JEE Main Mock Test Paper 20 JEE 2018 - FIITJEE paper/XII/XII-VIII.pdfJEE Main Mock Test Paper- 20...

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CHEMISTRY, PHYSICS & MATHEMATICS

Time Alloted: 3 Hours

Writing time – 09.30am – 12.30pm

Maximum Marks: 360

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. You are not allowed to leave the Examination Hall before the end of the test.

INSTRUCTIONS

A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheet, provided separately. 2. This question paper contains Three Sections. Section-1 is Chemistry, Section-2 is Physics and Section-3 is Mathematics. 3. This question paper booklet is single-sided. You may use other side of the printed part as Rough space. Do not use any

extra space for Rough work. No additional sheets will be provided for the same. 4. 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 or Blue Ball point pen only for each character of your

Enrolment No. and write in ink your Name, Test Centre and other details at the designated places. Bubble your answers also with the same pen / ink.

C. Marking Scheme For All Three Parts. Every question has only ONE correct option. For every question bubbled correctly, you will be allotted 4 marks. No marks will be allotted for unattempted questions. In all other cases, ¼ th marks (i.e. minus 1) will be deducted.

Name of the Candidate :_______________________________________________________________

Batch :_______________________ Enrolment Number : ____________________________

USEFUL DATA PHYSICS

Acceleration due to gravity : g = 10 m/s2 Planck constant : h = 6.6 3410 J s

Charge of electron : e = 1.6 1910 C Mass of electron :

319.1 10em kg

Permittivity of free space : 12 2 2

0 8.85 10 /C N m Density of water : water 3 310 /kg m

Atmospheric pressure : 5 210 /Pa N m Gas constant : R = 8.314 J 1 1K mol

USEFUL DATA CHEMISTRY

Gas Constant R = 8.314 J 1 1K mol = 0.0821 Lit atm 1 1K mol =1.987 2 Cal 1 1K mol

Avogadro’s Number aN = 6.023 2310 1 Faraday = 96500 coulomb 1 calorie = 4.2 joule

Planck’s constant h = 6.625 3410 .J s = 6.6252710 .erg s 1 amu = 1.66

2710 kg 1 eV =191.6 10 J

Atomic No: H = 1, He = 2, Li = 3, Be = 4, B = 5, C = 6, N = 7, = 8, F = 9, Ne = 10, 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: H = 1, He = 4, Li = 7, Be = 9, B = 11, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Si = 28, Al = 27, 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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JEE Main Mock Test Paper 20– JEE 2018 a FIITJEE team initiative

JEE Main Mock Test Paper- 20 a FIITJEE team initiative


Section – 1 CHEMISTRY 1. There are 201 equidistant rows or spectators sitting in a hall. A magician releases laughing gas N2O from the

front and the tear gas (M0=176) from the rear of the hall simultaneously. Which row of spectators will have a tendency to smile and weep simultaneously? (A) 114 (B) 134 (C) 124 (D) 144

2. Ice belongs to which of the following structures? (A) Cubic (B) Hexagonal (C) Orthorhombic (D) Tetragonal

3. In 321 the sum of angular momentum, spherical nodes and angular node is

(A) 6 4

2

h

(B)

63

2

h

(C)

6 2

2

h

(D)

6 8

2

h

4. If ( )d G

G H T S and G H TdT

then variation of EMF of a cell E, with temperature T is

given by

(A) G

nF

(B)

G

nF

(C)

S

nF

(D)

S

nF

5. One mole of a real gas is subjected to heating at constant volume from (p1,V1,T1) state to (p2,V2,T2) state. Then it is subjected to irreversible adiabatic compression against constant atmosphere till system reaches the final state (p3,V3,T3). If the constant volume molar heat capacity of real gas is Cv. Find out correct expression for H from state 1 to state 3.

