
H3C
H3C
CH2 OH
(D)
CHO
CH2 , HCOONa
CH3
CH3
3.
H3C
CH2 OH
CH3
For the reaction:

R X OH ROH X
The rate of reaction is given as follows.
Rate = 4.74 105 [R X] [OH] + 0.24 105 [RX].
What percentage of R X will react by SN2 path if [OH] = 103 molar
(A) 1.93
(B) 4.74
(C) 2.37
(D) 4.9
11
4.
CH2
H3 O
A, A is
CH3
(A)
(B)
OH
OH
CH3
CH3
HO
(C)
HO
OH
(D)
CH3
CH3
CH3
HO
5.
If the radius of Bohrs is x, then de Broglie wavelength of electron in 3rd orbit is nearly
(A) 4x
(B) 6x
x
(C) 8x
(D)
3
6.
Which of the following reagent solution can be used to distinguish between methanoic acid &
ethanoic acid?
(A) Tollens reagent
(B) FeCl3 solution
(C) FeSO4/H2O2
(D) Na2CO3 solution
7.
Si-F bond is stronger than C-F bond due to

(A) Larger size of silicon atom
(B) Larger electronegativity difference between Si & F
(C) The presence of p - d bonding
(D) Overlapping of P P atomic orbital
12
8.
Which of the following species have the bond order same an N2?
(A) CN
(B) OH
+
(C) NO
(D) CO
9.
In FCC lattice of NaCl structure, if the diameter of Na+ is X & radius of Cl is Y, then bond length
of NaCl in the crystal is
(A) 2x + 2y
(B) x + y
x y
x x
(C)
(D)
2 2
3 2
10.
CsCl has bcc structure with Cs+ at the centre and Cl ion at each corner. If rCs+ = 1.69 A &
rCs = 1.81 A . What is the edge lenght a of each cube?

5
6
(A)
(B)
2
3
7
4
(C)
(D)
3
3
11.
12.
In the metallurgy of iron, when lime stone is added to the blast furnace, the calcium ion ends up in
(A) slag
(B) gangue
(C) metallic calcium
(D) calcium carbonate
OH
B
OH
In the product (A), the electrophile will be attached to the which position w.r.t B(OH)2 group
(A) ortho
(B) para
(C) meta
(D) ipso
13.
Find total number of product as a result of given reaction:

Br2 /CCl4 /
CH3 CH CH CH2 COOAg
(A) 3
(B) 4
(C) 5
(D) 6
14.
The aqueous solution of each of the following salt is coloured except

(A) TiCl4
(B) FeCl3
(C) CuCl2
(D) MnCl2
13
15.
Which of the following salt will not produce black ppt on passing H2S(g) through their aqueous
salt solution in acidic medium?
(A) CuSO4
(B) PbCl2
(C) CdSO4
(D) NiCl2
16.
A current of 2A passing for 1.93 104 sec through a molten Tin salt depositing 23.8 g Tin. The
oxidation state of Tin in the salt is (given atomic number of Tin = 119)
(A) 2
(B) 4
(C) 1
(D) 3
17.
What volume strength of 200 ml H2O2 required for complete reaction of 7.9 g of KMnO4 in basic
medium?
(A) 1.86
(B) 11.2
(C) 1.4
(D) 5.6
18.
The molecular weight of an acid is 82. In a titration, 100 ml of solution of this acid containing
39 gm of acid per litre were completly neutralized by 95 cc of aqueous NaOH containing 40 gm
NaOH per litre. What is the basicity of the acid?
(A) 1
(B) 2
(C) 3
(D) 4
19.
Two sample of HI each of 5 gm were taken separately in two vessels of volume 5 & 10 litre
respectively at 27C. The extent of dissociation of HI will be
(A) more in 5 litre vessel
(B) more in 10 litre vessel
(C) equal in both vessel
(D) nota
20.
The ratio of equivalent weight of oxidant & reductant in

C2H5 OH OH I2
CHI3 HCO2 H2 O I
(A) 1:2
(B) 2:1
(C) 2:3
(D) 3:2
21.
What is the pH of 103 M solution of NH4OH (Kb = 1.85 105 M) at 25C?

