24-01-2023 - SR - Super60 - NUCLEUS & ALL - BT - Jee-Main-GTM-14 - Q.PAPER

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: Sr.Super60_NUCLEUS & ALL_BT JEE-MAIN Date: 24-01-2023
Time: 09.00Am to 12.00Pm GTM-14 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: ________________
24‐01‐23_Sr.Super60_NUCLEUS & ALL_BT_ Jee‐Main_GTM‐14_Test Syllabus
PHYSICS : TOTAL SYLLABUS
CHEMISTRY : TOTAL SYLLABUS
MATHEMATICS : TOTAL SYLLABUS
SRI CHAITANYA IIT ACADEMY, INDIA 24‐01‐23_ Sr.Super60_NUCLEUS & ALL_BT _ Jee‐Main_GTM‐14_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. The focal lengths of the objective and the eye –piece of a compound microscope are 2.0cm
and 3.0cm respectively. The distance between the objective and the eye-piece is 15.0cm. The
final image formed by the eye–piece is at infinity. The two lenses are thin. The distance (in
cm) of the object and the image produced by the objective measured from the objective lens
are respectively.
1) 2.4 and 12.0 2) 2.4 and 15.0 3) 2.0 and 12.0 4) 2.0 and 3.0
2. If a direct current of "a" ampere is super imposed on an alternating current I=bsin t flowing
through a wire, what is the effective value of resulting current in the circuit
12 12 12
 b2   a2   b2 
1)  a 2  

 2 

2) a 2  b 
2 12
3) 
 2

 b2 


4)  a 2 

 2



3. Statement-1: A nucleus having energy E1 decays by   emission to a daughter nucleus
having energy E2 but the   rays are emitted with a continuous energy spectrum having end
point energy E1  E2 .
Statement-2: To conserve energy and momentum in β- decay, at least three particles must
take part in transformation
1) Statement-1 and Statement-2 both are correct and Statement-2 is the correct explanation
of Statement-1.
2) Statement-1 is correct, Statement-2 is correct and Statement-2 is not the correct
explanation of Statement-1.
3) Statement-1 is correct, Statement-2 is correct
4) Statement-1 correct but Statement-2 is not correct
Sec: Sr.Super60_NUCLEUS & ALL_BT Page 2

4. A hollow sphere of radius R is made of metal whose specific gravity is  . The sphere will
float in water if thickness of wall of sphere is (thickness of wall << R)
R 2R R 4R
1)  2)  3)  4) 
3 3 3 3
5. A capacitor of capacitance C=3 F is first charged by connecting it across a 10V battery by
closing key K1 . It is then allowed to get discharged through 2 and 4 resistor by closing
the key K 2 and opening key K1 . The total heat energy dissipated in the 2 resistor is equal
to
1) 0.5 mJ 2) 0.05 mJ 3) 0.15 mJ 4) 0.10 mJ

