Aits 1718 CRT Iv Jeea Paper 2 PDF
Aits 1718 CRT Iv Jeea Paper 2 PDF
Aits 1718 CRT Iv Jeea Paper 2 PDF
Paper 2
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
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-C & Section-D.
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.
3. Section-D (21 – 23, 44 – 46, 67 – 69) contains 9 Numerical answer type questions with answer
XXXXX.XX and each question carries +4 marks for correct answer and –1 mark for wrong
answer.
Enrolment No.
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AITS-CRT-IV (Paper-2)-PCM-JEE(Advanced)/18 2
Useful Data
PHYSICS
CHEMISTRY
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3 AITS-CRT-IV (Paper-2)-PCM-JEE(Advanced)/18
Correct Method :
0 0 3 4 8 . 4 0
0 0 2 5 1 . 3 7
0 0 2 1 3 . 0 0
Wrong Method :
3 4 8 . 4
3 4 8 . 4
3 4 8 . 4
3 4 8 . 4
2 5 1 . 3 7
2 1 3 .
2 1 3 . 0
2 1 3 . 0
3 4 8 . 4 0
2 5 1 . 3 7
2 1 3 . 0 0
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Physics PART – I
SECTION – A
(One Options Correct Type)
This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE option is correct.
R R/2
2. A spherical cavity of radius is removed from a solid sphere of R
2
radius R as shown in fig. The sphere is placed on a rough horizontal
O
surface as shown. The sphere is given a gentle push. The sphere
performs SHM and its time period is.
177R 77R
(A) 2π (B) 2π
10g 10g
7R 177R
(C) 2π (D) 2π
10g g
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5 AITS-CRT-IV (Paper-2)-PCM-JEE(Advanced)/18
Situation I Situation II
(A)The magnitude of electric flux through the hemispherical surface in situation I will be EπR 2
(B)The magnitude of electric flux through the hemispherical surface in situation I will be 2EπR 2
EπR 2
(C)The magnitude of electric flux through the hemispherical surface in situation II will be
2
(D)The magnitude of electric flux through the hemispherical surface in situation II will be zero
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m
(A) Block of mass M will move up as A is moved slowly to the right
(B) Block of mass m will move up as A is moved slowly to the right
(C) It is possible, for a particle position of A, that M has no acceleration but m does have
acceleration
(D) The block of mass m will have a horizontal displacement
7. There are two weights of the same mass of 2.0 kg each attached to a string
looped over a braked pulley. The left weight is lying on the floor, the right
one is suspended 1.0 m above the floor. There is another weight of m
mass 0.5 kg attached to the string 20 cm above the right weight. The string d
except the part around the pulley is stretched vertically. We eventually
M
release the pulley.
h1
M
(A) The speed at which the lower right weight hits the floor is 1.48 m/s
(B) The height that the left weight rises to after the lower right weight falls inelastically to the floor
is 1.185 m
(C) The maximum height that the lower right weight rises back to is 1.185 m
(D) The maximum height that the lower right weight rises back to is 0.31 m
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(Paragraph Type)
This section contains ONE paragraph. Based on the paragraph, there are TWO questions. Each question
has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.
9. In the presence of above magnetic field, if the particle almost stops at a point 6m away from the
point projection the magnetic field is equal to:
4b 3b
(A) (B)
3q 4q
4q 3q
(C) (D)
3b 4b
Space for Rough work
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10. The strength of the magnetic field is now doubled in magnitude. How far (in meters) from the
point of projection will the particle come to an almost rest?
73 20
(A) (B)
2 73
40 30
(C) (D)
73 73
SECTION – C
(Single digit integer type)
This section contains TEN questions. The answer to each question is a single Digit integer ranging from 0
to 9, both inclusive.
11. A spherical planet of radius r, painted black, travels around the sun in a circular orbit at a distance
D from its centre r<<<D . The sun, a sphere of radius R, radiates as a blackbody at a
temperature T0 =6000K and subtends an angle 0.01 rad as seen from the planet. The
equilibrium temperature T of the planet is x×100 . Find x
12. In the figure all pulleys (P1, P2, P3…….) are massless and all the blocks (1, 2, 3…..) are
identical, each having mass m. The system consists of infinite number of pulleys and blocks.