(A) 10.75
(B) 10.14
(C) 9.65
(D) 9.10
22.
Which of the following compound would you expect to be molecular?

(A) N2O
(B) PCl5
(C) CaCl2
(D) both (A) & (B)
14
23.
Which one of the following shows maximum paramagnetic character?

(A) Cr H2 O 6
(C) Fe CN6
24.
(B) Fe CN6
(D) Cu H2 O 6
Boron has two isotopes
10
5
B and
11
5
B . If the atomic weight of boron is 10.81, the ratio of
10
5
B and
11
5
B in nature is
(A) 19/81
(C) 15/16
(B) 20/53
(D) 10/11
25.
Which of the following is non stoichiometric and metal deficient?

(A) FeO
(B) Fe3O4
(C) Fe2O3
(D) all of these
26.
Percentage of gold in 22 carat gold is

(A) 15
(C) 92.6
27.
(B) 85
(D) 37.5
CH3 CH2 OH Na
A
CH3
P
y
OHSOCl2
B
D
A B C
Find (C).
(A)
CH3
H
(C)
CH3
(B)
D
OC2H5
CH3
H5C2O
D
CH3
(D)
OCH2H5
OC2H5
H
15
28.
Potassium 40 decay to Argon 40 with a half life of 1.27 109 years. What is the age of rock in
40
40
which the mass ratio of Ar to K is 3.6?
9
9
(A) 3.2 10 years
(B) 4.2 10 years
9
(C) 2.8 10 years
(D) 6.4 108 years
29.
KMnO4 /OH /cold

HIO4 /
A
B
Compound B is
(A)
OHC
(C)
CHO
OH
(B)
(D)
CHO
None
OH
30.
The number of moles of Cr2O72 needed to oxidise 0.136 equivalent of N2H5+ by the reaction:
N2H5 Cr2 O72 N 2 Cr 3 H2O
is
(A) 0.136
(B) 0.272
(C) 0.816
(D) 0.0227
16
Mathematics
PART III
SECTION A
Straight Objective Type
This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices (A),
(B), (C) and (D), out of which ONLY ONE is correct
1.
If N 7 4 3
P B (n N) where P is the integral part of at N and B is the positive proper
fraction then the value of (1 B)(P + B)

(A) 1
(C) 3
2.
3.
4.
(B) 2
(D) 4.
2n
3
If {x} denotes the fractional part of x then find the value of
where n N.
8
1
1
(A)
(B)
2
4
1
1
(C)
(D)
.
8
16
The 8m term in the expansion of 1 2x

7
(A)
(C)
1.3.5...13 x7
6
7!
1.3.5...13
x6
6!
1/2
(B)
1.3.5...13 x 7
7!
(D) None of these.
If A0, A1, A2, A3, A4 and A5 be the consecutive vertices of a regular hexagon inscribed in a unit
circle. Then find the product of length of A0A1, A0A2, and A0 A4.
(A) 1
(B) 3
(C) 5
(D) 7
17
5.
Number of positive real value of x such that x, [x] and {x} are in H.P. (where [x] and {x} denotes
the greatest integer and fraction part of x) is equal
(A) 1
(B) 2
(C) 0
(D) 3.
6.
From the points on the circle x 2 + y2 = 4 tangents are drawn to the ellipse
7.
Let a1, a2, a3 a201 are in G.P. with a101 = 25 and
x2 y 2
1 . If the locus
4
3
2
2
2
2 2
of middle points of the chord of contact is the curve a (bx + cy ) = (dx + ey ) , then the value of
a b c d e
where ( [.] G.I.P.)