(A) 3 1 3 1 1 1( ) (p )VC T T V pV (B)

2 1 3 2 1 1( ) (p )VC T T V pV

(C) 2 1 3 1 1 1( ) (p )VC T T V pV (D) 2 1 3 1 1 1( ) (p )pC T T V pV

6. In a mixture of A and B if the mole fraction of the component A in vapor phase is x1 and mole fraction of

component A in liquid mixture is x2 (o

Ap =vapour pressure of pure A; o

BP = vapor pressure of pure B), then

total vapor pressure of the liquid mixture is:

(A) 2

1

o

Ap x

x (B) 1

2

o

Ap x

x (C) 1

2

o

Bp x

x (D) 2

1

o

Bp x

x

7. At a certain temperature, the equilibrium constant KC is 16 for the reaction,

32 2 ( ) ( ) ( ).g SSO g N g gO O NO . If 1.0 mol each of all the four gases is taken in a 1 L container the

concentration of NO2 at equilibrium would be (A)1.6 mol L–1 (B) 0.8 mol L–1 (C) 0.4 mol L–1 (D) 0.6 mol L–1

8. Buffer solution A of a weak monoprotic acid and sodium salt in the concentration ratio x:y has pH=(pH)1. Buffer solution B of the same acid and its sodium salt in the concentration ratio y:x has pH=(pH)2. If (pH)2 – (pH)1=1 unit and(pH)1+(pH)2=9.5 units, then

(A) 4.75apK (B) / 2.36x y (C) / 4.162x y (D) 4 5.25pK

Space for rough work



9. If the hydrogen electrodes in two solutions of pH = 3 and pH = 6 are connected by a salt bridge, the emf of the resulting cell is (A) 0.177 v (B) 0.3 V (C) 0.052 V (D) 0.104 V

10. The high temperature ( 1200 )K decomposition of 3 ( )CH COOH g occurs as follows as per simultaneous

first order reactions. 1

2

3 4 2

3 2 2

k

k

CH COOH CH CO

CH COOH CH CO H O

What would be the % of CH4 by mole in the product mixture (excluding CH3 COOH)?

(A)

1

1 2

50k

k k (B)

1

1 2

1000k

k k (C)

1

1 2

200k

k k (D) It depends on time.

11. Which is an Sesqui oxide (A) KO3 (B) NH4O3 (C) Cr2O3 (D) Both (A) and (B)

12. Regarding sulphur which of the following is/are correct? (A) Density of rhombic sulphur is more than that of monoclinic sulphur (B) Rhombic sulphur is bright yellow whereas monoclinic sulphur is transparent (C) In the gaseous state the atomicity of sulphur is two (D) All of the above are correct

13. Mark the wrong statement. Halogens are all coloured. (A) This is due to absorption of visible light by the molecules resulting in the excitation of outer elections to higher energy levels. (B) The small F2 molecules absorb high energy violet radiation and appear yellow (C) Large I2 molecule absorb low energy yellow and green radiations and appear violet in colour. (D) The excitation energy required by the small fluorine atoms is smaller than required by the large iodine atom.

14. Which of the following hydrated salts will give anhydrous salt on heating?

(A) 2 2,6MgCl H O (B)

2 2,6CaCl H O (C) 3 2,6Alcl H O (D)

2 2,2SnCl H O

15. Mn(H2O)62+ is almost colourless while Mn(CN)6

4– blue violet in their aqueous solution. Because

(A) In Mn(H2O)62+ the is quite lesser do that it absorb in the IR region whereas d-d transition of electron in

the case of Mn(CN)64– belongs to visible region.

(B)In Mn(H2O)62+ the is quite lesser do that it absorb in the UV region whereas d-d transition of electron in

the case of Mn(CN)64– belongs to visible region.

(C) In Mn(H2O)62+transition of electron would not occur because of spin forbidden transition whereas in

Mn(CN)62+ transition of electron would occur because transition of electron is not spine forbidden.

(D) Both (A) and (C) are correct




16. In which of the following hybridisation state of the central atom would be change if transformed from monomeric to dimeric or polymeric species.

2 2( ) ( )BeCl g BeCl s ;3 2 6( ) Al ( )AlCl g Cl l

2 2BeH ( ) BeH ( )g s ; 3 2 6( )ICI g I Cl

(A) sp2 to sp3 (B) sp to sp3 (C) sp3d to sp3d2 (D) All the above

17. Be(OH)2 forms bridge bonding structure in their polymeric from of the compounds as given below : (I) [Be3(OH)8]2– (II) [Be4(OH)10]2–

Which type of bond formation takes place in the above compounds. (A) 3 C – 2c bond (B) 3C – 4e bond (C) both (A) and (B) (D) None of these

18. Which of the following compounds contains both 2C – 2e–– bond and 3C – 4e–– bond?

(A) 2 4 Be Cl (B)

2 4B Cl (C) 2( )SnCl

(D) Both (A) to (C)

19. Use the following data answer the question below

Calculate the resonance energy of anthracene (A) 84 kcal/mol (B) 100kcal/mol (C) 110 kcal/mol (D) 116kcal/mol

20.

