MOCK TEST

(JEE-MAIN)
Time : 3 Hours Max. Marks: 300

Please read the instruction carefully. You are allotted 5 minutes specifically for this purpose.
Do not open this Test Booklet until you are asked to do so.
Read carefully the following Instructions on this Test Booklet.
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 Booklet consists of 25 × 3 = 75 questions.
4. There are Three Parts in the question paper. The distribution of marks subjectwise in each part is as under
for each correct response.
Part A : MATHEMATICS (100 marks) - Question No 1 to 25 consist FOUR (4) marks each for correct
response.
Part B : PHYSICS (100 marks) - Question No 26 to 50 consist FOUR (4) marks each for correct
response.
Part C : CHEMISTRY (100 marks) - Question No 51 to 75 consist FOUR (4) marks each for correct
response.
5. Each correct answer carries 4 marks, while 1 mark will be deducted for every wrong answer. Guessing of
answer is harmful.
6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on the Answer Sheet. Use
of pencil is strictly prohibited.
7. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone,
any electronic device etc.
8. On completion of the test, the candidate must hand over the Answer Sheet (OMR) to the Invigilator on duty
in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.

MATHEMATICS 5. The equation sin x – /2 + 1 = 0 has one root in the

interval
1. Let a , b , c are unit vectors such that a is
    
perpendicular to both b and c . The angle between the (a)  0,  (b)   , 0
2 2
vectors b and c is /6. If a  n  b  c  then n =  3    
(a) 0 (b) ± 1 (c)  ,  (d)  , 
2 2
(c) ± 2 (d)  3
 0 a
2. If there are 6 periods in each working day of a school, 6. Let A   then the value of (A + I)50 – 50A
 0 0
then the number of ways that you can arrange 5 (where I is 2 × 2 unit matrix) is
subjects during the working day is (a) A (b) I
(a) 720 (b) 3600 (c) Null matrix (d) 2A
(c) 240 (d) 1800
7. Let A be a non-singular matrix such that
3. The coefficient of x8 in (x – 1)(x – 2).....(x –10) is
(a) 1320 (b) 1230 1 1 1
1
(c) – 1320 (d) –1230 A  4 6 8
. Then the value of det |2A|.
100 100 99
4. 10 persons are seated at round table. If 3 persons are
selected at random the probability that no two persons (a) 8 (b) – 4
are adjacent to each other is (c) 16 (d) – 8
(a) 5/12 (b) 6/7
(c) 3/4 (d) 7/10
TAKSHILA INSTITUTE CORPORATE OFF : D-11/148, SEC-8, (OPP. METRO PILLAR 390), ROHINI-110085 PH:- 011-47155238, 9310378303, 9868445900
 8
C0 8 18. The volume of a spherical ball increases at the rate of
8.  C1 8 C 2 .6 8 C3 .62  .... 8 C8 .67 is equal to c.c./sec. then the rate of increase of radius when the
6
volume is 288  c.c is
(a) 0 (b) 67
(a) 1/36 (b) 1/72
58 (c) 1/18 (d) 1/9
(c) 68 (d)
6
 R 
9. Rolle's theorem holds for the function 19. In a right angled at A, the value of cos 1  is
 r2  r3 
f  x  x  bx  cx in 1  x  2 at the point 4/3 then
3 2
(a) 30º (b) 60º
the value of “b + c” is (c) 90º (d) 45º
(a) 1 (b) 2
(c) 3 (d) 4 20. The contrapositive of   p  q    q   r  is
(a)  p  q     q  p  (b)   p  r     p  q 
10. A tangent to the parabola y2 = 8x , making an angle
(c)   q  r    p  q  (d)   p  r    p  r 
45º with the line y = 3x + 5 is
(a) 2x + y + 1 = 0 (b) 2x – y + 1 = 0
INTEGER TYPE
(c) x + 2y + 2 = 0 (d) x– 2y – 6 = 0
21. The smallest value of k, for which both the roots of
11. The area bounded by y = 2x – x2 and y = –x is the equation x2 – 8kx + 16(k2 – k + 1) = 0.
(a) 9/2 (b) 43/6
(c) 35/6 (d) 10/3 22. The coefficients of three consecutive terms of
(1 + x)n + 5 are in the ratio 5 : 10 : 14. Then n =
12. A variable ‘x’ takes values 1, 2, 3, 4, 5 with
corresponding frequencies 1, 2, 3, 4, 5. Then the mean 23. Two parallel chords of a circle of radius 2 are at a
deviation of x, from mean is distance 3  1 apart. If the chords subtend at the
(a) 2/3 (b) 16/5  2
(c) 6/5 (d) 16/15 center, angle of and , where k > 0, then the
4 k
value of [k] is.
13. A straight line L with negative slope passes through
the point A (8, 2) and cuts the positive co-ordinate axes [Note: [k] denotes the largest integer less than or equal
at the points P and Q. As 'L' varies the absolute to k]
minimum value of OQ + OP where 'O' is origin is
(a) 10 (b) 12 24. Let m and n be two positive integers greater than 1. If
(c) 16 (d) 18  ecos( an )  e  m
lim      e  then the value of is
14. If a, b, c are sides of a triangle then the minimum value a0  m  2 n
 
