FIITJEE JEE (Advanced)-2016

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CONCEPT RECAPITULATION TEST – I

Paper 1

Time Allotted: 3 Hours Maximum Marks: 264

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 Pl ea s e r ea d t h e i n s t r u ct i o n s c a r ef u ll y . Yo u a re a l l o t t ed 5 m in u t 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 l l o wed t o l ea v e t h e E xa m i n at i o n Ha l l b ef o r e t h e en d o f
ALL INDIA TEST SERIES

t h e t es t .

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 is further divided into three sections: Section-A, Section-B & 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 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 – 10) contains 10 multiple choice questions which have one or more than one
correct answer. Each question carries +4 marks for correct answer and – 2 marks for wrong
answer.

(ii). Section – B (01 – 02) contains 2 Match the following Type questions. Each question having 4
statements in Column I & 5 statements in Column II with any given statement in Column I having
correct matching with 1 or more statement (s) given in Column II. Each statement carries +2
marks for correct answer and – 1 mark for wrong answer.

(iii). Section-C (01 – 08) contains 8 Numerical based questions with answers as numerical value
from 0 to 9 and each question carries +4 marks for correct answer. There is no negative
marking.

Name of the Candidate

Enrolment No.

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Useful Data

PHYSICS
2
Acceleration due to gravity g = 10 m/s

Planck constant h = 6.6 1034 J-s

Charge of electron e = 1.6  1019 C

Mass of electron me = 9.1  1031 kg

Permittivity of free space 0 = 8.85  1012 C2/N-m2

Density of water water = 103 kg/m3

Atmospheric pressure Pa = 105 N/m2

Gas constant R = 8.314 J K1 mol1

CHEMISTRY

Gas Constant R = 8.314 J K1 mol1

= 0.0821 Lit atm K1 mol1
= 1.987  2 Cal K1 mol1
Avogadro's Number Na = 6.023  1023
Planck’s constant h = 6.625  1034 Js
= 6.625  10–27 ergs
1 Faraday = 96500 coulomb
1 calorie = 4.2 joule
1 amu = 1.66  10–27 kg
1 eV = 1.6  10–19 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.

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Physics PART – I

SECTION – A
(One or More than One Options Correct Type)
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONE or MORE THAN ONE are correct.

1. In the series L – C – R circuit, the voltage across resistance, capacitance and inductance are 30V
each at frequency f = f0.
(A) It the inductor is short-circuited, the voltage across the capacitor will be 30 2 V.
30
(B) If the capacitor is short-circuited, the voltage drop across the inductor will be V.
2
(C) If the frequency is changed to 2f0, the ratio of reactance of the inductor to that of the capacitor
is 4 : 1.
(D) If the frequency is changed to 2f0, the ratio of the reactance of the inductor to that of the
capacitor is 1 : 4.

2. A ball is released form a point, it goes vertically downwards and

collides with a fixed smooth inclined plane of angle of inclination of
300. After the collision the ball goes horizontally. The coefficient of
restitution between the ball and the inclined plane is
1 1
(A) (B)
2 3
(C) 1 (D) None of these 300

3. In the circuit shown in figure A C F

(A) E = 6.6 V
E 12V 4V
(B) i1 = 1.1 A
(C) i2 = 0.5 A 2 4 6
(D) E = 4.4 V

B D G
1A
2

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4. A cylindrical vessel contains a liquid of density  up to height h. The

m, A
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
 mg 
(A) 2gh (B) 2  gh 
 A 
v
 mg  mg
(C) 2  gh  (D) 2gh 
 A  A

5. A closed organ pipe of length 28 cm closed at one end is found to be at resonance when a tuning
fork of frequency 850 Hz is sounded near the open end. If velocity of sound in air is 340 m/s, then
the
(A) air in the pipe is vibrating in fundamental mode.
(B) air in the pipe is vibrating in first overtone.
(C) end correction of the pipe is 1 cm.
(D) end correction of the pipe is 2 cm.

