Sri Chaitanya IIT Academy.,India.
 A.P  T.S  KARNATAKA  TAMILNADU  MAHARASTRA  DELHI  RANCHI
A right Choice for the Real Aspirant
ICON Central Office - Madhapur - Hyderabad
SEC: LIIT
JEE-MAIN
Time: 09:30AM to 12:30PM
CTM-03
Date: 16-10-22
Max. Marks: 300
IMPORTANT INSTRUCTION:
1.
Immediately fill in the Admission number on this page of the Test Booklet with Blue/Black Ball
Point Pen only.
2.
The candidates should not write their Admission Number anywhere (except in the specified space)
on the Test Booklet/ Answer Sheet.
3.
The test is of 3 hours duration.
4.
The Test Booklet consists of 90 questions. The maximum marks are 300.
5.
There are three parts in the question paper 1,2,3 consisting of Physics, Chemistry and
Mathematics having 30 questions in each subject and subject having two sections.
(I) Section –I contains 20 multiple choice questions with only one correct option.
Marking scheme: +4 for correct answer, 0 if not attempt and -1 in all other cases.
(II) Section-II contains 10 Numerical Value Type questions. Attempt any 5 questions only, if
more than 5 questions attempted, First 5 attempted questions will be considered.
∎ The Answer should be within 0 to 9999. If the Answer is in Decimal then round off to the nearest
Integer value (Example i,e. If answer is above 10 and less than 10.5 round off is 10 and if answer is from
10.5 and less than 11 round off is 11).
To cancel any attempted question bubble on the question number box.
For example: To cancel attempted question 21. Bubble on 21 as shown below
.
Question Answered for Marking
Question Cancelled for Marking
Marking scheme: +4 for correct answer, 0 if not attempt and -1 in all other cases.
6.
Use Blue / Black 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, mobile phone
any electron device etc, except the Identity Card inside the examination hall.
8.
Rough work is to be done on the space provided for this purpose in the Test Booklet only.
9.
On completion of the test, the candidate must hand over the Answer Sheet to the invigilator on duty in
the Hall. However, the candidate are allowed to take away this Test Booklet with them.
10.
Do not fold of make any stray marks on the Answer Sheet
Name of the Candidate (in Capital): ________________________________________________
Admission Number:
Candidate’s Signature: __________________ Invigilator’s Signature: ____________________
Sri ChaitanyaIIT Academy, India
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
16-10-2022_LIIT_Jee-Main_CTM-03_Test Syllabus
PHYSICS
: Units and dimensions, Errors and approximations, Kinematics,
Newtons's Laws Of Motion, Friction, Circular Motion, Work,Energy&
Power
CHEMISTRY
: Atomic Structure, Classification of elements and periodicity in
properties, Chemical Bonding up to Valency Bond theory, Chemical
Bonding, Gaseous State, IUPAC Nomenclature, Structural Isomerism
& tautomerism, Geometrical isomerism, Optical isomerism &
Conformational isomerism, GOC-1: Electronic effects, Reaction
intermediates, GOC-2: Aromaticity, acidic Strength and basic
Strength
MATHEMATICS : Fundamental of Mathematics, Trigonometry, Quadratic Equations &
Expressions and Theorey of Equations, Sequence & Series,
mathematical reasoning, Permutations & Combinations
Sec: LIIT
Page 2
Sri ChaitanyaIIT Academy, India
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
PHYSICS
Max Marks: 100
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be
correct.
Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases.
1.
2.
3.
A particle retards from a velocity V0 while moving in a straight line. If the magnitude of
deceleration is directly proportional to the square root of the speed of the particle, Find
its average velocity for the total time of its motion.
V
V
2V
3
1) 0
2) 0
3) V0
4) 0
3
3
2
2
20
A diwali rocket moves vertically up with a constant acceleration a1  m / s 2 . After
3
some times, its fuel exhausted and then it falls freely with an acceleration a2  10m / s 2 .
If the maximum height attained by the diwali rocket is ‘h’. Find its speed when the fuel is
just exhausted  h  50m 
1) 20m/s
2) 10m/s
3) 4m/s
4) 8m/s
The acceleration versus time graph of a particle moving in a straight line is shown in
figure. The velocity – time graph of the particle would be
a  m / s2 
4
0
4.
5.
t s
1) A straight line 2) A parabola
3) A circle
4) A ellipse
A scooter accelerates from rest for time t1 at constant rate a1 and the retards at constant
rate a2 for time t2 and comes to rest. The correct value of t1 / t2 will be
a  a2
a
a
a  a2
1) 1
2) 1
3) 2
4) 1
a1
a2
a1
a2