a b c
of   is 1
1 x  12  9 x 2 
bca cab abc 25. If   9 x  3tan
(a) 2 (b) 3  (e )  2   dx
0  1 x 
(c) 4 (d) 5
where tan–1x takes only principal values, then the value
15. If  are the roots of the equations ax2 + bx + c = 0  3 
1 of  loge |1   |   is
 4 
then Lt e1 ax 
2
 bx  c x 
is
x  PHYSICS
(a) log | ( – )| (b) log |a( – )|
(c) ea(–) (d) ea(+) 26. The deceleration experienced by a moving motor boat
after its engine is cut off, is given by dv/dt = –kv3 where
16. If 8 f(x) + 6 f (1/x) = x + 5 then f (1) = k is a constant. If v0 is the magnitude of the velcocity
(a) 0 (b) 1 at cut-off, the magnitude of the velocity at a time t after
(c) 1/2 (d) –1 the cut-off is
v0
x y 1 z  3 (a) (b) v 0 e  kt
17. If the angle between the line   and the
1 2  2v02 kt  1 
 5  (c) v 0 / 2 (d) v0
plane x + 2y + 3z = 4 is cos 1   then  is equal to
 14 
27. A money is decending from the branch of a tree with
(a) 2/5 (b) 3/5
constant acceleration. If the breaking strength is 75%
(c) 2/3 (d) 3/2 of the weight of the monkey, the minium acceleration

3 TAKSHILA INSTITUTE CORPORATE OFF : D-11/148, SEC-8, (OPP. METRO PILLAR 390), ROHINI-110085 PH:- 011-47155238, 9310378303, 9868445900
 with which monkey can slide down without breaking  V2  n  2  V1  V2 
(b) nRT log10  V  n   n  V V 
the branch is  1   1 2 
(a) g (b) 3g/4  V  n  2  V1  V2 
(c) g/4 (d) g/2 (c) nRT log e  2   n  V V 
V
 1  n    1 2 
28. The moment of inertia of a uniform semicirular wire  V1  n   VV 
of mass m and radius r, about an axis passing through (d) nRT log e    n 2  1 2 
 V2  n   V1  V2 
its centre of mass and perpendicular to its plane is
33. A sonometer wire of length 1.5 m is made of steel. The
k
mr2  1  2  . Find the value of k tension in it produces an elastic strain of 1%. What
   is the fundamental frequency of steel if density and
(a) 2 (b) 3 elasticity of steel are 7.7 × 103 kg/m3 and 2.2 × 1011
(c) 4 (d) 5 N/m2 respectively?
29. A body starts from rest from a point distance R0 from (a) 188.5 Hz (b) 178.2 Hz
the centre of the earth. The velocity acquired by the (c) 200.5 Hz (d) 770 Hz
when it reaches the surface of the earth will be (R 34. A hollow cylinder has a charge q coulomb within it.
represents radius of the earth). If  is the electric flux in units of voltmeter associated
with the curved surface B, the flux linked with the
 1 1
(a) 2GM  1  1  (b)
2GM    plane surface A in units of voltmeter will be
R R  R
 0 R 
 0 
q
 1
(c) GM   1  (d) 2GM  1  1  (a) 2
 R R  0
 R R0   0 