6. The given figure shows a YDSE apparatus.

Parallel monochromatic coherent light rays are
2
incident on slits S1andS2 ( S1S2  mm ) at
3 S1
an angle 30o with the horizontal. The medium on
300 P
left side of the slits is water   w  4 / 3  . To
obtain the central maxima at point P, a glass slab
S2
 
 g  3 / 2 inside water is introduced in front D
of slit S1. The thickness of the glass slab required
for this purpose is
(A) 2mm (B) 4/3 mm
(C) 4 mm (D) 8/3 mm

7. When photons of energy 4.25 eV strike the surface of a metal A, the ejected photoelectrons have
maximum kinetic energy TA eV and de-Broglie wavelength A. The maximum kinetic energy of
photoelectrons liberated from another metal B by photons of energy 4.70 eV is TB=(TA – 1.50) eV.
If the de-Broglie wavelength of these photoelectrons is B = 2A then
(A) the work function of A is 2.25 eV (B) the work function of B is 4.20 eV
(C) TA = 2.00 eV (D) TB = 2.75 eV

Space for Rough work

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8. In a cylindrical region of radius R, there exists a time varying magnetic

×
dB × R ×
field B such that  k(  0) . A charged particle having charge q is
dt × × ×
O ×
placed at the point P at a distance d (> R) from its centre O. Now, the × × ×
particle is moved in the direction perpendicular to OP (see figure) by an
external agent upto infinity so that there is no gain in kinetic energy of d
the charged particle. Choose the correct statement/s.
qR2 P
(A) Work done by external agent is k if d = 2R
4
qR2
(B) Work done by external agent is k if d = 4R
8
qR2
(C) Work done by external agent is k if d = 4R
4
qR2
(D) Work done by external agent is k if d = 6R
4

9. Consider a case of thin film interference as shown. Thickness

of film is equal to wave length of light in 2
(A) Reflected light will be maximum if 1   2  3 1
(B) Reflected light will be maximum if 1   2  3
(C) Transmitted light will be maximum if 1  2   3 2
(D) Transmitted light will be maximum 1  2  3
3

10. A beaker filled with water kept on a weighing balance weighs w1. Now an iron block of weight w2
is suspended through a thread inside water. The weighing machine will now read ‘w’ given
(A) w = w1 + w2 (B) w1 < w < w1 + w2
(C) w > w1 + w2 (D) w + w1

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SECTION – B
Matrix – Match Type
This section contains 2 questions. Each question contains statements given p q r s t
in two columns, which have to be matched. The statements in Column I are
A p q r s t
labelled A, B, C and D, while the statements in Column II are labelled p, q, r,
s and t. Any given statement in Column I can have correct matching with B p q r s t
ONE OR MORE statement(s) in Column II. The appropriate bubbles
corresponding to the answers to these questions have to be darkened as C p q r s t
illustrated in the following example:
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s D p q r s t
and t; then the correct darkening of bubbles will look like the following:

1. Referring to the given circuit, match Column-I with Column-II: 10 mH 100 1F


V = 10 sint(Volt)

Column I Column II
(A) For  = 8000 rad/s (p) Peak current in the circuit is less than
0.1 A
(B) For  = 10000 rad/s (q) Voltage across the combination and the
current are in same phase
(C) For  = 10500 rad/s (r) Voltage across the combination leads the
current
(D) For  = 10000 rad/s, if R = 50  (s) Current through the circuit leads the
instead of 100  voltage across it

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2. An optical component and an object S placed along its optic axis are given in Column I. The
distance between the object and the component can be varied. The properties of images are
given in Column II. Match all the properties of images form Column II with the appropriate
components given in Column I. indicate your answer by darkening the appropriate bubbles of the
4  4 matrix given in the ORS.
Column I Column II
(A) (p) Real image
S

(B) (q) Virtual image

S

(C) (r) Magnified image

S

(D) (s) Image at infinity

S

SECTION – C
(One Integer Value Correct Type)
This section contains 8 questions. Each question, when worked out will result in one integer from 0 to 9
(both inclusive).

1. Magnetic field due to long solid cylindrical wire carrying current uniformly distributed over the
cross-section is same at a distance of 4.00 cm and 1.00 cm from the axis of the wire.
The magnitude of magnetic field is maximum in between these two points. Find the radius of the
wire in cm.

2. 2 kg of ice at –22.50C is mixed with 2.5 kg of water at 250C in an insulating container. If the
specific heat of ice and water are 0.5 cal/gm°C and 1 cal/gm°C respectively. Latent heat of fusion
of ice = 80 cal/gm. Find the amount of water present in the container (In kg).