Which of the following orders is correct for heat of hydrogenation of these compounds? (A) I > III > II (B) III > II > I (C) III > I > II (D) II > I > III

21. Determine the absolute configuration of the lebeled carbons (a and b):

(A) a= R ; b = R (B) a =R ; b = S (C) a = S ; b= R (D) a = S ; b = S

22. Which of the following molecules is (are) chiral?

(A) I and II (B) III and IV (C) II, IV and VI (D) I, II, III and VI




23.

The given product can not be obtained in the above reaction. Identify the correct product obtained.

(A)

(B)

(C)

(D)

24. Which of the following is not the product of an intermolecular aldol condensation? (A)

(B)

(C)

(D)

25. Find iso-electric point of given amino acid

(A) 3.3 (B) 5.9 (C) 9.6 (D) 11.8

26.

x = moles of anhydride consumed (A)1 (B) 2 (C) 3 (D)4

27. Which of the following compounds give positive Tollen’s test? (A)

(B)

(C)

(D)

28. SN1 and SN2 reaction are (A) Both stereospecific (B) Both stereoselective (C) Stereoselective and stereospecific respectively (D) Stereospecific and stereoselective respectively

29. Which of the following electrolytes is least effective in caushing flocculation of ferric hydroxide solution? (A) K2[Fe(CN)6] (B) K2CrO4 (C) KBr (D) K2SO4

30. Graph between log k and ( 1/T) is linear of slope S ( magnitude) Hence Ea is (A) R×S (B) S/R (C) R/S (D) 2.303 RS




Section – 2 PHYSICS 1. In the circuit shown in the figure k1 is open. The charge on capacitor C in steady state is q1.

Now key is closed and at steady state charge on C is q2. The ratio of charges q1/q2 is (a) 5/3 (B) 3/5 (C) 1 (D)2/3

2. The period of oscillation of magnet in a vibration magnetometer is 2 seconds. The period of oscillation of a magnet whose magnetic moment is four times that of the first magnet is (A) 1 sec (B) 4 sec (C) 8 sec (D) 0.5 sec

3. The p-n junction diode used given figure has a cut- in voltage of 1 volt and forward resistance of 2 k . If diode can dissipate a maximum power of 200 mW. Find the maximum possible value of the battery voltage VB.

(A) 83 Volt (B) 131 Volt (C) 153 VOlt (D) 183 Volt.

4. A monochromatic light is used in Young’s double slit experiment. When one of the slits is covered by a

transparent sheet of thickness 1.8×10–5m, made of material of refractive index 1, number of fringes which

shift is 18. When another sheet of thickness 3.6×10–5m, made of material of refractive index 2 is used, number

of fringes which shift is 9. Relation between 1 and 2 is given by

(A) 42–1=3 (B) 41–2=3 (C) 32–1=4 (D) 21–2=4.

5. A uniform magnetic field intensity 1T is applied in a circular region of radius 0.1m, directed into the plane of

paper. A charged particle of mass 5×10–5kg and charge q=5×10–4C enters the field with velocity 1

3m/s making

an angle of with a radial line of circular region in such a way that it passes through centre of applied field the

angle is (A) 60° (B) 30° (C) 45° (D) 90°

6. A hemispherical bowl of radius 10cm is filled with liquid of refractive index =4/3. A glass plate of refractive index 1.5 is placed on the top of bowl. If for the observer above the plate the shift in position of a point P on the bottom is 3cm, find the thickness of glass plate. (A) 1.5cm (B) 1cm (C) 7cm (D) 10cm.