6. A conducting rod of length l is hinged at point O. It is free to rotate in a vertical plane.

There exists a uniform magnetic field B in horizontal direction. The rod is released from the
horizontal position as shown. The potential difference between the ends of the rod when it
has turned by  (as shown in figure) is proportional to
12
1) l1 2 2) l 2 3) sin  4)  sin  
7. If a dipole of dipole moment Piˆ is placed at point (0, y) and a negative point charge at the
origin of coordinate system, net electric field at point (x, x + y) vanishes. If x and y both are
positive, the coordinate y is equal to
1) x 2) 2x 3) 2.5x 4) 3x
8. Weight of a body at the equator of a planet is half of that at the poles. If peripheral velocity
of a point on the equator of this planet is v 0 .What is the escape velocity of a polar particle?
1) v 0 2) 2v0 3) 3v0 4) 4v0
9. A piece of metal weighs 46g in air. When it is immersed in a liquid of specific gravity 1.24
at 27ºC, it weighs 30g. When the temperature of liquid is raised to 42ºC, the metal piece
weighs 30.5g. Specific gravity of liquid at 42ºC is 1.20. Calculate the coefficient of linear
expansion of the metal.
1 1 1 1
1) / C 2) / C 3) / C 4) / C
36200 43200 54100 23200
10. A small solid ball is dropped from a height above the free surface of a liquid. It strikes the
3
surface of the liquid at t=0. The density of the material of the ball is 500kg / m and that of
3
liquid is 1000kg / m . If the ball comes momentarily at rest at t = 2 sec then initial height of
the ball from the surface of liquid was (neglect viscosity) g=10m/s 2
1) 20 m 2) 10 m 3) 15 m 4) 25 m
11. Water (density  ) is flowing through the uniform horizontal tube of cross-sectional area A
with a constant speed v as shown in the figure. The magnitude of force exerted by the water
on the curved corner of the tube is (neglect viscous forces)
 Av 2
1) 3 Av2 2) 2  Av 2 3) 2  Av 2 4)
2
12. A frog sits at the end of a long board of length L. the board rests on a smooth horizontal
surface. The frog wants to jump to the opposite end of the board. What is the minimum take
off speed i.e relative to the ground that allows the frog to do the trick? Assume that frog and
board have equal masses
gL gL gL gL
1) 2) 3) 4)
1 3 2 4
13. A small spherical ball of mass M is dropped form a height H above a heap of sand. The ball
penetrates up to a depth ‘h’ from surface of heap of sand. Assuming force on the ball by
sand is constant throughout the motion of the ball in the sand, this force in magnitude is
H  H  H  H
1) Mg 2) Mg  1+  3) Mg  1-  4) Mg 1+ 
h  h  h  h
14. Two soap bubbles of equal radii 4 cm are touching each other with an intermediate film
N
separating them. Surface tension of solution forming bubbles is 7  102 . What is the
m
distance between the centres of soap bubbles (in cm)?
1) 4 2) 6 3) 0 4) 2 3
15. A particle is projected vertically upwards from a point A on the ground. It takes t1 time to
reach a point B but it continues to move up. If it takes further t 2 time to reach the ground
from point B, then height of point B from the ground is
1 2 1 2 1
1) g  t1  t2  2) gt1t2 3) g  t1  t2  4) gt1t2
2 8 2
16. One mole of diatomic gas is being heated in a closed tank from 300K up to 1000 K. During
the process part of the molecules dissociate. At 1000 K the energy of the diatomic molecules
are only half of that of the whole gas. By what factor has the gas pressure increased
 Pfinal / Pinitial  ? (The oscillation of the molecules are not to be taken in account).
160 16 3 2
1) 2) 3) 4)
33 11 2 3
17. In a region there exist a magnetic field B0 along positive x-axis. A metallic wire of length 2a
and one side along x-axis and one side parallel of y-axis is rotating about y-axis with a
angular velocity  Then at the instant shown, magnitude of induced emf between P and R is
1 1
1) B a 2 B a 2 2) 3) B a 2 4) zero
2 4
18. A disc of radius r is rotating about its centre with an angular speed 0 . It is gently placed on
a rough horizontal surface. After what time it will be in pure rolling?
0 r 0 r 0 r 30 r
1) 2) 3) 4)
2 g 3 g g 2 g
19. A car moves towards a hill with speed vc . It blows a horn of frequency f which is heard by
an observer following the car with speed v0 . The speed of sound in air is v.
v
1) the wavelength of sound reaching the hill is
f
v  vC
2) the wavelength of sound reaching the hill is
f
v  v1
3) the beat frequency observed by the observer is f
v  vc
2vc  v  v0  f
4) the beat frequency observed by the observer is
v2  v2
c
20. Expression of time in terms of G (universal gravitational constant), h (Planck’s constant) and
c (speed of light) is proportional to
Gh hc5 c3 Gh
1) 2) 3) 4)
c3 G Gh c5
(NUMERICAL VALUE TYPE)
Section-II contains 10 Numerical Value Type questions. Attempt any 5 questions only. First 5 attempted questions will be considered if more than 5
questions attempted. 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.
21. A diode detector is used to detect an amplitude modulated wave of 60% modulation by using
a condenser of capacity 250 Pico- farad in parallel with a load resistance 100 kilo ohm. Find
the maximum modulated frequency which could be detected by it in KHz. (round of answer
to nearest integer )
22. Damped harmonic oscillator consists of a block  m=2kg  , a spring k=8 2 N/m , and a  
damping force  F=-bv  . Initially, it oscillates with an amplitude of 25 cm. Because of the
damping, the amplitude falls to three-fourth of this initial value at the completion of four
oscillations. If b is x×10-3 kg/sec then x is. (Assume small damping and take:
3
ln    0.28
4
23. Photons with energy 5 eV are incident on a cathode C, on a photoelectric cell. The maximum
energy of the emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on
C, no photoelectrons will reach the anode A if the stopping potential of A relative to C is ( in
magnitude)
24. A meter bridge is set-up as shown, to determine an unknown resistance “X” using a standard
10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The
end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value
of ‘X’ is
25. In the circuit diagram shown, X C  100, X L  200 & R  100 .The effective current
through the source is :