The resultant of P and Q is R . If Q is doubled R is doubled. When Q is reversed, R
is again doubled , Find ratio of P : Q : R is
1) 1 : 1 : 1
6.
2
2) 1: 2 : 3
3) 2 : 3 : 2
4) 3 : 2 : 2
If E represents energy, J represents Angular momentum, M represents mass and G
M xG y
represents universal gravitational constant and
is to be a dimensionless
EJ z
expression, then the values of X,Y and Z are respectively.
1) 5, 2, 2
2) 2, 5, 2
3) 2, 2, 5
4) -5, 2, 2
Sec: LIIT
Page 3
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7.
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
V0
sin   t 2  where

V0 and  are constants. The dimensions of V0 and  are respectively
The force acting on a particle at time t is given by the equation, F 
1)  M 1 L1T 2  & T 2 
8.
3)  M 1 L1T 4  & T 2 
4)  M 1 L1T 2  & T 1 
A particle moving in the xy plane experiences a velocity dependent force



F  K VY i  Vx J , where Vx and Vy are x and y compoments of its velocity V . If a is

9.
10.
2)  M 1 L1T 2  & T 2 

the acceleration of the particle, then which of the following statement Is true for the
particle?
 
1) Quantity V  a is constant in time

2) F arises due to a magneticfield
3) Kinetic energy of particle is constant intime
 
4) Quantity V .a is constant in time
A particle is moving in a circle of radius ' r ' under the action of force F   r 2 which is
directed towards the centre of the circle. Total mechanical energy of the particle.
1
5
4
1)  r 3
2)  r 3
3)  r 3
4)  r 3
2
6
3
Two blocks A and B of masses 6kg and 3kg rest on a smooth. Horizontal surface as
shown in figure. If Co- efficient of friction between A and B is 0.4. The maximum
horizontal force which can make them move without separation is
3kg
6kg
11.
F
1) 72N
2) 40N
3) 36N
4) 20 N
A block of mass ‘m’ is lying on a wedge having inclination angle   Tan 1 1 / 5 
.wedge is moving with a constant acceleration a  2 m / s 2 .The minimum value of Coefficient of friction  so that m remains stationary w.r .t wedge is
m
a  2m / s 2

1)
Sec: LIIT
2
9
2)
5
12
3)
1
5
4)
2
5
Page 4
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12.
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
A circular road of radius 1000 m has banking angle 450 , The maximum safe speed
 in ms  of a car having a mass 2000kg will be    0.5
1
13.
14.
1) 172
2) 124
3) 99
4) 86
7
A ship of mass 3  10 kg , initially at rest, is pulled by a force of 5  104 N through a
distance of 3m , Assuming that the resistance due to water is negligible, the speed of the
ship is
1) 1.5 m/s
2) 60 m/s
3) 0.1 m/s
4) 5 m/s
A block of mass m welded with a light spring of stiffness K is in equilibrium on an
smooth inclined plane with angle of inclination  . If a variable external force is applied
slowly till the spring comes to its relaxed position. find the work done by spring force
m