5
(A) 4
(B) 5
(C) 6
(D) 9.
201
201
i 1
to
(A) 5
(C) 125
ai 625 . Then one value of a

i 1
is equal
(B) 25
(D) 1.
2
8.
9.
10.
dy
If x = sec cos and y = sec cos then the value of at x = 0 is
dx
(A) 0
(B) 2
(C) 4
(D) 9.
3
x y
1
1
1
1 is a variable line, where
2 2 (c is a constant). Locus of the foot of
2
a b
a
b
c
perpendicular drawn from origin to the variable line is
(A) x2 y2 = c2
(B) x2 + y2 = c2
2
2
2
(C) x + y = c
(D) x2 y2 = c2
If the locus of the middle point of the chords of the parabola y2 = 4ax which subtends angle at
the vertex is (32 + y2 4x)2 tan2 = 64 (8x y2) then the value of a is
(A) 1
(B) 2
(C) 3
(D) 4.
18
11.
The sum of real values of k for which the cubic x 3 kx + k 1 = 0 has exactly two distinct real
solution
13
15
(A)
(B)
4
4
3
11
(C)
(D)
4
4
12.
In triangle, if = a2 (b c)2 then tanA is equal to

7
8
(A)
(B)
15
15
11
13
(C)
(D)
.
15
15
tan 2n 1
13.
The value of the expression
n 1
(A)
(C)
1
2
1
6
4
2n 1
is
(B)
(D)
1
3
2
.
3
14.
Let f(x) = (1 + b2)x2 + 2bx + 1 and let m(b) be one minimum value of f(x). As b varies, the range of
m(b) is
1
(A) [0, 1]
(B) 0,
2
1
(C) , 1
(D) 0,1 .
2
15.
A line y = x + 2 is drawn on the co-ordinate plane. This line is rotated by 90 clockwise about the
point (0, 2). A line y = 2x + 10 is drawn and area of this triangle is , then the value [] is ( []
is G.I.F.)
(A) 128
(B) 64
(C) 21
(D) 20.
19
16.
17.
Number of integers satisfying the inequalities

1
log3 x3
2
log3 x 1
2 0 , is
1
log3
3
(A) 5
(C) 7
(B) 1
(D) 4
Let A x : x 2 x 4 0 , and B x : x 2 ax 4 0 if A B = A, then the largest integral

value of a is
(A) 3
(C) 5
19.
(B) 6
(D) 8.
If the equation x 3 2 p , where p is a constant integer has exactly three distinct solution
then the number of integral values of p, is
(A) 0
(C) 2
18.
(B) 4
(D) 6.
2cos 2 1
If cos1 =
where 1, 2 (0, ), then the value of
2 cos 2
(A) 1
(C) 3
1
2 is equal to
2 2
tan
2
tan2
(B) 2
(D) 4.
20.
Let P(x) = x5 + x2 + 1 have roots x1, x2, x3, x4 and x5 g(x) = x2 2, then the value of
g(x1) . g(x2) . g(x3) . g(x4) . g(x5) 30g(x1x2x3x4x5) is
(A) 1
(B) 2
(C) 4
(D) 7.
21.
If a + b + c = 0 and a2 + b2 + c2 = 1 then the value of 2(a4 + b4 + c4) is

(A) 1
(B) 2
(C) 3
(D) 3.
22.
23.
20
If the value of 0,2 such that the inequality sin x sin x 0 is true for all that
3
p
number x, is equal to
where p and q are relatively prime positive integers, then the value of
q
(p + q) is
(A) 3
(B) 5
(C) 7
(D) 9
5
3
2
f(x)= x + px + qx + 6, where p, q R if f(x) is negative in largest possible interval , 1 ,
3
then the value of (p + q) is

(A) 3
(B) 5
(C) 7
(D) 9
24.
In a ABC, the tangent of half the difference of two angles is one third the tangent of half the the
sum of same angles. The ratio of the sides opposite to the angles.
(A) 2 : 1
(B) 1 : 2
(C) 2 : 4
(D) 4 : 2.
25.
If cos1x + cos1y + cos1z = 3 then compute the value of