7. Three rods AB, BC and BD of same length and cross sectional are A are arranged as shown. The end D is immersed in ice at 00C, whose mass is 440 gm. Heat is being supplied at constant rate of 200 cal/sec from the end A. Time in which whole ice will melt is [Given: Lfusion of ice = 80 cal/gm, K = 100

cal/m-sec-0C, A = 10 m2, =1m)

(A) 40

3min (B) 700sec (C) 20/3min (D)Indefinitely long time




8. A uniform rod of mass M and length is moving on a smooth horizontal plane, such that its one end is moving with a velocity v0 and other end is moving with a velocity 2v0 in the same direction as shown. Then the kinetic energy of the rod is

(A) 2

0

13

24Mv (B) 2

0

24

31Mv (C) 2

0

31

24Mv (D) 2

0

7

6Mv

9. For a gas specific heat capacity for a process is given as C = (4×104+3P) Joule/kg/k. If the state of a gas is changed from temperature 200K and volume 120 litre (P represents pressure of gas in N/m2) to temperature 250K and volume 150 litre, then heat exchanged for one mole of gas is (A) 4.07×106J (B) 8.14×104J (C) data insufficient (D) –4.07×106J

10. AB is a small, fixed dipole of dipole moment p. M is a point at a distance x on the axis of dipole and N is another point at a distance x from centre but on the line making an angle of 60° with the initial position of dipole. If a charged particle of magnitude q is moved from M to N, work done by external force is

(A) 2

0

1 1

2 4

pq

x

(B)

2

0

1 1

2 4

pq

x

(C) 2

0

1

4

pq

x

(D) zero

11. A combination of inductors and resistances are connected across an ac source as shown in the figure. The phase difference between the current flowing through R1 and R2 (in radians) is

(A) 37

180 (B)

2

(C)

16

180 (D) cannot be decided.

12. A pilot in a plane wants to go 500km towards north. To reach straight to his desired position the pilot has to

drive his plane 53° west of north in presence of wind, which is blowing in due east. The time taken by pilot to reach his destination is 10hr. The velocity of wind is (A) 200/3 km/hr (B) 100/3 km/hr (C) 200 km/hr (D) 150 km/hr

13. On a fixed smooth semicircular ring of radius R, one end of a spring of spring constant k

and natural length R/3 is attached at end A as shown in the figure. The other end of the spring is fixed to a massless bead which can slide without friction on the ring. The bead is placed in such a position that the spring makes angle 30° with diameter of AB. If the bead is released, then the acceleration of the bead is (The system lies on a horizontal plane)

(A) 2

kR

m (B)

3 1

kR

m (C)

3 1 kR

m

(D)

3

kR

m




14. A particle of mass 3m is dropped from certain height at t=0. At time t=t0, the particle explodes and breaks into

two parts m and 2m. At time t=3t0 velocity of lighter mass is 1 2v v i v j . The velocity of heavier mass at t=t0

(just after explosion) is (if y represents vertical and x represents horizontal).

(A) 2vi v j (B)

2 015

2 2

v gtvi j

(C)

2 015

2 2

v gt jvi

(D) None of above

15. A photon of maximum wavelength 1 strikes a He+ ion in its first excited state and is capable of exciting it to

higher state. Photon imparts its whole energy to it. As a result He+ ion emits a radiation of 2, ratio of 1(max)

2(max)

A) 1:1 (B) 32:5 (C) 4:3 (D) None of these

16. A source of sound with frequency f0 is fitted on a circular plank of radius 1m which

is moving with an angular velocity . S1 and S2 are two stationary observers at 3 m and 4m from centre of circular plank. Statement 1: S1 and S2 will never hear same frequency at any instant. Statement 2: If the velocity of the source is perpendicular to the line joining the observer and the source, then the observer hears the same frequency as that of the source. Choose the correct option. (A) Both statements are correct, and statement 2 is correct explanation of statement 1. (B) Both statements are correct, and statement 2 is NOT the correct explanation of statement 1. (C) Statement 1 is correct, statement 2 is wrong. (D) Statement 1 is wrong, statement 2 is correct.