 mg sin  
15.
16.
2
 mg sin  
2
2
2  mg sin  
2mg sin 
1)
2)
3)
4)
4k
2k
4k
k
A bullet leaving the muzzle of a rifle barrel with a velocity V penetrates a plank and loses
one – fifth of its velocity. It then strikes second plank, which it just penetrates through.
Find the ratio of the thickness of the planks supposing the average resistance to the
penetration is same in both the cases
16
9
25
16
1)
2)
3)
4)
9
16
16
25
The acceleration- displacement graph of a particle moving in a straight line as shown in
figure , Initial velocity of particle is zero . Find the velocity of the particle when
displacement of the particle is S=12m
4
2
0
1) 4 3 m / s
Sec: LIIT
2
2) 3 m / s
8
3) 4 m / s
10
12
 m
4) 3 2 m / s
Page 5
Sri ChaitanyaIIT Academy, India
17.
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
The velocity- displacement graph for an airplane travelling on a straight runway is shown
determine the acceleration of the Plane at S=50 m
V m / s
50
40
100
1) 4 m / s 2
18.
2) 6 m / s 2
200
3) 8 m / s 2
5 m
4) 2 m / s 2
A stone is dropped from the top of a tower and one second later , a second stone is
thrown vertically downward with a velocity 20 m/s. The second stone will overtake the
first after. Travelling a distance of  g  10m / s 2 
1) 13m
19.
2) 15m
3) 11.25m
4) 19.5m
The horizontal and vertical displacement of a particle moving along a curved line are
given by x  5t , and y  2t 2  t . Time after which its velocity vector makes an angle of
450 with the horizontal is
1) 0.5 S
20.
2) 1 S
3) 2 S
4) 1.5 S
A block is placed on the top of a plane inclined at 300 with horizontal. The length of the
plane is 5m. The block slides down the plane and reaches the bottom Find the speed of
the block at the bottom of the Inclined plane is smooth  g  9.8m / s 2 
5m
300
1) 7 m/s
2) 4 m/s
3) 8 m/s
4) 5m /s
(NUMERICAL VALUE Type)
Section-II contains 10 Numerical Value Type questions. Attempt any 5 questions only. If more than 5 questions attempted, First 5
Attempted questions will be considered. The Answer should be within 0 to 9999. If the Answer is in Decimal then round off to the nearest
Integer value (Example i,e. If answer is above 10 and less than 10.5 round off is 10 and if answer is from 10.5 and less than 11 round off is
11).
Marking scheme: +4 for correct answer, 0 if not attempt and -1 in all other cases.
Sec: LIIT
Page 6
Sri ChaitanyaIIT Academy, India
21.
22.
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
The PE of a certain spring when stretched from natural length through a distance of 0.3
m is 5.6 J. Find the amount of work in joule that must be done on this spring to stretch it
though an additional distance 0.15m
In figure shown all the surface are friction less and mass of the block m=100g. The block
and the wedge are held initially at rest Now the wedge is given a horizontal acceleration
of 10m / s 2 by applying a force on the wedge, so that the blocks does not slip on the
wedge then find work done in joules by the normal force in ground frame on the block in
1sec
10m / s 2
m
M

23.
24.
25.
26.
27.
28.
29.
30.
A block A of mass m is placed over a plank B of mass 2m. plank B is placed over a
smooth horizontal surface. The coefficient of friction between A and B is 0.4. Block A is
xg
given a velocity V0 towards right . The acceleration of B relative to A is
. The value
4
of xis
V0
A
B
A block of mass 1kg lies on a horizontal surface in a truck the co-efficient of static
friction between the block and the surface is 0.6. If the acceleration of the truck is 5m / s 2
, Find the frictional force acting on the block is (in N)
A circular track has a radius of 10m . If a vehicle goes round it at an average speed of
18kmh 1 . What should be the proper angle (in degrees) of banking Tan140  0.25 
A point moves along a circle having a radius 20cm with a constant tangential acceleration
5cm / s 2 . How much time is needed after motion begins for the normal acceleration of
the point to be equal to tangential acceleration? (in sec)
A car is travelling along a circular curve that has a radius of 50m. If its speed is 16m/s
and is increasing uniformly at 8m / s 2 determine the magnitude of its acceleration at this
instant. (in m/s2)
A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of
radius 3m rotating about its vertical axis . The coefficient of friction between the wall and
his clothing is 0.15. What is minimum rotational speed of the cylinder to enable the man
to remain stuck to the wall ( without falling) when the floor is suddenly removed? (in
rad/sec)
Two bodies were thrown simultaneously from the same point , one straight up, and the
other, at an angle of   300 to the horizontal. The initial velocity of each body is 20m/s.
Neglecting air resistance, the distance between the bodies at t=1.2 s later is (in m)
A ball is projected with a velocity 20m/s at angle to the horizontal. In order to have the
maximum Range. Its velocity (in m/s) at the highest position must be  cos 450  0.7 
Sec: LIIT
Page 7
Sri ChaitanyaIIT Academy, India
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
CHEMISTRY
Max Marks: 100
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be
correct.
Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases.
31.
The first emission line of Balmer series for H-spectrum has the wave no. equal to
7 RH
cm 1
144
The orbital represented by  4,2,0
1)
32.
9 RH
cm 1
400
2)
3)
3RH
cm 1
4
4)
5RH
cm 1
36
1) 4d z
2) 4 px
3) 4 pz
4) 4d xy
The IUPAC Nomenclature of Roentgenium
1) Unnilunnium 2) Unununnium 3) Unnilseptium 4) None of these
The following statements concern element in the periodic table. Which of the following is
true.
1) For group 15 elements the stability of +5 oxidation state increases down the group
2) Elements of group 16 have lower I.P value Compared to those of group 15 in the
corresponding periods
3) The group 13 elements are all metals
4) All the elements in group 17 are gases
The cololur of First line of Balmar series is
1) Red
2) Blue
3) Violet
4) Green
2
3