Strings are light and in extension and horizontal surfaces are smooth. Pulley P1 is moved to left
with a constant acceleration of a0 . The acceleration of block 1 will be (Assume the strings to
remain horizontal) ka 0 . Find 2k
P2
P3
. .
P1
. . 3
2
a0 1
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0 4 t(s)
16. Nuclei of radioactive element A are produced at rate 't 2 ' at any time t. The element A has decay
dN
constant .Let N be the number of nuclei of element A at anytime t. AT time t=t 0 , , is
dt
Nt 0 -λt 02
minimum. Then the number of nuclei of element A at time t=t 0 is found to be . Find the
λ
value of N
17. If 10000 V is applied across an X-ray tube, if the ratio of de-Broglie wavelength of the incident
electrons to the shortest wavelength of X-ray produced (e/m for electron is 1.8×1011c kg -1 ) is r.
Find 2/5r.
18. The internal energy of a monatomic ideal gas is 1.5 nRT. One mole of helium is kept in a
cylinder of cross-section 8.5 cm 2. The cylinder is closed by a light frictionless piston. The gas is
heated slowly in a process during which a total of 42 J heat is given to the gas. The temperature
rises through 2°C. The distance moved by the piston is given as a × 10b m in scientific notation.
Find the value of a + b. [Take R=25/3 in SI unit, atmospheric pressure = 100 kPa]
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SECTION – D
(Numerical Based XXXXX.XX answer Type)
This section contains 3 questions. Each question, when worked out will result in numerical answer Type
with answer xxxxx.xx.
3 8 2
21. Steel has density 7800 kg/m and will break if tensile stress exceeds 7.0 × 10 N/m . A person
wants to make a guitar string from 4.0 gm of this steel. The guitar string must be able to withstand
a tension of 900 N. The maximum speed of transverse wave can be x.xx 100 m/s
23. A ring of radius r and mass 2m, rests on a rough circular track of
radius R.A small point mass of mass m is mounted on its R
periphery. If friction is sufficient to avoid any slipping then the
m
r
minimum ratio of is x.xx
R r
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Chemistry PART – II
SECTION – A
(One Options Correct Type)
This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE option is correct.
24. Give the correct order of initials T(True) or F(False) for following statements:
(I) In an antifluorite structure, anions form FCC lattice and cations occupy all tetrahedral voids
(II) If the radius of cations and anions are 0.2 Ǻ and 0.95 Ǻ then co-ordination number of cation
in the crystal is 4
(III) An atom/ion is transferred from a lattice site to interstitial position in Frankel defect
(IV) Density of crystal always increase due to substitutional impurity defect
(A) TFFF (B) FTTF
(C) TFFT (D) TFTF
25. When one mole of A(g) is introduced in a closed rigid one litre vessel maintained at constant
temperature, the following equilibria are established:
A g B g C g ; K C1
C g D g B g ; K C2
Ceq 1 Kc2
The pressure at equilibrium is twice the initial pressure if , then is equal to
Beq 5 K c1
(A) 16/5 (B) 4
(C) 16 (D) 5/16
26. The specific conductivity of 0.5 M aq. solution of a monobasic acid (HA) after subtracting the
specific conductance of water is found to be 0.006 Scm 1. If its molar conductivity at infinite
dilution is 200 Scm2mol1, then the osmotic pressure of 0.1 M aq. solution of HA will be
(R = 0.0821 dm3 atm mol1K1)whole experiment took at 1365K.
(A) 0.72 atm (B) 1.72 atm
(C) 12.72 atm (D) 7.72 atm
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27. Copper glance to pure copper undergoes which of the following processes?
(A) Hydrometallurgy (B) Electrolytic refining
(C) Roasting (D) poling
CH3 H
H
(A) (B)
H H H CH3
H H
Ph Ph
OH H
H COOH
(C) H
H
H
H
(D) H H
COOH
H
HOOC H
H OH
COOH H
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29. The following mechanism has been proposed for the exothermic catalysed complex reaction:
Fast
A B k1
JAB
k2
AB J PA
if k1 is much smaller than k2, then the incorrect qualitative plot of potential energy (PE) vs reaction
coordinate for the above reaction is/are
AB+J A+P
(A) P.E. (B) P.E.