17. Two bodies A and B of each of mass 100 gm are allowed to move along a frictionless typical path as shown below. In order to have the same kinetic energy for both the bodies at M, the initial velocity that should be given to B, if A starts from rest, is

(A) 10m/s (B) 2 m/s (C) 11 m/s (D) 102 m/s

18. Ends of two wires A and B, having resistivity -5 -5

A Bρ =6×10 Ωm, ρ =18×10 Ωm , of same cross section area are

pointed together to form a single wire. If the resistance of the joined wire does not change with temperature,

then find the ratio of their length ( / )A B , given that temperature coefficient of resistivity of wires A and B

are 54 10 /A C and 64 10 /B C . Assume that mechanical dimensions do not change with

temperature. (A) 3:10 (B) 10:3 (C) 1:3 (D) 3:1




19. As shown in the figure AC and BD are straight lines and CED and AFB are semicircular with radii r and 4r respectively. The entire setup is lying in the same plane. If i is current entering at A what fraction of i will flow in the ACEDB such that resultant magnetic field at O is zero. (A) i/5 (B) 4i/5 (C) 3i/5 (D) no current through bigger semicircular part.

20. A cylindrical pipe open from one end is filled with water upto its brim. Water is allowed to drain out at a constant speed. A tuning fork with frequency 165 Hz is vibrated at the mouth of pipe. Drop in level of water from its initial position so that resonance occur is (speed of sound=330 m/s)

(A) =2.5m (B) =1.0m (C) =0.75m (D) None of these

21. A block of mass m is moving with a velocity v0 and makes collision with another mass 2m which is at rest. If coefficient of restitution is 0.8, then impulse between the two blocks during the collision is

(A) mv0 (B) 03

5mv (C) 0

53

mv (D) 06

5mv

22. Binding energy of A=X MeV, B= Y MeV, C = Z MeV [X > Y > Z]. A person in a lab tries to break each nucleus into its constituents with the help of energy S MeV. If [Y < S < X], then which of the following nuclei may break? (A) B and C (B) C and A (C) A and B (D) Only C

23. A block with a square base having area (A=a × a) measuring a × a, and height h is placed on an inclined plane.

The coefficient of friction between the block is . The angle of inclination of the plane is gradually increased. The block will

(A) topple before sliding if a

h (B) topple before sliding if

a

h

(C) slide before toppling if a

h (D) None of these

24. Block A is placed on block B (where MB>MA). There is friction between the two blocks whereas between the block and the horizontal surface friction is absent. If a horizontal time

dependent force varying as F=t acts on A ( is constant), then the graph drawn between acceleration of A (a1) and acceleration of B (a2) w.r.t. time is best represented by

(A)

(B)

(C)

(D)




25. As shown in the figure, a disc of mass M and radius R is placed on horizontal smooth surface. A constant force F act at a distance x above centre so that body start rolling. The value of X is (A) R/2 (B) 3R/4 (C) 2R/3 (D) R

26. A conductor of length 5 cm, and resistance 2 is moving on frictionless rails with a constant velocity of 5 cm/s in a magnetic field of intensity 3 Tesla as shown below. If conductor is connected to a circuit as shown, by two lead wires of almost negligible resistance, then current flowing in it is (A) 0.25A (B) 2.5Amp (C) 2.5mA (D) 0.25×104amp

27. The pitch of a screw gauge is 1mm and there are 100 divisions on circular scale. When their faces are just touching each without putting anything between the studs 32nd division of the circular scale coincides with the reference line. When a glass plate is placed between the studs, the liner scale reads 4 divisions and the circular scale reads 16 divisions. Zero of liner scale is not hidden form circular scale when their faces touch each other. The thickness of the glass plate is.

(A) 4.16 mm (B) 3.84 mm (C) 4.46 mm (D) 4.48 mm

28. A block of mass 100gm connected to a spring constant 0.1 2N/m is lying on a frictionless horizontal surface as shown in the figure. When the compression in

the spring is maximum, the block experiences an acceleration of 42 cm/s2 away from the spring. If the block moves by 20 cm from maximum accelerated position in ‘t’ second, then the value of ‘t’ is (A) 1/3 sec (B) 1/2sec (C) 1/6sec (D) None of these

29. If two uniform spherical drops of a liquid having same mass, radius and falling freely with a terminal velocity of 3 16 m/s, coalesce to form a bigger drop, then the terminal velocity with which the bigger drop falls is

(A) 8m/s (B) 4m/s (C) 10 m/s (D) none of these

30. According to Kepler’s third law of motion (law of periods) which of the following is a best represented graph between log T and log R (where T-time period of a planet, R-Radius of the orbit)