Space for Rough work

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x 3 9x 2
3. Potential energy of a particle moving along x-axis is given by U =   20x . Find out
3 2
position of stable equilibrium state.

4. A plane progressive wave of frequency 25 Hz, amplitude 2.5  105 m, and initial phase zero
moves along the negative x axis with a velocity of 300 m/s. A and B are two points at a separation
x
of 6m in the line of propagation the phase difference is . Find x.
2

5. A satellite is moving in a circular orbit around earth at a height R above earth surface
(R being radius of earth) It’s velocity should be increased to k times its initial orbital speed
value, so as to make it escape from earth gravitational pull and reach infinity. Find k.

6.  
A charged particle is projected in a magnetic field B  xiˆ  4ˆj 102 T . The acceleration of the

 8ˆ 
particle is found to be a a   i  2ˆj  m / s2 . Find the value of x.
3 

7. A gas containing hydrogen like ions with atomic no Z, emits photons in transition n + 2  n,
where n = Z. There photons fall on a metallic plate and eject electrons having minimum
de – Broglie wavelength  of 5Å. Find the value of ‘Z’ if the work function of metal is 4.2 eV.

8. In Young’s double slit experiment, the slits are 0.5 mm apart and interference is observed on a
screen placed at a distance of 100 cm from the slits. It is found that the 9th bright fringe is at a
distance of 8.835 mm from the 2nd dark fringe from the centre of fringe pattern. If the wavelength
of light used is 2.945n x 10-7 m, then n =

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Chemistry PART – II

SECTION – A
(One or More than One Options Correct Type)
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONE or MORE THAN ONE are correct.

1. Which of the following property(ies) depend(s) on only magnetic quantum number?

(A) Splitting of orbital angular momentum vector
(B) Orientation of atomic orbitals
(C) Splitting of spectral lines of H– ion
(D) Spin multiplicity of an atom

2. Which of the following molecule(s) has/have tetrahedral shape?

(A) CF4 (B) SF4
(C) XeF4 (D) SeF4

3. Which of the following characteristic(s) of a chemical reaction increase(s) by increasing

temperature?
(A) Rate constant (B) Half-life period
(C) Rate of reaction (D) Activation energy

4. Which of the following solution(s) is/are hypertonic to 0.1 M KCl solution?

(A) 0.2 M C6H12O6 (B) 0.1 M CaCl2
(C) 0.05 M AlCl3 (D) 0.1 M C12H22O11

5. How many octahedral void(s) is/are present in a FCC unit cell?

(A) 2 (B) 4
(C) 8 (D) 6

6. Pt|H2(1 atm)|H+(1 M)
Which of the following statement(s) is/are correct for the above electrode?
(A) E = Eo
(B) Eo = 0 V
(C) It is used to measure the electrode potential of other electrodes
(D) It is a reference electrode

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7. Which of the following undergo(es) elimination reaction(s)?

o
AlC.KOH Cu/ 300 C
(A) CH3CH2Cl 
 (B) CH3 CH2OH 
Zn/  Zn Hg
(C) BrCH2CH2Br   (D) CH3 CH2CHO 
Conc.HCl


8. Which of the following reagent(s) is/are used to convert C2H5OH to C2H5Cl?

(A) SOCl2 (B) PCl5
(C) NaCl (D) Cl2

9. Which of the following reaction(s) form(s) racemic product(s)?

NaCN HCl
(A) CH3CHO  HCN   (B) CH3CH  CHCH3  

H CCl
(C) CH3 CH2CHO  NH2OH  (D) CH3  CH  CH2  Cl2 
4


10. Which of the following transition element(s) form(s) compounds by using only one oxidation state?
(A) Cu (B) Zn
(C) Fe (D) Mn

SECTION – B
Matrix – Match Type
This section contains 2 questions. Each question contains statements given p q r s t
in two columns, which have to be matched. The statements in Column I are
A p q r s t
labelled A, B, C and D, while the statements in Column II are labelled p, q, r,
s and t. Any given statement in Column I can have correct matching with B p q r s t
ONE OR MORE statement(s) in Column II. The appropriate bubbles
corresponding to the answers to these questions have to be darkened as C p q r s t
illustrated in the following example:
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s D p q r s t
and t; then the correct darkening of bubbles will look like the following:

1. Match the complexes mentioned in Column - I with their properties mentioned in Column – II.

Column – I Column – II
(A) K4[Fe(CN)4(Cl)2] (p) Shows geometrical isomerism
(B) [Cr(NH3)4(Cl)2]Br (q) Shows ionization isomerism
(C) [Ni(NH3)2(Cl)2] (r) Coordination number is six
(D) [Cr(en)2(Cl)(Br)]NO2 (s) Ionizes in water
(t) One d-orbital of the metal ion participate
in hybridization

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2. Match the compounds mentioned in Column-I with their distinction tests mentioned in Column-
II.
Column – I Column – II
(A) CHO CHO (p) Fehling’s test

and

(B) COCH3 CHO (q) Tollen’s test

and

(C) OH CHO (r) Reaction with Na

and

(D) COCH2CH3 (s) Iodoform test

OH

and

(t) Lucas test

SECTION – C
(One Integer Value Correct Type)
This section contains 8 questions. Each question, when worked out will result in one integer from 0 to 9
(both inclusive).

1. A buffer contains CH3COOH and CH3COONa. What would be the maximum pH of the buffer
beyond which it cannot display buffer action? [Ka of CH3COOH = 10–5]

Heat
2. NH4NO 2  s    Product  s 
How many gas(es) containing nitrogen is/are formed in the above reaction?

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3. MnO4  C2O24  H  Mn2  CO2  H2O

What would be the coefficient of C2O42 if the above equation is balanced in acidic medium?

4. An alkyl polychloride on hydrolysis forms 3-oxobutanoic acid. How many chlorine atom(s) is/are
present in the polychloride?

5. The molecular mass of a polyhydric alcohol increases by 168 units when it forms product by
reacting with CH3COCl in presence of pyridine. How many OH groups are present in the alcohols?

6. The spin magnetic moment of a chloride of iron is 35 B.M. How many unpaired electron(s)
is/are present in the chloride?

7. What should be the maximum value of van’t Hoff factor of AlCl3 in its aqueous solution?

8. The formula of an interhalogen compound of iodine is IFn. What would be the value of ‘n’ if iodine
contains a lone pair of electron in this compound?

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Mathematics PART – III

SECTION – A
(One or More than One Options Correct Type)
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONE or MORE THAN ONE are correct.

1
1. If the imaginary part of the complex number  z  1 cos   i sin     z  1 cos   i sin   is
zero, then
(A) z  1 (B) z  1  1
(C) arg  z    (D) arg  z  1  

2. If  is the angle subtended at P  x1, y1  by the circle S  x 2  y 2  2gx  2fy  c  0, then

S1  S1
(A) cot   (B) cot 
g2  f 2  c 2 g2  f 2  c
2 g2  f 2  c  g2  f 2  c 
(C) tan   (D)   2 tan1  
S1  S 
 1 
2 2
where S 1  x  y  2gx1  2fy1  c
1 1

3. If I  sec 2 x cos ec 4 x dx  K cot 3 x  L tan x  M cot x  C then


1
(A) K  (B) L  2
3
(C) M  2 (D) none of these

dy
4. The solution of  y  x is given by
dx
(A) x  C  2 y  x  2log y  x  1  (B) x 2  C  2 y  x  log  y  x 1 
2
(C) x  C   y  x   log  y  x  1 (D) y  x  1  C ' e x/ 2 y x

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5. If a, b and c be non coplanar unit vectors equally inclined to one another at an acute angle  . If
a  b  b  r  pa  qb  rc then
1 2cos 
(A) p = r (B) p  , q
1  2 cos  1  2cos 
1 2cos 
(C) r  (D) p 
1  2cos  1  2 cos 

6. If a  b  2i  2j  k, a  b  i  2j  4k then
1 1 3 13
(A) a  i  j  k; b  i  j  5k (B) a  j  2k; b  i  4j  6k
4 4 4 4
1 7 5 19 1 1 3 13
(C) a   i  j  2k; b  i  j  7k (D) a  i  j; b  i  j  4k
4 4 4 4 2 2 4 4