6
x 2004 y2004 z2004 2003
2003
x
y
z2003
(A) 0
(B) 1
(C) 2
(D) none of these.
21
26.
Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals

2
(A) |m + n|(m n)2
(B)
mn
(C)
27.
1
m n
1
.
mn
(D)
Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r, If PS and
RQ intersect at a point x on the circumference of the circle, then 2r equals.
PQ RS
(A)
PQ . RS
(B)
2
(C)
28.
2PQ . RS
PQ RS
PQ
(D)
RS2
2
If a > 2b > 0 then positive value of m for which y mx b 1 m2 is a common tangent to x 2 + y2

= b2 and (x a)2 + y2 = b2 is
(A)
(C)
2b
a2 4b2
2b
a 2b
a2 4b2
2b
(B)
(D)
b
.
a2
29.
The locus of the orthocentre of the triangle formed by the lines

(1 + p)x py + p(1 + p) = 0
(1 + q)x qy + q(1 + q) = 0 and y = 0, where p q is
(A) a hyperbola
(B) a parabola
(C) an ellipse
(D) a straight line.
30.
Let a1 a2 a10 be in A.P. h1 h2 h10 be in H.P. if a1 = h1 = 2 and a10 = h10 = 3, then a4 h7is
(A) 2
(B) 3
(C) 5
(D) 6

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ALL INDIA INTEGRATED TEST SERIES

JEE (Main), 2016

Time Allotted: 3 Hours

Maximum Marks: 432

B. Filling of OMR Sheet

C. Marking Scheme For All Three Parts.

Name of the Candidate

Acceleration due to gravity

h = 6.6 1034 J-s

Permittivity of free space

0 = 8.85 1012 C2/N-m2

water = 103 kg/m3

H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,

A spherical metal ball of radius r is lying at the bottom of a stationary

(C) r 2 3P0 7rg

sin( ' t ) where '

Space for rough work

A small section of area A is removed from a uniform spherical

100 N/m are given velocities 4i m/s and 3i m/s when

Two blocks of masses 2kg and 3kg are connected by string

Space for rough work

dimension are shown in figure. The moment of inertia about

and 5m/s (i)

Space for rough work

A ball is released from rest at a height of 10m on an inclined plane

Figure shows the pressure P versus volume V graphs for a

If the moment of inertia of a isosceles right angle plate is I about an axis

Space for rough work

Two springs, each of spring constant k = 100 N/m are attached

Which of the following statements is incorrect?

Three small spheres A, B and C of masses 1kg, 2kg and

A block of mass 2kg is kept gently on a moving tape of a machine in

choose the correct statement.

Space for rough work

The velocity of electron in the second orbit of He+ will be

(D) 6.8 106 m / s

For the reaction:

Si-F bond is stronger than C-F bond due to

rCs = 1.81 A . What is the edge lenght a of each cube?

Find total number of product as a result of given reaction:

The aqueous solution of each of the following salt is coloured except

The ratio of equivalent weight of oxidant & reductant in

What is the pH of 103 M solution of NH4OH (Kb = 1.85 105 M) at 25C?

Which of the following compound would you expect to be molecular?

Which one of the following shows maximum paramagnetic character?

Boron has two isotopes

B . If the atomic weight of boron is 10.81, the ratio of

Which of the following is non stoichiometric and metal deficient?

Percentage of gold in 22 carat gold is

Space for rough work

KMnO4 /OH /cold

P B (n N) where P is the integral part of at N and B is the positive proper

fraction then the value of (1 B)(P + B)

The 8m term in the expansion of 1 2x

(D) None of these.

Let a1, a2, a3 a201 are in G.P. with a101 = 25 and

where ( [.] G.I.P.)

ai 625 . Then one value of a