(A)

(B)

(C)

(D)




Section – 3 MATHEMATICS

1. If

x 1 x x , x 1f(x)

0 , x 1, where [.] denotes the greatest integer function, then at x = 1, f(x) is

(A) both continuous as well as differentiable (B) continuous but not differentiable (C) neither continuous nor differentiable (D) not continuous but differentiable

2. If (1 + tan A) (1 + tan B) = 2, then the number of values of A + B in the interval

2

3,

2

3 is

(A) 1 (B) 2 (C) 3 (D) 4

3. Ifx

f(x)1 x

, then

(A) f (x) is differentiable x R (B) f (x) is no where differentiable (C) f (x) is not differentiable at finitely many points (D) None of these

4. If A = log2log2log4 256 + 2 2log2

, then A =

(A) 2 (B) 3 (C) 5 (D) 7

5. The value of

1 2

5 4 5

10 7 8

m m m

m m m

m m m

i i i

i i i

i i i

, where i = 1 is

(A) 1 if m is multiple of 4 (B) 0 for all real m (C) –i if m is a multiple of 3 (D) none of these

6. Urn A has 5 black balls and one white ball and urn B has 6 black balls. If two balls are randomly picked up from urn A and transferred to urn B and again two balls are randomly picked up from urn B and transferred to urn A, then the probability that white ball is now in urn A is

(A) 5/6 (B) 1/3 (C) 2/3 (D) 3/4

7. Let natural numbers a and b be two arbitrary constants and f(x) = 2 2sin 3 cos 7a x b x .

Let T be the least natural number such that f(x+T)=f(x) xR. Then T =

(A) (B) 2 (C) 2

7b3a 22 (D) none of these

8. If the equations x = ay + z, y = az + x and z = ax + y are the consistent having non-trivial solution, then (A) a3 = 1 (B) a3 + 1= 0 (C) a + 1 = 0 (D) none of these

9. When f(x) is of the form ax2 + bx + c where

1

0

dx12

a)x(f = k[f (0) + f (1/2) + f (1)] then k equals to

(A) 2 (B) 3 (C) 1/2 (D) 1/3

10. If a line makes angles , , with the axes, then cos2 + cos2 + cos2 =

(A) 1 (B) 1 (C) 2 (D) 2




11. Let x

g(x) 2f f(2 x)2

and f (x) < 0 in 0 x 2 then g (x)

(A) decreases in

3

2,0 (B) decreases in

2,

3

4 (C) increases in

3

2,0 (D) increases in

1,

3

2

12. In a quadratic equation with leading coefficient 1, a student reads the coefficient 16 of x wrongly as 19 and obtains the roots as –15 and –4. The correct roots are (A) 6, 10 (B) –6, –10 (C) –7, –12 (D) 7, 12

13. If

2nn

n

r 1

ra log3 , n N

r n r

, then a1 + a2 + a3 + ….. to is ____. [You may use r

x

r 0

xe

r

.]

(A) (1 + log 3) (9 log 3) (B) (1 – log 3) (9 log 3) (C) (1 + log 3) (log 3) (D) (2 + log 3) (9 log 3)

14. Consider an infinite geometric series with first term a and common ratio r. if its sum is 4 and the second

term is 4

3, then

(A) 7 3

a , r4 7

(B) 3

a 2, r8

(C) 3 1

a , r2 2

(D) 1

a 3, r4

15. If 1

( )1

f xx

and , ( ) be the values of x, where f(f(x)) is not defined, then a ray of light parallel

to the axis of the parabola 2 4y x after reflection from the internal surface of the parabola will necessarily

pass through the point

(A) , (B) , (C) , (D) None

16. The co-ordinates of the vertices of rectangle ABCD; where A(0, 0), B(4, 0), C(4, 2), D(0, 2) undergoes following ‘3’ successive transformations

a. (x, y) (y, x) b. (x, y) (x + 3y, y) c. (x, y)

