JEE (Main)
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AIETS PAPER 1
S E I R Time Allotted: 3 Hours Maximum Ma ximum Ma Marks: rks: 360 Please read the instructions carefully. You are allotted 5 minutes E specifically for thi s purpose. You are not allowed to leave the Examination Hall before the end of S the test. T INSTRUCTIONS S A. Gener al Ins tr uc tion ti on s E T . G G N E A I
1. The clock will will be set at the server. server. The countdown countdown timer timer in the top right right corner of screen screen will display display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination. 2. Procedure Procedure for answering answering a multiple multiple choice choice type type question: question: a. To select select your answer, answer, click click on the button button of one one of the options. options. b. To change your your chosen chosen answer, click on the the button of of another option. option. c. To save save your answer, answer, you you MUST click on the Next Next button. button. 3. 1/4 {one fourth) fourth) marks i. e. one one mark will be deducted deducted for indicatin indicating g incorrect incorrect response response of each question. No deduction from the total score will be made if no response is indicated for a question. 4. No candidate candidate is allowed to use any textual textual material, printed printed or written, written, bits of papers, pager, pager, mobile phone, any electronic device, etc., while attempting the test.
Specific Instruct Instructions: ions: D B. Exam Specific N I
1. There will be 90 questions and 180 minutes duration will be given to attempt these questions. Mathematics and Physics, containing 2. The questions are divided into 3 sections: Chemistry , Mathematics and Physics, containing 30 questions each. 3. Each question is allocated 4 (four) marks for each correct. 4. One fourth marks will be deducted for incorrect question of each question. No deduction from the total score will be made if no answer is given. 5. There is only one correct answer for each question.
L L A S O O T E Name Name of t he Candidate
Useful Data
PHYSICS 2
Acceleration due to gravity gravity
g = 10 m/s
Planck constant
h = 6.6 10 J-s
Charge of electron
e = 1.6 10 C
Mass of electron
me = 9.1 10 kg
Permittivity of free space
0 =
Density of water
water =
34
19
31
12
2
8.85 10 C /N-m 3
10 kg/m 5
2
3
2
Atmospheric Atmospheric pressure pressure
Pa = 10 N/m
Gas constant
R = 8.314 J K mol
1
1
CHEMISTRY
Gas Constant
R
Avogadro's Number Na Planck’s constant h 1 Faraday 1 calorie 1 amu 1 eV Atomic No:
= = = = = = = = = =
1
1
8.314 J K mol 1 1 0.0821 Lit atm K mol 1 1 1.987 2 Cal K mol 23 6.023 10 34 6.625 10 Js –27 6.625 10 ergs 96500 coulomb 4.2 joule –27 1.66 10 kg –19 1.6 10 J
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: masses: H=1, He=4, He=4, Li=7, Be=9, 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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Chemistry
1.
AgCl is crystallized from molten AgCl containing a little CCl2. The solid obtained will have (a) cationic vacancies equal to number of Cd2+ ions incorporated (b) cationic vacancies equal to double the number of Cd2+ ions (c) anionic vacancies (d) neither cationic nor anionic vacancies 1. Sol. (a) In the crystallization, some Ag+ ions will get replaced by as many half of Cd2+ ions. Thus the cation vacancies will be the same as the number of Cd2+ is ions incorporated. 2.
–1
For the reaction at 25°C, X 2O4 (l) → 2XO2(g) ΔH = 2.1 Kcal and ΔS = 20 cal K . The reaction would be
2. 3.
3. 4.
4. 5.
(a) spontaneous (b) non-spontaneous (c) at equilibrium (d) unpredictable Sol. (a) A C60 molecule has the geometry of a soccer ball having (a) both single and triple bonds with C — C bond lengths being 1.54 Å and 1.20 Å respectively. (b) both single and double bonds with C — C bond lengths being 1.54 Å and 1.34 Å respectively (c) both double and triple bond with C — C bond lengths being 1.34 Å and 120 Å respectively (d) both single and double bonds with C — C bond lengths being 1.45 Å and 1.38 Å respectively Sol. (d) While Fe3+ is stable, Mn3+ is not stable in acid solution because (a) O2oxidises Mn2+ to Mn3+ (b) O2oxidises both Mn2+ to Mn3+ and Fe2+ to Fe3+ (c) Fe3+oxidises H2O to O2 (d) Mn3+ oxidises H2O to O2 Sol. (b)
A compound ―X‖ is white, amphoteric solid. It becomes yellow on heating but again becomes while on cooling. Compound ―X‖ is
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5. 6.