A+B JAB A+B
A+P JAB
AB+J
Reaction Co-ordinate Reaction Co-ordinate
31. Elements of 15th group form hydrides of general formula MH3. Which of the following
characteristic(s) of these hydrides decreases regularly on moving down the group (from NH3 to
BiH3)?
(A) decomposition temperature (B) boiling temperature
(C) reducing character (D) HMH bond angle
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(Paragraph Type)
This section contains ONE paragraph. Based on the paragraph, there are TWO questions. Each question
has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.
The concentration of potassium ions inside a biological cell is at least twenty times higher than
the outside. The resulting potential difference across the cell is important in several processes
such as transmission of nerve impulses and maintaining the ion balance. A simple model for such
a concentration cell involving a metal M is:
M(s) M+(aq; 0.05 molar)M+(aq), 1 molar)M(s)
For the above electrolytic cell the magnitude of the cell potential Ecell= 70 mV.
33. If the 0.05 molar solution of M+ is replaced by 0.0025 molar M+ solution, then the magnitude of the
cell potential would be
(A) 35 mV (B) 70 mV
(C) 140 mV (D) 700 mV
SECTION – C
(Single digit integer type)
This section contains TEN questions. The answer to each question is a single Digit integer ranging from 0
to 9, both inclusive.
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35. Which is the most favoured position for the attack of an electrophile
1 2
F 3C 6
4 5
36. Br
Li/Hg
P
F
O
What is the degree of unsaturation in P.
Z
37. Calculate the value of . Where
10
Z = Co-ordination number of 2D-square close packing
+
Coordination number of 2D-hcp
+
Co-ordination number of 3D-square close packing
+
Co-ordination number of 3D, ABCABC………Packing
+
Co-ordination number of 3D, ABAB……… packing
38. The standard reduction potential of a silver chloride electrode (metal-sparingly soluble salt
electrode) is 0.209 V and for silver electrode is 0.80V. If the moles of AgCl that can dissolve in
10L of a 0.01M NaCl solution is represented as 10-z then find the value of Z.
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40. Among the following, the total number of compounds whose aqueous solution turns red litmus
paper blue is:
NaCN KCl CH3COONH 4 NaH 2 PO 4 ZnCl 2 Na 3PO 4
Fe(NO3 )3 Na 2CO3 NH 4Cl NaHCO3 Na 2C2O 4 Na 2 HPO4
Given:
Acid Ka1 Ka2 Ka3
3 8
H3PO 4 10 10 1012
H 2CO3 106 10 11 -
Conc. 8 [A]
(M) 6
4 [C]
2
0
Time
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43. How many of the following decompose easily as compared to CaCO3 to evolve CO 2
CdCO3 , PdCO3 , COCO3 , MnCO3 , Na 2CO3 , BaCO3 , FeCO3 , BeCO3 , Ag 2CO3
SECTION – D
(Numerical Based XXXXX.XX answer Type)
This section contains 3 questions. Each question, when worked out will result in numerical answer Type
with answer xxxxx.xx.
o
44. When a liquid that is immiscible with water was steam distilled at 95.2 C at a total pressure of
748torr, the distillate contained 1.25g of the liquid per gram of water. The vapour pressure of
water is 648 torr at 95.2oC , what is the molar mass of liquid in g/mol.
45. The graph of compressibility factor (Z) vs. P for one
mole of a real gas is shown in following diagram. dZ 1
= atm -1
The graph is plotted at constant temperature 273K. If dP 2.8
Z
dZ
the slope of graph at very high pressure is
dP
1 -1
atm , then calculate volume of one mole of P
2.8
real gas molecules (in L/mol) Given:
22.4
N A =6×1023 and R= L atm K -1 mol-1
273
46. 40g Ba(MnO 4 ) 2 (mol.mass =375) sample containing some inert impurities in acidic medium
completely reacts with 125mL of ‘’33.6 V’’ of H 2 O 2 . What is the percentage purity of the sample?