2

yx,

2

yx

Then the final figure formed will be

(A). a square (B) a rhombus (C) a rectangle (D) a parallelogram

17. If candb

are two non-collinear vectors such that 4cb.a

and cysinb6x2xcba 2 ,

then the point ( x, y) lies on

(A) x =1 (B) y =1 (C) y = (D) x + y = 0




18. A variable tangent of the ellipse 1b

y

a

x2

2

2

2

, meets the coordinate axis at the points A and B. Minimum

area of circumcircle of triangle OAB, ‘O’ being the centre of the ellipse, is

(A) 2ba4

(B) (a2 + b2) (C) 22 ba4

(D) 2ba4

19. equals1cos

11sintan 1

(A) 0 (B) 2

1

(C) 12

(D)

42

1

20. Using mathematical induction, the numbers an’s are defined by a0=1, an+1=3n2+n+an, (n 0),nN

Then, an is equal to

(A) n3 + n2 + 1 (B) n3 n2 + 1 (C) n3 n2 (D) n3 + n2

21. The inequality log2x < sin–1 (sin5) holds if

(A) x (0, 25-2) (B) x (25-2 , ) (C) x (22 -5 , ) (D) None of these

22. (p q) (q p) (p r) (r s)

(A) tautology (B) contradiction (C) contradiction if truth value of s is “true” (D) none of these

23. Equation ax2 + 2bxy + by2 = 0 represents a pair of lines. Combined equation of lines that can be obtained by

reflecting these lines about the x axis is

(A) b x2 2 b x y + a y2 = 0 (B) a x2 + 2 b x y + b y2 = 0

(C) b x2 + 2 b x y + a y2 = 0 (D) a x2 2 b x y + b y2 = 0

24. If n

n r

r

r 0

1 x C x

,then

1n

n

1

2

0

1

C

C1.....

C

C1

C

C1

(A) !)1n(

n 1n

(B) !)1n(

)1n( 1n

(C)

!n

1nn

(D)

!n

1n1n

25. If the curve y = f (x) passes through the point P(1, 1). The normal to the curve at P is

a(y 1) + (x 1) = 0. If the slope of the tangent at any point is proportional to the ordinate of the point then equation of the curve f (x) is given by

(A) y = )1x(a 2

e (B) y = exa (C) y = ln x + a (D) y = ea(x1)




26. If f () = cos sin 0

sin cos 0

0 0 1

, then f ( ) f ( ) is equal to

(A) f ( –) (B)

f (C) f ( + ) (D) All of the above

27. The lines 3x – 4y + = 0 and 6x – 8y + = 0 are tangents to the same circle. The radius of the circle is

(A) 20

2 (B)

20

2 (C)

20

2 (D) none of these.

28. The value of

2 4 8cos cos cos cos

5 5 5 5 is

(A) 16

1 (B)

1

2 (C)

1

8 (D)

1

32

29. If the equations x² – px + q = 0 and x² – ax + b = 0 have a common root and the other root of the second equation is the reciprocal of the other root of the first, then (q – b)² = (A) aq (p – b)² (B) bq (p – a)² (C) bq (p – b)² (D) bq² (p – b)²

30. A triangle is inscribed in a circle. The vertices of the triangle divide the circle in to three arcs of length 3, 4 and 5 units, then area of the triangle is equal to,

(A)

2

3139

(B)

2

1339

(C)

22

3139

(D)

22

1339



Answer Key – JEE Main Mock Test Paper 20 – JEE 2018

a FIITJEE team initiative

CHEMISTRY

1. B 2. D 3. A 4. C 5. C 6. A 7. C 8. A 9. B 10. A

11. C 12. D 13. D 14. B 15. C 16. D 17. B 18. D 19. A 20. A

21. A 22. D 23. B 24. C 25. B 26. C 27. C 28. C 29. C 30. D

PHYSICS

1. A 2. A 3. C 4. A 5. A 6. A 7. A 8. D 9. A 10. A

11. C 12. A 13. D 14. C 15. A 16. D 17. D 18. A 19. A 20. A

21. D 22. A 23. A 24. C 25. A 26. C 27. B 28. A 29. B 30. D

MATHEMATICS

1. B 2. C 3. A 4. C 5. B 6. D 7. B 8. D 9. D 10. A

11. B 12. B 13. A 14. D 15. B 16. D 17. A 18. D 19. D 20. B

21. A 22. A 23. D 24. C 25. D 26. C 27. A 28. A 29. B 30. A

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