6.
7.
7.
in association with
SCOBOTIC
(a) CaO (b) Al2O3 (c) As2O3 (d) None of these Sol. (d) A 100 ml solution of 0.1 N HCl was titrated with 0.2 N NaOHsolution. The titration was discontinued after adding 30 ml of NaOH solution. The remaining titration was completed by adding 0.25 N KOH solution. The volume of KOH required for completing the titration is (a) 70 ml (b) 32 ml (c) 35 ml (d) 16 ml Sol. (d)
The value of k p for the reaction at 27°C B r2 ( l) C l 2 ( g) 2B rC l( g) is ‗1 atm‘. At equilibrium in a closed container partial pressure of BrCl gas is 0.1 atm and at this temperature the vapour pressure of Br 2(l) is also 0.1 atm. Then what will be minimum moles of Br 2(l) to be added to 1 mole of Cl2, initially, to get above equilibrium situation:
(a) 10/6 moles (b) 5/6 moles (c) 15/6 moles (d) 2 moles Sol. (c)
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o A g
9.
SCOBOTIC
The EMF of the cell is for this reaction Mg(s) |Mg2+ (0.1 M)||Ag+ (1 × 10-4M)|Ag E
8.
in association with
0 .8 V , E /Ag
(a) 2.96 V (c) 1.9 V Sol. (a)
o Mg
2
2 .3 7 V /M g
(b) 3.2 V (d) 4.4 V
9.
Which of the following statements is not correct? (a) A colloidal solution is a heterogeneous two-phase system (b) Silver sol in water is an example of lyophilic solution. (c) Metal hydroxides in water are examples of lyophobic solution (d) Liquid-liquid colloidal solution is not stable system Sol. (b)
10.
Which of the following will show optical isomersim as well as geometrical isomerism.
(a)
(c)
10.
(c) Sol. (d)
(b)
(d)
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Mathematics
31.
If S(n) = 1 +
1
1
2
3
......
1
, (n
N)
n
, then S(1) + S(2) + ………+ S(n-1) is equal to
(a) nS(n) – n (b) nS(n) – 1 (c) (n - 1)S(n - 1) – n (d) None of these 31.
Sol. (a)
32.
The largest power of 2 that divides [(3 + √11)2n+1] is
32.
(where [.] greatest integer function) (a) n (b) n + 1 (c) n – 1 (d) None of these Sol. (b)
33.
If (ax2 + c)y + (a‘x2 + c‘) = 0 and x is a rational function of y and ac is negative, then (a) ac‘ + a‘c = 0 (b)
a a'
c c'
(c) a + c2 = a‘2 + c‘2 2
(d) ac‘ + a‘c = 1
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33.
Sol. (b)
34.
If Z = ii, where i = √-1, then (a) z is purely real (b) z is purely imaginary (c) |z| = 1 (d)
34.
a rg ( Z ) ta n
1
SCOBOTIC
1
2
Sol. (a)
35.
If A is a square matrix of order 3 such that |A| = 2, then |(adjA – 1) – 1| is (a) 2 (b) 4 (c) 8 (d) 16 Sol. (c)
36.
If f is continuous function, f : [0, 1] → R and satisfy the equation f ( x )( x f ( x ))d x
36.
then (a) f(x) = x (b) f(x) = x2/4 (c) f(x) = x/2 (d) none of these Sol. (c)
35.
0
1 12
,
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37.
SCOBOTIC
If A(z1) and B(z2) are two points on circle |z| = r, then the tangents tot the circle at A and B will intersect at 2
(a) (c) 37.
in association with
2
z1 z 2 z1 z 2 2 z 1z 2 z1 z 2
Sol. (c)
(b)
z 1z 2 z1 z 2 2
(d)
2
z1 z 2 2 z1 z 2
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38.
If y = f(x) be concave upward function and y = g(x) be a function such that f‘(x).g
38.
(x).f(x) = x 4 + 2x2 + 10, then (a) g(x) has atleast one root between two consecutive roots of f(x) = 0 (b) g(x) has at most one root between two consecutive roots of f(x) = 0 (c) if α and ß are two consective roots of f(x) = 0, the αß > 0 (d) when f(x) increases g(x) decreases Sol. (a)
39.
39.
For a point P on ellipse the circle with PS and PS‘ and PS‘ as diameter intersect the auxiliary circle of ellipse at A, A 1 and B, B1 respectively, then which of the following is/are incorrect? (a) A and A1 coincide, B and B1 coincide (b) segment AB is tangent to ellipse at P (c) tangents at A and B on auxiliary circles are perpendicular (d) SA and S‘B are parallel Sol. (c)
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40.