2
The correct order of the ionic radii of O , N , F , Mg , Na  and Al 3 is
1) N 3  O 2  F   Na   Mg 2  Al 3
2) Al 3  Na   Mg 2  O 2  F   N 3
3) Al 3  Mg 2  Na   F   O 2  N 3 4) N 3  F   O 2  Mg 2  Na   Al 3
The number and type of bonds in C22 ion in CaC2 are
1) One  bond and one  bond
2) One  bond and two  bond
3) Two  bond and two  bond
4) Two  bond and one  bond

The shape of IF6 is
1) Trigonally distorted octahedran
2) Pyramidal
3) Octahedral
4) Square planar
2
33.
34.
35.
36.
37.
38.
39.

For an ideal gas the value of   is
40.
1) Positive
2) Zero
3) Negative
4) Interchangeable
The figure shows graphs of pressure verses density for an ideal gas at two temperatures
T1 and T2 which is correct?
 v T
T1
T2
Pressure
Density
1) T1  T2
Sec: LIIT
2) T1  T2
3) T1  T2
4) None of these above
Page 8
Sri ChaitanyaIIT Academy, India
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
41.
Consider the following species :
42.
3
3
2
(A) OH
(B)
(C)
(D)
Arrange these species in their decresing order of nucleophilicity.
1) C  D  B  A
2) B  A  C  D
3) A  B  C  D
4) C  A  B  D
Decreasing order of stability for the following radicals is :
CH O
NH
CH
CH3
CH2
CH2 CH,CH2CH CH 2 ,
(I)
,
(II)
(III)
43.
44.
(IV)
1) II  III  I  IV
2) III  II  I  IV
3) III  II  I  IV
4) I  IV  II  III
Which of the following exhibit electromeric effect?
1) Alkanes
2) Aldehydes
3) Alkyl halides
4) Alkyl amines
Which of the following compounds will exhibit d-orbital resosnance?
H
OH
45.
H PH
Cl
1)
2)
3)
4)
Arrange the following cations in decreasing order of stability:
CH2 CHCH2
(Q)
PhCH2
(R)
CH3 CH2
(S)
(P)
1) P  R  Q  S
3) Q  R  P  S
Sec: LIIT
2) R  P  S  Q
4) P  Q  S  R
Page 9
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46.
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
Write the order of basic strength:
O
N
N
N
(Q)
H
(R)
1) Q  R  S  P
2) P  R  Q  S
3) R  P  S  Q
4) P  Q  R  S
The correct order of decreasing acidic strength of the following is
COOH
COOH
COOH
H3C
COOH
CH3
H3C
48.
(S)
H
(P)
47.
N
CH3
NO2
NO2
NO2
SOH
3
(P)
(Q)
(R)
(S)
1) P  Q  R  S
2) S  R  P  Q
3) S  Q  P  R
4) S  R  Q  P
Which of the following compounds will exhibit tautomerism?
OH
OMe
OMe
49.
NO
NO
1)
2)
3)
Compare acidic strength of the following compound.
O
O
O
4)
NO
O
O
O
O
O
O
(P)
1) P  Q  R
3) R  P  Q
Sec: LIIT
(Q)
(R)
2) Q  P  R
4) R  Q  R
Page 10
Sri ChaitanyaIIT Academy, India
50.
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
Which of the following pairs of compounds may be regarded both as functional isomer
and positional isomer?
1) Benzyl alcohol and methoxy benzene
2) o-cresol and p-cresol
3) Benzyl alcohol and o-cresol
4) Benzyl alcohol and benzyl methyl ether
(NUMERICAL VALUE TYPE)
Section-II contains 10 Numerical Value Type questions. Attempt any 5 questions only. If more than 5 questions attempted, First 5
Attempted questions will be considered. The Answer should be within 0 to 9999. If the Answer is in Decimal then round off to the nearest
Integer value (Example i,e. If answer is above 10 and less than 10.5 round off is 10 and if answer is from 10.5 and less than 11 round off is
11).
Marking scheme: +4 for correct answer, 0 if not attempt and -1 in all other cases.
51.
52.
53.
54.
The value of magnetic quantum number of the outer most electron for Zn  ion is _____
The number of paramagnetic species among the following is ___ B2 , Li2 , C2 , C2 , O  and He2
Total number of lonepair of electrons in I 3 ion is
At 300k the density of a certain gaseous molecule at 2 bar is doubled to that of di
nitrogen  N 2  at 4 bar. The molecular mass of gaseous molecule is
55.
The I .E1 of “H” is 13.6 ev. It is exposed to electron magnetic wave of 1028 A and given
out induced radiation. Find the energy level of these induced (After excitation) radiation.
Find out number of stereogenic centers present in following compound simvastatin
56.
2
0
O
OH
O
O
O
57.
58.
Find out number of structural isomers possible for C6 H14
Find out number of benzylic hydrogen in
59.
How many resonating structures are possible for the compound.
O
(Furan)
60.
The total number of constitutional isomers possible for C4 H11 N
Sec: LIIT
Page 11
Sri ChaitanyaIIT Academy, India
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
MATHEMATICS
Max Marks: 100
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be
correct.
Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases.
61.
For 0   
1)
62.