26. Consider an optical communication system operating at   600nm . Suppose, only 1% of the
optical source frequency is the available channel bandwidth for optical communication. How
many channels can be accommodated for transmitting audio signals requiring a bandwidth of
8kHz? _____ 106
27. An electron experiences no deflection if subjected to an electric field of 3.2  105V / m and a
magnetic induction of 2.0  103 T . Both the fields are applied perpendicularto thepath of
electron and also to each other. If the electric field is removed, then the electronwill revolve
in an orbit of radius______(in centimetres) (mass of the electron 9  1031 kg )

28. A Lamp emits mono chromatic light uniformly in all directions. The lamp consumes 100W
of power and is 3 % efficient in converting electric power into em waves. The amplitude of
electric field of electromagnetic waves at a distance of 5 m from the lamp is______ (in V/m)
(Take 5  2.24 ) (round of answer to nearest integer )
29. Least count of a standard vernier callipers is 0.01cm. When the two jaws are in contact, the
5th division of vernier scale coincides with main scale division and the zero of the vernier
scale lies to the left of the zero of the main scale. While measuring diameter of the sphere,
the zero mark of vernier scale lies between 2.4cm and 2.5cm and 6th vernier division
coincides with a main scale division. The diameter of the sphere is d=x  102 cm then x is
30. In Young’s double slit experiment how many maximas can be aimed on a screen (including
0 0
the central maximum) on both sides of the central fringe. If   2000 A and d  7000 A.

CHEMISTRY Max Marks: 100
correct.
31. The correct statement(s) related to colloids is
1) The process of precipitating colloidal sol by an electrolyte is called peptization.
2) Colloidal solution freezes at lower temperature than the true solution at the same
concentration
3) Surfactants form micelle above critical micelle concentration (CMC). CMC depends on
temperature
4) Micelles are macromolecular colloids.
32. Which among the following statement(s) is false for the extraction of aluminium from
bauxite?
1) Hydrated Al2O3 precipitates, when CO2 is bubbled through a solution of sodiummeta
aluminate.
2) Addition of Na3 AlF6 lowers the melting point of alumina
3) CO2 is evolved at the anode during electrolysis.
4) The anode is a steel vessel with a lining of carbon.
33. Which one of the following is the correct PV vs P plot at constant temperature for an ideal
gas? (P and V stand for pressure and volume of the gas respectively)
PV PV
1) P 2) P
PV PV
3) P 4) P

34. Choose the correct option from the following
1) Natural rubber is polyisoprene contains trans alkene units
2) Nylon-6 has amide linkages
3) Cellulose has only   D  glucose units that are joined by glycosidic linkages
4) Teflon is prepared by heating trifluoroethene in presence of a persulphate catalyst at high
pressure
35. The electrons are more likely to be found:
1) in the region a and b 2) in the region a and c

3) only in the region c 4) only in the region a
36. Match List-I with List-II
List - I List - II
A Sphalerite I FeCO3
B Calamine II PbS
C Galena III ZnCO3
D Siderite IV ZnS
Choose the most appropriate answer from the options given below:
1) (A)-(IV), (B)-(III), (C)-(II), (D)-(I) 2) (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
3) (A)-(II), (B)-(III), (C)-(I), (D)-(IV) 4) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
37. Given below are two statements. One is labelled as Assertion A and the other is labelled as
Reason R.
Assertion A: Energy of 2s orbital of hydrogen atom is greater than that of 2s orbital of
lithium.
Reason R: Energies of the orbitals in the same subshell decrease with increase in the atomic
number. In the light of the above statements, choose the correct answer from the options
given below.
1) Both A and R are true and R is the correct explanation of A
2) Both A and R are true and R is NOT the correct explanation of A
3) A is true but R is false
4) A is false but R is true