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SECTION – A
(One Options Correct Type)
This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE option is correct.
x2 dx
47. I
( x cos x sin x) ( x sin x cos x)
x cos x sin x x sin x cos x
(A) ln c (B) ln c
x sin x cos x x cos x sin x
x sin x cos x x cos x sin x
(C) c (D) c
x cos x sin x x sin x cos x
2
48. Find the minimum value of ( x1 x2 )
2
1 x12 12 2 x2
2 2
(A) 70 2 (B) 80 1
2 2
(C) 70 1 (D) 80 1
49.
Y
P
Q
(x,0)
X
O C2 R
C1
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1
52. If A1 ,A 2 ,A 3 ,.....A1006 be independent events such that P(Ai)= (i=1,2,3,....1006) and
2i
!
probability that none of the events occurs be
then
2 ( !)2
(A) is of form 4k 2, k I (B) 2
(C) is a composite number (D) is of form 4k , k I
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( z1 z 2 )( z 2 z3 )( z3 z1 )
(C) Im 0
z1. z2 .z3
z z
(D) If z1 z 2 2 z1 z3 2 z2 z3 , then Re 3 1 0
z3 z2
(Paragraph Type)
This section contains ONE paragraph. Based on the paragraph, there are TWO questions. Each question
has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.
The centres of two circles c1 and c 2 of radii 4 and 9 respectively are at a distance of 15units from
each other. Let L1 be one correct common tangent to these circles.
55. There are n circles which touches both the circle C1 and C2 and also the line L1 then n is
(A) 2 (B) 4
(C) 3 (D) 8
56. Let r1 ,r2 ,......rn be the radii of these circles then find max (r1 ,r2 ,......rn ) ?
25 50
(A) (B)
2 9
(C) 50 (D) 1
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SECTION – C
(Single digit integer type)
This section contains TEN questions. The answer to each question is a single Digit integer ranging from 0
to 9, both inclusive.
2
57. Find the largest integer value of x satisfying the inequality log 0.09 ( x 2 x) log 0.3 x2.
1 1 1 1
58. Let H n =1+ + +...+ and Tn = , then the value of (T1 +T2 +T3 +...+) is:
2 3 n (n+1)H n H n+1
59. Complex numbers a, b and c are zeroes of polynomials P(z)=z3 +qz+r (where q,r R )and
a 2 + b 2 + c 2 =250 . If the points corresponding to a, b and c in complex plane are the vertices
h2
of a right angled triangle with hypotenuse h, then .
125
60. If N denotes the number of non-empty subsets of {1,2,3,…,12} having property that the sum of
largest element and smallest element is 13, then number of divisors of N divisible by 5 is:
2
1 1 1
61. The number of distinct terms in expansion of x+y+z+ + + is m and that in
xy yz zx
2
1 1 1
expansion of x+y+z+ + + is n, then m n is equal to:
x y z
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62. There are 4 bowlers, 4 batsman and 1 all-rounder (who is bowler as well as batsman). Randomly
a team of 4 players consisting of at least two bowlers and at least two batsman is formed. If the
4
probability that all-rounder has been selected in team is , then p is equal to:
p
63. Find the sum of all integral values of a values of a where a [10,10] such that the graph of the
function f ( x) x 2 a 3 has exactly three x-intercepts.
1 7 cos 2 x g ( x)
65. Suppose 7 2
dx 7 C , where C is an arbitrary constant of integration. Then
sin x cos x sin x
the value of g '(0) g '' .
4
1
66. Let f be a differentiable function defined such that f :[0, 27] , 6 and f '( x) 0x D f .If
3
27 3
2
xf '( x)dx 3 x f ( x3 )dx then find the value of .
0 0
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SECTION – D
(Numerical Based XXXXX.XX answer Type)
This section contains 3 questions. Each question, when worked out will result in numerical answer Type
with answer xxxxx.xx.
69. Let f be real function defined on R (the set of real numbers) such
2
that f’ x 100 x 1 x 2 ( x 3) 3 .......( x 100)100 , for all x R . If g is a function defined
x x
f (t )
on R such that e dt g ( x t )dt 2 x 3 , If some of the all the values of x for which g(x)
a 0
has a local extremum be then find
3
Space for Rough work
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