, the solution of
2

4
2)

6
6

 cos ec  
m 1
 m  1   cos ec   m   4

3)
4



12


4)
4 
2 is
7
12

Let S   x    ,   : x  0,   .The sum of all distinct solutions of the equation
2

3 sec x  cos ecx  2  tan x  cot x   0 in the set S is equal to
1) 
63.
7
9
2
9
3) 0
4)
5
9
The maximum value of  cos 1  cos  2  ......  cos  n  under the restrictions
0  1 ,  2 ,......,  n 
1) 1 / 2 n/ 2
64.
2) 

and  cot 1  .  cot  2  ......  cot  n   1 is
2
2) 1/ 2n
3) 1/ 2
4) 1
If  ,  ,  ,  are the smallest positive angles in ascending order of magnitude which have
their sines equal to the positive quantity k, then the value of 4sin




 3sin  2 sin  sin
2
2
2
2
is equal to
1) 2 1  k
65.
2) 2 1  k
3) 2 k
4) None of these
If A,G and H are the Arithmetic mean, Geometric mean and Harmonic mean between
two unequal positive integers, Then the equation Ax 2  G x  H  0 does not have
66.
1) Both roots fractions
2) One negative fraction root
3) Exactly one positive root
4) No root greater than 2
If a,b,c are positive rational numbers such that a>b>c and the quadratic equation
 a  b  2c  x2   b  c  2a  x   c  a  2b   0 has a root in the interval (-1,0), then
1) c+a >2b
2) Both roots of the given equation are irrational
3) The equation ax 2  2bx  c  0 has both negative real roots
4) The equation cx 2  2ax  b  0 has both positive real roots
Sec: LIIT
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Sri ChaitanyaIIT Academy, India
67.
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
Let [a] denote the greatest integer less than or equal to a . Given that the quadratic
equation x 2   a 2  5a  b  4  x  b  0 has roots 5 and -1. Then the set of values of a is

1)  1,

5 3 5  5  3 5 
,6


2   2

3)  ,  1   6,  
68.
4)  ,  
No.of quadratic equations which are unchanged by squaring their roots is ________
1) 4
69.
 53 5 53 5 
,

2 
 2
2) 
2) 3
3) 2
4) 1
If a  0, b  0, c  0 and the minimum value of a  b 2  c 2   b  c 2  a 2   c  a 2  b 2  is  abc ,
then find the value of 
1) 2
70.
2) 1
3) 6
4) 3
If S r denotes the sum of the first r terms of an AP, and the value of
S3 r  S r 1
 pr  q
S 2 r  S 2 r 1
then find the value of p+q
1) -1
71.
2) 1
3) 3
4) None of these
If H1 , H 2 ,........H n are n harmonic means between a and b   a  then find the value of
H1  a H n  b