38. Which of the following is an example of conjugated diketone?
O
O O H2
H3C C C O
H2 H2 H2
1) H3C C C C C C CH3 2)
O
O
H2
C C C CH3
H2
O O
3) 4)
39. Which of the following is not a broad spectrum antibiotic?
1) Vancomycin 2) Ampicillin
3) Ofloxacin 4) Penicillin G
40. Given below are two statements one is labelled as Assertion A and the other is labelled as
Reason R:
Assertion A: lithium halides are somewhat covalent in nature.
Reason R: Lithium possess high polarization capability. In the light of the above statements
choose the most appropriate answer from the options given below:
41. Which one of the following compounds is used as a chemical in certain type of fire
extinguishers?
1) Baking Soda 2) Soda ash 3) Washing Soda 4) Caustic Soda
42. Given below are two statements one is labelled as Assertion A and the other is labelled as
Reason R:
Assertion A: The melting point of monocarboxylic acid with even number of carbon atoms
is higher than that of with odd number of carbon atoms acid immediately below and above it
in the series.
Reason R: The solubility of monocarboxylic acids in water decreases with increase in molar
mass.
Choose the most appropriate option:
43. In the flame test of a mixture of salts, a green flame with blue centre was observed. Which
one of the following cations may be present?
1) Cu 2  2) Sr 2  3) Ba 2  4) Ca 2
44. Which of the following is not an example of a condensation polymer?
1) Nylon 6,6 2) Decron 3) Buna-N 4) Silicone
45. For the following Assertion and Reason, the correct option is:
Assertion: The p H of water increases with increase in temperature.
Reason: the dissociation of water into H  and OH  is an exothermic reaction.
1) Assertion is not true, but reason is true
2) Both assertion and reason are false
3) Both assertion and reason are true, and the correct explanation for the assertion
4) Both assertion and reason are true, but the reason is not the correct explanation for the
assertion
46. During halogen test, sodium fusion extract is boiled with concentrated HNO3 to
1) remove unreacted sodium
2) decompose cyanide or sulphide of sodium
3) extract halogen from organic compound
4) maintain the pH of extract
47. Which of the following ketone will NOT give enamine on treatment with secondary amines?
O
O
C
C
1) C2H5 C2H5 2) C2H5 CH3
O
C
3) t-Bu t-Bu 4)
48. An antiseptic dettol is a mixture of two compounds ‘A’ and 'B' where A has 6 electrons
and B has 2 electrons. What is ‘B’?
1) Bithionol 2) Terpineol
3) Chloroxylenol 4) Chloramphenicol

49. Oxidation of toluene to Benzaldehyde can be easily carried out with which of the following
reagents?
1) CrO3 / acetic acid, H3O  2) CrO3 / acetic anhydride, H3O 
3) KMnO4 / HCl, H3O 4) CO / HC1, anhydrous A1C13

50. Which of the following is most stable?
1) 2) 3) 4)
51. The total number of possible isomers for  Pt  NH3 4 C12  Br2 is________.
52. In the chemical reaction between stoichiometric quantities of KMnO 4 and KI in weakly
acidic medium , what is the number of moles of I 2 released for 4 moles of KMnO 4
consumed?
53. An acidified solution of potassium chromate was layered with an equal volume of amyl
alcohol. When it was shaken after the addition of 1mL of 3% H 2O 2 , a blue alcohol layer
was obtained. The blue color is due to the formation of a chromium (VI) compound ’X’.
What is the number of oxygen atoms bonded to chromium through only single bonds in a
molecule of X?
54. Total number of isomers, considering both structural and stereoisomers, of cyclic ethers with
the molecular formula C4 H8O is_________.
55. The osmotic pressure of blood is 7.47 bar at 450K. To inject glucose to a patient
intravenously, it has to be isotonic with blood. The concentration of glucose solution in gL1
is _________(Molar mass of glucose = 180 g mol1 R = 0.083 L bar K 1mol1 ) (Nearest

integer)

56. In the cobalt-carbonyl complex: Co 2  CO 8  , number of Co-Co bonds is "X" and terminal
CO ligands is "Y". X + Y =______

57. The standard entropy change for the reaction 4Fe  s   3O2 ( g )  2 Fe2O3 ( s )
is  550 JK 1 at 298K . [Given: The standard enthalpy change for the reaction is
165 kJ mol1] the temperature in (Kelvin) at which the reaction attains equilibrium is .
(Nearest Integer)
58. Elevation in boiling point for 1.5 molal solution of glucose in water is 4K. The depression in
freezing point for 3 molal solution of glucose in water is 4K.The ratio of molal elevation
constant to molal depression constant Kb / K f is.  