7. If sines of the angle A and B of a triangle ABC satisfy the equation c 2 x 2  c  a  b  x  ab  0,

then the triangle
(A) is acute angled (B) is right angled

(C) is obtuse angled (D) satisfies sin A  cos A 

a  b 
c

x a b
8. If   b x a , then, a factor of  is
a b x
(A) a  b  x (B) x 2   a  b  x  a2  b2  ab
(C) x 2   a  b  x  a2  b 2  ab (D) a  b  x

n
 1
9. In the expansion of  x 2  1   , n  N,
 x2 
(A) number of terms is 2n  1 (B) coefficient of constant term is 2n  1
2n  2 2
(C) coefficient of x is n (D) coefficient of x is n

Space for Rough work

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10. If n objects are arranged in a row, then the number of ways of selecting three of these objects so
that no two of them are next to each other is
1 n2
(A)  n  2 n  3 n  4  (B) C3
6
(C) n  3 C3  n  3 C2 (D) none of these

SECTION – B
Matrix – Match Type
This section contains 2 questions. Each question contains statements given p q r s t
in two columns, which have to be matched. The statements in Column I are
A p q r s t
labelled A, B, C and D, while the statements in Column II are labelled p, q, r,
s and t. Any given statement in Column I can have correct matching with B p q r s t
ONE OR MORE statement(s) in Column II. The appropriate bubbles
corresponding to the answers to these questions have to be darkened as C p q r s t
illustrated in the following example:
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s D p q r s t
and t; then the correct darkening of bubbles will look like the following:

1. Match the sequence a1,a 2 , a3 ,......... whose nth term is given on the left with properties of the
sequence on the right.

Column-I Column-II
(A)  /2 1  cos 2nx (p) a1,a 2 ,a3 ...... are in A.P.
an   dx
0 1  cos 2x
(B) / 4 1 (q) a1,a 2 ,a3 ,....... are in G.P.
In   tann x dx and an 
0 In1  In 3
(C) sin2 nx
 /4 (r) a1,a2 ,a3 ,...... are in H.P.
In   dx  n  0 and
0 sin x
an  In  In 1 n  1
(D)  /2 sin2 nx (s) a1,a2 ,a3 ,...... is constant
bn   dx, an  bn  bn1  n  1
0 sin2 x sequence.
(t) an1  an  an2

Space for Rough work

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2. Lines y 2  xy  0 make Intercepts on curve given on R.H.S of Matrix.

Column-I Column-II
(A) 2 (p) x 2
 y2  1
3
(B) 4 (q) y2
x2  1
3
(C) 6 (r) x2  y2  4
(D) 2 3 (s) y2  2 2 x
(t) x2  y2  2

SECTION – C
(One Integer Value Correct Type)
This section contains 8 questions. Each question, when worked out will result in one integer from 0 to 9
(both inclusive).

x2 y2
1. If CF is perpendicular from the centre C of the ellipse   1 on the tangent at any point P,
49 25
and G is the point where the normal at P meets the minor axis, then (C.F. PG)2 is equal to
2
 40    then   _____________

2. P, Q, R, S are the points (1, 2, –2), (8, 10, 11), (1, 2, 3) and (3, 5, 7) respectively. If s denotes the
projection of PQ on RS then 29s2  29 is equal to  8130    where  is ____

 1   n2 n2
3. Let f be a continuous function on R such that f  
 4n 
 
sin en
e  
n2  1
. Then the value of

f  0  is

Space for Rough work

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tan x tan  x  h  tan  x  2h  

3  
  x   tan  x  2h  tan  x  h  then the value of lim  3  is 10   2
4. tan x 2  
h 0 h
tan  x  h  tan  x  2h  tan x
where   ___________

5. Let P (x) be a polynomial of degree 4, with P  2   1, p '  2   0, p"  2   2, p "'  2   12
Piv  2   24 . If value of P " 1 is 5 2   then  = ____________

2
6. If (u, v) are the coordinates of the point on the curve x 3  y  x  4  where the ordinate is
2
minimum then uv is equal to  20    where   _______

  /2
7. If 
0
 
x f cos2 x  tan4 x dx   k 
0
 
f cos 2 x  tan4 x dx, then the value of k is

8. The degree of the remainder when x 2007  1 is divided by x 2  1 x 2  x  1   

Space for Rough work

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