H1  a H n  b
1) n  1
72.
3) 2n
4) 2n  3
If a1 , a2 ,......an are in H.P., then the expression a1a2  a2 a3  ......  an1an is equal to
1) n  a1  an 
73.
2) n  1
2)  n  1 a1  an 
3) na1an
4)  n  1 a1an
If S *  p, q, r  is the dual of the compound statement S(p,q,r) and S(p,q,r)
  p     q  r   then S *   p,  q,  r  is equivalent to
1) S  p, q, r 
74.
2)  S   p,  q,  r  3)  S  p, q, r 
4) S *  p, q, r 
  p  q     p     q   is
1) A tautology
2) A contradiction
3) Neither a tautology nor contradiction
4) Cannot come any conclusion
Sec: LIIT
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Sri ChaitanyaIIT Academy, India
75.
76.
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
The statement is p   q  p  equivalent to
1) p   p  q 
2) p   p  q 
3) p   p  q 
4) p   p  q 
In the truth table for the statement  p  q     p  q  the last column has the truth value
in the following order is
77.
1) TTFF
2) FFFF
3) TTTT
4) FTFT
The number of distinct natural numbers up to a maximum of four digits and divisible by
5, which can be formed with the digits 0,1,2,3,4,5,6,7,8,9, each digit not occurring more
than once in each number, is
78.
1) 1246
2) 952
3) 1106
4) None of these
6 white and 6 black balls are distributed among ten identical urns, so that there is atleast
one ball in each urn. Balls are all a like except for the colour and each box can hold any
number of balls. The number of different distributions of the balls is :
79.
1) 26250
2) 132
3) 12
4) 10
Number of ways in which two Americans, two British, one Chinese, one dutch and one
Egyptian can sit on a round table so that persons of the same nationality are separated is
80.
1) 48
2) 240
3) 336
4) None of these
In an examination of 9 papers a candidate has to pass in more papers than the number of
papers in which he fails in order to be successful. The number of ways in which he can be
unsuccessful is
1) 255
2) 256
3) 193
4) 319
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Sri ChaitanyaIIT Academy, India
16/10/22_LIIT_Jee-Main_CTM-03_Q.P.
(NUMERICAL VALUE TYPE)
Section-II contains 10 Numerical Value Type questions. Attempt any 5 questions only. If more than 5 questions attempted, First 5
Attempted questions will be considered. The Answer should be within 0 to 9999. If the Answer is in Decimal then round off to the nearest
Integer value (Example i,e. If answer is above 10 and less than 10.5 round off is 10 and if answer is from 10.5 and less than 11 round off is
11).
Marking scheme: +4 for correct answer, 0 if not attempt and -1 in all other cases.
81.
If a,b,c are three natural numbers in AP such that a+b+c=21 and if possible number of
ordered triplet (a,b,c) is  then the value of    5  is
82.
In a single correct match the column question, column I contain 10 questions and column
II contain 10 answers written in some arbitrary order. If the number ways a student can
answer this question so that exactly 6 of his matching are correct is k, then (sum of digits
of k)/2 is equal to
83.
There are 720 permutations of the digits 1,2,3,4,5,6. Suppose these permutations are
arranged from smallest to largest numerical values, beginning from 123456 and ending
with 654321. Then the digit in unit place of number at 267th position is …..
84.
The number of solutions of the equation
85.
Number of solution(s) of the equation
1
 log15 cos x )
51/2  51/2 log5  sin x  152
for x  0,100  is
sin x sin 3x sin 9 x
 


 0 in the interval  0,  is
cos 3x cos 9 x cos 27 x
 4
______.
86.
Number of integral value(s) of m for which the equation sin x  3 cos x 
4m  6
has
4m
solutions, x   0, 2  is
87.
If 2-i is a root of the equation ax 2  12 x  b  0 (where a and b real), then the value of ab is
equal to
2
3
6 10 14
   .....is
32 33 34
88.
The sum of infinite terms of the series 1  
89.
The 20th term of the series 2+3+5+9+16+…… is
90.
Two consecutive numbers from 1,2,3,…..,n are removed. If the arithmetic mean of the
remaining numbers is 105/4 then
Sec: LIIT
n
is equal to
10
Page 15