59. For the following graphs, if x is the number of graphs which represent first
order and y is the number of graphs which represent zero order. Then x y is.
(b) t
1
(a) Rate 2
Initial
Time concentraction
Rate Rate
(d)
(e)
concentraction concentraction
60. Alitame is sweeter than sucrose by ______number of times

MATHEMATICS Max Marks: 100
correct.
1 1
61. If  and  are the roots of the equation x 2 +px+2=0 and and are the roots of the
 
 1  1  1  1
equation 2x 2 +2qx+1=0 , then                is equal to
       
1)
9
4

9  p2  2)
9
4

9  q2  3)
9
4

9  p2  4)
9
4

9  q2 
62. If the system of linear equations 8 x  y  4 z  2 , x+y+z=0,  x-3y= has infinitely many
 1
solutions, then the distance of the point   ,  ,   from the plane 8x  y  4 z  2  0 is
 2
26 10
1) 3 5 2) 4 3) 4)
9 3
63. Let z be those complex numbers which satisfy z  5  4 and z 1  i   z 1  i   10, i  1
2
. If the maximum value of z  1 is    2, then the value of     is______. Where
 &  are natural numbers.
1) 84 2) 48 3) 88 4) 44
64. Consider the two statements:
 S1  :  p  q     q  p  is a tautology.  S2  :  p   q     p  q  is a fallacy.
1) only  S1  is true 2) both  S1  and  S2  are false
3) only  S2  is true 4) both  S1  and  S2  are true
65. Three circles of radii a,b and c (a<b<c) touch each other externally. If they have x-axis as a
common tangent, then
1 1 1 1 1 1
1)   2)  
a b c c a b
1 1 1
3) a , b , c are in A.P 4)  
b a c
66. Let f(x) be a polynomial function such that f  x   f '  x   f " x   x5  64 . Then, the value
f  x
of lim
x 1 x  1
1) -15 2) -60 3) 60 4) 15
67. If the parabolas y 2  4b  x  c  and y 2  8ax have a common normal other than x-axis, then
which one of the following is a valid choice for the ordered triad (a,b,c)?
1  1 
1) (1,1,0) 2)  , 2,3  3)  , 2, 0  4) (1,1,3)
2  2 
1, if i=j

68. Let A  [ aij ] be a 3  3 matrix, where aij   x if i  j  1 Let a function be defined as
2 x  1, otherwise

f  x   det  A  . Then the sum of maximum and minimum values of f on R is equal to
88 20 88 20
1) 2) 3)  4) 
27 27 27 27
e

2 x 2 bx c   1  2  x2  bx  c 
69. If  ,  are the distinct roots of x 2  bx  c  0 , then lim
x  x   2
is equal to

1) 2 b 2  4c  2) b 2  4c 
3) 2 b 2  4c  4) b 2  4c
xa y 2 z b
70. If the foot of the perpendicular from point (4,3,8) on the line L1 :   ,l  0
l 3 4
x2 y 4 z 5
is (3,5,7) then the shortest distance between the line L1 and line L2 :   is
3 4 5
equal to:
1 1 2 1
1) 2) 3) 4)
2 6 3 3

 
71. If y  y  x  , x   0,  be the solution curve of the differential equation
 2
sin 2 2 x  dydx  8sin 2 2 x  2sin 4 x  y  2e4x  2sin 2x  cos 2x  , with y  4   e ,
 
then y   is equal to
6
2 2 /3 2 2 /3 1 2 /3 1 2 /3
1) e 2) e 3) e 4) e
3 3 3 3
      
72. Let a  2iˆ  ˆj  2kˆ and b  iˆ  ˆj. If c is a vector such that a.c  c , c  a  2 2 and the
    
 
angle between a  b and c is , then the value of
6
 a  b   c is
3 2
1) 3 2) 4 3) 4)
2 3
100
73. If
 0
sin 2 x
 x  x 
    
e   
dx 
 3
1  4 2
,  R
where [x] is the greatest integer less than or equal to x,
then the value of  is

1) 200 1  e 1  
2) 150 e 1  1  3) 50  e  1 4) 100 1  e 
74. The probabilities of Ramesh using car or scooter or bus or train for going to office are
1 3 2 1
respectively , , and . The probabilities of his reaching the office late using these
7 7 7 7
2 1 4 1
modes of transport are respectively , , and . On one day Ramesh reaches his office on
9 9 9 9
time. Then the probability that he used car on that day is
1 1 1 2
1) 2) 3) 4)
8 7 6 5

75. Let A1 , A2 , A3 ,.... be an increasing geometric progression of positive real numbers. If
1 7
A1 A3 A5 A7  and A2  A4  , then, the value of A6  A8  A10 is equal to
1296 36
1) 33 2) 37 3) 43 4) 47
9 9
2
76. If   xi  5  9 and   xi  5  45 , then the standard deviation of the 9 items
i 1 i 1
x1 , x2 ,....., x9 is
1) 3 2) 9 3) 4 4) 2
77. PQR is a triangular park with PQ  PR  200m . A TV tower stands at the mid-point of QR.
If the angles of elevation of the top of the tower at P,Q and R are, respectively, 45 , 30 and
30 , then the height of the tower (in m) is

1) 50 2 2) 100 3) 50 4) 100 3
78. Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If
AD=8 m, BC=11 m and AB=10 m; then the distance (in meters) of a point M on AB from
the point A such that MD 2  MC 2 is minimum is.