30. Two liquids of densities d1 and d2 are flowing in (b)
3
identical capillary tubes under the same pressure
difference. If t1 and t2 are time taken for the flow of q 1 q 
(c)    (d) 2     
equal quantities (mass) of liquids, then the ratio of 0  0 
coefficient of viscosity of liquids must be 35. A parallel plate capacitor is made of two plates of
d1t1 t1 length l, width w and separated by distance d. A
(a) d t (b) t
2 2 2 dielectric salb (dielectric constant K) that fits exactly
d2 t 2 d1 t 1 between the plates is held near the edge of the plates.
(c) d t (d) d2 t 2 U
1 1 It is pulled into the capacitor by a force F  
x
31. One end of a thermally insulated rod is kept at a where U is the energy of the capacitor when dielectric
temperature T1 and the other at T2 . The rod is compsed is inside the capacitor up to distance x (See figure).
of two sections of length l 1 and l2 and thermal If the charge on the capacitor is Q then the force on
conductivites K1 and K2 respectively. The temperature the dielectric when it is near the edge is:
at the interface of the two sections is

 K1l1T1  K 2 l2 T2   K 2 l2 T1  K1l1T2  Q2d Q2

(a) K (b) (K  1)
(a)
 K1l1  K1l2  (b)
 K1l1  K 2 l2  2 l 2  0 2dl2 0
Q2 d Q2 w
 K 2 l1T1  K1l2 T2   K1l2 T1  K 2 l1T2  (c) (K  1) (d)
2dl 2 0
K
(c) (d) 2wl2  0
 K 2 l1  K1l2   K1l2  K 2 l1 
36. A cylindrical solid of length L and radius a is having
32. Work done by a system under isothermal change from
a volume V1 to V2 for a gas which obeys Vander Waal’s varying resistivity given by   0 x, where 0 is a
2
positive constant and x is measured from left end of
 
equation  V   n   P  n   nRT is solid. The cell shown in the figure is having emf V
 V  and negligible internal resistance. The electric field as
 V2  n  2  V1  V2  a function of x is best described by
(a) nRT log e  V  n   n  V V 
 1   1 2 

TAKSHILA INSTITUTE CORPORATE OFF : D-11/148, SEC-8, (OPP. METRO PILLAR 390), ROHINI-110085 PH:- 011-47155238, 9310378303, 9868445900 4
 V VR1R 2
(c) R at t = 0 and at t  
2 R12  R 22
V  R1  R 2  V
(d) at t = 0 and R at t  
2V 2V R1R 2 2
(a) x (b)  L2 x
L2 0 41. The electric field of an electromagnetic wave travelling
V through vaccum is given by the equation E = E0sin (kx
(c) x (d) None of these –t). The quantitiy that is independent of wavelength
L2
is
37. A moving coil galvanometer has 150 equal divisions. k
(a) k (b)
Its current sensitivity is 10-divisions per milliampere 
and voltage sensitivity is 2 divisions per millivolt. In (c) k 2  (d) 
order that each division reads 1 volt, the resistacne in 42. f the rfractive index of the material of a prism is
ohms needed to be connected in series with the coil A
will be cot and the angle of prism is A, then angle of
2
(a) 105 (b) 103 minimum deviation is
(c) 9995 (d) 99995 (a)   2A (b)   A
38. A long insulated copper wire is closely wound as a  
(c)  2A (d) A
spiral of ‘N’ turns. The spiral has inner radius ‘a’and 2 2
outer radius ‘b’. The spiral lies in the XY plane and 43. The intensity at the maximum in a Young’s double slit
a steady current ‘I’ flows through the wire. The Z- experiment is I0. Distance between two slits is d = 5,
component of the magnetic field at the centre of the where  is the wavelength of light used in the
spiral is experiment. What will be the intensity in front of one
of the slits on the screen placed at a distance
D = 10d?
I
(a) I0 (b) 0
4
3 I0
0 NI 0 NI (c) I 0 (d)
b ba 4 2
(a) 2 b  a n  a  (b) 2 b  a n  b  a 
        44. Photoelectric emission is observed from a metallic
 0 NI  b   0 NI  b  a  surface for frequencies v1 and v2 of the incident light
(c) n   (d) n   rays (v1 > v2). If the maximum values of kinetic energy
2b a 2b  ba 
of the photoelectrons emitted in the two cases are in
39. A magnetic dipole is under the influence of two the ratio of 1 : k, then the threshiold frequency of the
magnetic fields The angle between the field directions metallic surface is
is 60° and one of the fields has a magnitude of 1.2 × v  v2 kv1  v 2
10–2 T. If the dipole comes to stable equilibrium at an (a) 1 (b)
k 1 k 1
angle of 15° with this field, what is the magnitude of kv 2  v1 v  v1
other field? (c) (d) 2
k 1 k
(a) 4.4 × 10–3 tesla (b) 5.2 × 10–3 tesla
(c) 3.4 × 10–3 tesla (d) 7.8 × 10–3 tesla 45. In that Bohr’s model of hydrogen-like atom the force
between the nucleus and the electron is modified as
40. In the circuit shown below, the key K is closed at e2  1  
F  ,
t = 0. the current through the battery is 4 0  r 2 r 3  where  is a constant. For this atom,
the radius of the n th orbit in terms of the Bohr radius
 0 0 h 2 
a   is
 me 2 
VR1R 2 V (a) rn  a 0 n   (b) rn  a 0 n 2  
(a) at t = 0 and R at t  
(c) rn  a 0 n 2   (d) rn  a 0 n  
R12  R 22 2