40.
If u and
v
u v w
is
are two unit vectors such that
(a) 1 (b) – 1 (c) 0 (d) None of these Sol. (a)
in association with
u v u w
and
w u v
SCOBOTIC
then value of
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SCOBOTIC
Physics
61.
61.
62.
62.
A particle is moving so that its displacement s is given as s = t3- 6t2 + 3t + 4 meter. Its velocity at the instant when its acceleration is zero will be (a) 3 m/s (b) -12 m/s (c) 42 m/s (d) -9 m/s Sol. (d)
A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10s is x 1, next 10 s is x2 and the last 10 s is x3. Then x1 : x2 : x3 is the same as (a) 1 : 2 : 4 (b) 1 : 2 : 5 (c) 1 : 3 : 5 (d) 1 : 3 : 9 Sol. (c)
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SCOBOTIC
In the arrangement shown in figure, pulleys are massless and frictionless and threads are inextensible. The Block of mass m1 will remain at rest, if
(a) (c) 63.
in association with
1
m1 4
1 m
m1
Sol. (c)
2
1 m3
2
1 m
1 m3
(b) m1 = m2 + m3 (d)
1 m3
2 m
2
3 m1
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in association with
SCOBOTIC
Two objects A and B of masses mA and mB are attached by strings as shown in fig. If they are given upward acceleration, then the ratio of tension T1 : T2 is -
(a) (c)
m A
mB
mB m A m B m A m B
(b) (d)
m A
mB
m A m A m B m A m B
64.
Sol. (a)
65.
A uniform square plate ABCD has a mass of 10kg. If two point masses of 3 kg each are placed at the corners C and D as shown in the adjoining figure, then the centre of mass shifts to the point which is lie on (a) OC (b) OD (c) OY (d) OX Sol. (c) For square plate ABCD centre of mass is at O but when two point masses of 3 kg placed at C & D then centre of mass shifts on the line OY because centre of mass is in that part which has higher mass.
65.
66.
Two particles having mass ratio n : 1 are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is : 2
2
(a) (n – 1) g
(b)
n 1 g n 1
(d)
n 1 g n 1
2
(c)
n 1 g n 1
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66.
Sol. (c)
67.
A small sphere is moving at a constant speed in a vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere I - kinetic energy II - gravitational potential energy III - momentum Which of these quantities will change as this sphere moves around the circle ? (a) I and II only (b) I and III only (c) III only (d) II and III only
67.
Sol. (d)
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68.
in association with
SCOBOTIC
A system of two blocks A and B are connected by an inextensible massless strings as shown. The pulley is masselss and frictionless. Initially the system is at rest when, a bullet of mass 'm' moving with a velocity 'u' as shown hits the block 'B' and gets embedded into it. The impulse imparted by tension force to the block of mass 3m is :
(a) 5mu / 4 (c) 2mu / 5 Sol. (d)
69.
(b) 4mu / 5 (d) 3mu / 5
A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than 90°. At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.
(a)
(b)
(c)
(d)
TARGET JEE 2018 JEE Main MT – 1
69.
Sol. (c) At highest point velocity is zero. After word it fall freely
70.
Equations y = 2A cos2ωt and y = A(sin ωt + particles. (a) Only one of these is S.H.M (b) Ratio of maximum speeds is 2 : 1 (c) Ratio of maximum speeds is 1 : 1 (d) Ratio of maximum accelerations is 1 : 4
70.
Sol. (c)
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3
SCOBOTIC
cos ωt) represent the motion of two
JEE Main - XI Mock Test 1
Physics - Maths Question No. 33 The percen age of oe in a oeI } sal c be deemne by usg a hoshe a on. 0.35 g of coe{I sal was issol v ed iateand aded o an xce of o ass oe so o lier ing odie orng o he lo ng e o 2C " () + 4J- ) = Cl) + 2 q) Th i 4 3 f 1 l ·3 hh 2? + l) - + ,' by n I) l [A 6] 1
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Question No. 3 e 1 2 he mecl ves e If 1 Uz r e e s sele e o sysems o me,
Op
0
n,u
=
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Oe Anl ysis
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Ht & Souto
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Question No. 3 e 1 2 he mecl ves e If 1 Uz r e e s sele e o sysems o me,
Op
0
n,u
=
u
(n, -u,) = ( -u)
Hn Phs qa y (p) = Numcalv x U t If p qu ty r n « 1/u
Prv Scn