1) 10 2) 5 3) 4 4) 1
79. Statement-1:- for any three positive real a,b&c
   
9 25a 2  b 2  25 c 2  3ac  15b  3a  c  then a,b,c are in A.P
Statement-2:- If x,y,z are in A.P & tan 1 x, tan 1 y, tan 1z are also in A.P then x=y=z.
1) only  S1  is true 2) both  S1  and  S2  are false
3) only  S2  is true 4) both  S1  and  S2  are true
80. 
Consider a hyperbola H : x 2  2 y 2  4 . Let the tangent at a point P 4, 6 meet the x-axis at 
Q and latus rectum at R  x1, y1  , x1  0 . If F is a focus of H which is nearer to the point P,
then the area of QFR is equal to

7
1) 4 6 2) 6 1 3) 2 4) 4 6  1
6
10
81. If the coefficient of a 7b8 in the expansion of  a  2b  4ab  is K. 216 , then sum of the
digits of K is.
82. 
The area of the region  x, y  : x  1  y  5  x 2 is equal to 
π
λ +μ then  λ-μ  is
4
. is G.I.F
83.   
Let   max 82sin 3 x.44cos3 x and  = min 82sin 3 x.44cos3 x . If 8 x 2  bx  c  0 is a
xR xR

1
 c  b  is equal to
quadratic equation whose roots are  1/5 and  1/5 , then the value
7
84. The number of integral values of k for which the line 3x+4y=k intersects the circle,
x 2  y 2  2 x  4 y  4  0 at two distinct points is______.

85. The number of 5-digit natural numbers, such that the product of their digits is 36, is K then
K
is.
20
 9  x 2   9  x 2 
86. Let Max     and Min  .
0 x  2  5  x  0  x  2  5  x 
2 1  9  x 2  8 1   2
If  Max 
 5  x
, x 

dx  1   2 log e 
 15


then
17
is equal to.
8

3
2  3p 2 p
87. Let E1, E2 , E3 be three mutually exclusive events such that P  E1   , P  E2  
6 8
1 p
and P  E3   . If the maximum and minimum values of p are P1 and P2 , respectively
2
then 3  P1  P2  is.

88. If p(x) be a polynomial of degree three that has a local maximum value 8 at x=1 and a local
24
minimum value 4 at x=2; then  5 is.
p  0
89. If 5, 5r and 5r 2 are the lengths of the sides of triangle, then [r] is . is G.I.F
 2x  1   2x  1 
 a tan 1 
dx
90. If    b   C , x  0 where C is the constant of
 
2  3  2
2
x  x 1  x  x  1 
integration, then the value of 9  

3a  b  7 is

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Sri Chaitanya IIT Academy.,India.

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 2

5. A capacitor of capacitance C=3 F is first charged by connecting it across a 10V battery by

1) 0.5 mJ 2) 0.05 mJ 3) 0.15 mJ 4) 0.10 mJ

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 7

8kHz? _____ 106

in an orbit of radius______(in centimetres) (mass of the electron 9  1031 kg )

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 8

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 9

1) in the region a and b 2) in the region a and c

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 10

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 12

1) CrO3 / acetic acid, H3O  2) CrO3 / acetic anhydride, H3O 

3) KMnO4 / HCl, H3O 4) CO / HC1, anhydrous A1C13

is _________(Molar mass of glucose = 180 g mol1 R = 0.083 L bar K 1mol1 ) (Nearest

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 13

CO ligands is "Y". X + Y =______

constant to molal depression constant Kb / K f is.  

60. Alitame is sweeter than sucrose by ______number of times

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 14

3) only  S2  is true 4) both  S1  and  S2  are true

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 16

then the value of  is

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 17

30 , then the height of the tower (in m) is

the point A such that MD 2  MC 2 is minimum is.

3) only  S2  is true 4) both  S1  and  S2  are true

then the area of QFR is equal to

x 2  y 2  2 x  4 y  4  0 at two distinct points is______.

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 19

integration, then the value of 9  

Sec: Sr.Super60_NUCLEUS & ALL_BT Page 20

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