V V R1  R2 
(b) R at t = 0 and at t  
2 R1R2

5 TAKSHILA INSTITUTE CORPORATE OFF : D-11/148, SEC-8, (OPP. METRO PILLAR 390), ROHINI-110085 PH:- 011-47155238, 9310378303, 9868445900
 INTEGER TYPE 52. Which of the following is the correct order for
increasing bond angle ?
46. A ring of radius r is suspended from a point on its (a) NH3 < PH3 < AsH3 < SbH3
circumference. The angular frequency of oscillation (b) H2O < OF2 < Cl2O
2 (c) H3Te+ < H3Se+ < H3S+ < H3O+
is found to be   Find n.
nr (d) BF3 < BCl3 < BBr3 < BI3
53. The correct order of decreasing first ionisation
potential is :
(a) Ca > K > Rb > Cs (b) Cs > Rb > K > Ca
(c) Ca > Cs > Rb > K (d) K > Rb > Cs > Ca
53. The pressure exerted by 1 mole of CO2 at 273 K, is
34.98 atm. Assuming that volume occupied by CO2
molecules is negligible, the value of van der Waals’
constant for attraction of CO2 gas is:
47. A diatomic ideal gas is compressed adiabatically to (a) 3.59 dm6 atm mol–2 (b) 2.59 dm6 atm mol–2
1
of its initial volume. If the initial temperature of (c) 1.25 dm6 atm mol–2 (d) 1.59 dm6 atm mol–2
32
the gas is Ti (in Kelvin) and the final temperature is 54. An aqueous solution of 6.3 g oxalic acid dihyrate is
aTi, the value of a is made upto 250 mL. The volume of 0.1 N NaOH
required to completely to neutralise 10 mL of this
48. A series R-C combination is connected to an AC solution is:
voltage of angular frequency  = 500 rad/s. If the (a) 40 mL (b) 20 mL
impedance of the R-C circuit is R 1.25 , the time (c) 10 mL (d) 4 mL
constant (in milli second) of the circuit is
55. For a cell reaction
49. A cubical vessel with non-transparent walls is to be Pt |H 2 (l atm) H (Pt) || H (1M)| H2 (latm) | Pt . Cell
located that the eye E of an observer cannot see its potential is ‘X’ volt, Then PH will be given as
bottom but can see all the wall CD. The height should X X
water be filled in the vessel for the observer to see an (a) PH  (b) PH  
.0591 .0591
object O placed at a distance b = 10 cm from the corner  1

C is found to be n.9. Find n.  of water = 4/3. (c) PH   log  H  (d) PH   log  H  

56. For, Ag(CN  ) 2  Ag   2CN 

KC = 4 × 10–19 at 25ºC
Calculate Ag+ concentration in a solution which is
originally 0.1 M in KCN and 0.03 M in AgNO3.
(a) 7.5 × 10–18 M (b) 7.5 × 10–15 M
(c) 6.2 × 10 M–15 (d) 3.4 × 10–15 M
57. When one mole of monoatomic ideal gas T K
undergoes reversible adiabatic change under a constant
external pressure of 1 atm changes volume from 1 litre
50. For a transistor connected in common emitter mode, to 2 litre. The final temperature in kelvin would be:
the voltage drop across the collector is 2V and is 50. T 2
If Rc is 2 k, the base current is n  10–5 A. What is (a) 23 (b) T 
(2) 3  0.081
the value of n?
3
CHEMISTRY (c) T (d) T 
2  0.0821
58. Which of the following statements regarding Bohr
51. The correct order of acidic strength is :
(a) Cl2O7 > SO2 > P4O10 theory of hydrogen atom is not correct ?
(b) CO2 > N2O > SO3 (a) The ionization energy of atom is equal to the
energy equivalent to Rydberg constant
(c) Na2O > MgO > Al2O3
(b) Speed of electron in the n = 2 orbit is larger than
(d) K2O > CaO > MgO
that in the n = 1 orbit

TAKSHILA INSTITUTE CORPORATE OFF : D-11/148, SEC-8, (OPP. METRO PILLAR 390), ROHINI-110085 PH:- 011-47155238, 9310378303, 9868445900 6
 (c) Radius of orbit is directly proportional to square Find correct order of the reactivity of carbonyl groups
of quantum number n with LiAlH4 is:
(d) The distance between successive orbits increases (a) A > B > C > D (b) B > C > D > A
with increase in the value of quantum number n. (c) D > C > B > A (d) B > D > C > A
59. One mole of A at pressure P in a closed container of1
litre shows the following equilibria :
Ag  B ( g )  C ( g ) ; K1 65. Product (B) is:
C ( g )  D( g )  B ( g ) ; K 2
[C ]eq.
The pressure at equilibrium is 2P and  2.1 .
[ A]eq.
The ratio of K1/K2 can be given by: (a) (b)
(a) 3 : 1 (b) 4 : 1
(c) 2 : 1 (d) 1 : 2

60.
(c) (d)

Compare basic strength:

(a) a > b > c (b) b > a > c
(c) c > a > b (d) c > b > a 66.

20% D2SO4in D 2O / Hg
61. Ph — C  C — Me   (P)
Principle organic product is :
(a) (b)

(a) (b)

(c) (d)
(c) (d)
67. SbF4 reacts with XeF4 to form an adduct. The shapes
of cation anion in the adduct are respectively.
62. Which of the following is not optically active?
(a) square planar, trigonal bipyramidal
(a) [Co(en)3]3+ (b) [Cr(Ox)3]3– (b) T-shaped, octahedral
(c) cis-[CoCl2(en)2]+ (d) trans-[CoCl2(en)2]+ (c) square pyramidal, octahedral
63. What is the major alkene formed in the following (d) square planar, octahedral
reaction? 68. 25 g ethylene glycol is present in 100 g of water. The
solution is cooled to –10°C. Kf for H2O is 1.86 K kg
mol–1. The amount of ice separated on cooling is:
(a) 25g (b) 50g
(c) 75g (d) 20 g
69. The bcc structure of an element has density 7.12
kg/m3 and edge length of unit cell is 2.88 Å. The
number of atoms present in 288 g of element is :
(a) 3.4 × 1022 (b) 3.4 × 1023
(a) i (b) i 24
(c) 3.4 × 10 (d) 3.4 × 1021
(c) iii (d) iv
70. A solution of 200 mL of 1 M KOH is added to 200 mL
of 1M HCl and the mixture after attaining reaction
equilibrium shows a rise in temperature by T1. The
64.
experiment is repeated by using 50 mL of 1M KOH
and 50 mL 1 M HCl which at equilibrium shows a rise
in temperature byT2. Thus:
7 TAKSHILA INSTITUTE CORPORATE OFF : D-11/148, SEC-8, (OPP. METRO PILLAR 390), ROHINI-110085 PH:- 011-47155238, 9310378303, 9868445900
 (a) T1  T2 (b) T1  4  T2
(c) T1  2  T2 (d) T1  T2

INTEGER TYPE
71. Total number of buffer solution, that can be prepared
using equimolar solutions of CH3COOH, CH3COONa, 74. The total number of gases produced during complete
KOH, HNO3 ____________. process of reaction
Zn(s)  HNO3  
 Pr oduct
72. 500 ml solution of CaCl2 (Molecular weight = 111 (very dilute)
gm/mol) containing 1.11 gm solute is electrolysed by
75. The ratio of  bonds to  bonds inthe product of
passing 9.65 ampere current for 10 minutes. After
following reaction is
electrolysis pH of solution is found to be x. Then the
value of z is
73. How many Geometrical isomers are possible for the
product in the following reaction.

ANSW ERS KEY

Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. c d a 3 a b b d c a a d d c c c c b b c
Que. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. 2 6 3 2 7 a c c b a d a b d c a c a a b
Que. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Ans. b a d b c 2 4 4 8 2 a c a a a a a b b c
Que. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
Ans. a d c b c a b a c a 3 7 6 4 7

TAKSHILA INSTITUTE CORPORATE OFF : D-11/148, SEC-8, (OPP. METRO PILLAR 390), ROHINI-110085 PH:- 011-47155238, 9310378303, 9868445900 8