JEE Main Mock Test Paper 4 JEE 2018 paper/XII/XII-IV.pdfJEE Main Mock Test Paper- 4 Page 2 a FIITJEE...

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 4 – JEE 2018 a FIITJEE team initiative

JEE Main Mock Test Paper- 4 a FIITJEE team initiative

Section – 1 CHEMISTRY 1. 100 mL of H2SO4 solution having molarity 1M and density 1.5 g/mL is mixed with 400 mL of water. Calculate final

molarity of H2SO4 solution, If final density is 1.25 g/mL: (A) 0.20 M (B) 0.145 M (C)0.52 M (D) 0.227 M

2. An electron is allowed to move freely in a closed cubic box of length of side of 10 cm.. the uncertainty in its velocity will be:

(A) –4 13. s35 1 c0 em (B) –4 15. 0 c8 1 sem (C) – 1510 c4 sem (D) – 1610 c4 sem

3. A low pressure, if 2 .RT a p , then the volume occupied by a real gas is:

(A)2RT

P (B)

2P

RT (C)

2

RT

P (D)

RT

P

4. For the real gases reaction 2 22 2 ; 560 .CO g O g CO g H kJ In 10 litre rigid vessel at 500 K the

initial pressure is 70 bar and after the reaction it becomes 40 bar. The change in internal energy is : (A)–557 kJ (B) –530 kJ (C) –563 kJ (D) –550 kJ

5. Enthalpy of neutralization of H3PO3 acid is –106.68 kJ/mol using NaOH. Enthalpy of neutralization of HCl by

NaOH is –55.84kJ/mol. Calculate ionizationH of H3PO3 into its ions:

(A) 50.84 kJ/mol (B) 5 kJ/mol (C)25 kJ/mol (D) 10kJ/mol

6. 2 3I aq I aq I aq we started with 1 mole of 2I and 0.5 mole of I in one litre flask After equilibrium

is reached, excess of AgNO3 gave 0.25 mole of yellow precipitate Equilibrium constant is (A) 1.33 (B) 2.66 (C) 2.0 (D) 3.0

7. 3 2A B is a sparingly soluble salt of molar mass 1M g mol and solubility x g litre–1. The ratio of the molar

concentration of 3B to the solubility product of the salt is:

(A)5

5

108

1

x

M (B)

4

4

1

108

M

x (C)

4

4

1

54

M

x (D) 108

4

4

108

1

M

x

8. A crystal is made of particle ,X Y and .Z X forms fcc packing. Y occupies all the octahedral voids of &X Z

occupies all the tetrahedral voids of X . If all the particle along one body diagonal are removed then the formula of the crystal would be:

(A) XYZ 2 (B) 2 2X YZ (C) 8 4 5X Y Z (D) 5 4 8X Y Z

9. Total vapour pressure of mixture of 1 mol 150XX P torr and 2 mol 300YY P torr is 240 torr. In this case:

(A) There is a negative deviation from Raoult’s law (B) There is a positive deviation from Raoult’s law (C) There is no deviation from Raoult’s law (D) Cannot be decided

Space for rough work

FIITJEE Ltd., 3A. DL Tower, Near Parishad Bhawan, JLN Marg, Jaipur website: www.fiitjee.com


10. A 250.0 mL sample of a 0.20 M Cr3+ is electrolysed with a current of 96.5 A. If the remaining 3[ ]Cr is 0.1 M ,

the duration of process is: (A) 25 sec (B) 225 sec (C) 150sec (D) 75 sec

11. When ethyl acetate was hydrolysed in presence of 0.1 M HCl, the rate constant was found to be–5 –15.4 10 s .

But in pressure of 0.1 M 2 4H SO the rate constant was found to be –5 –16.25 10 s . Thus it may be concluded that:

(A) H2SO4 furnishes more H+ than HCl (B) H2SO4 furnishes less H+ than HCl (C)both have the same strength (D) Will depend on concentration of ethyl acetate

12. Identify the correct statement regarding enzymes: (A) Enzymes are specific biological catalysts that normally works at high temperature (B) Enzymes are normally heterogeneous catalysts which decress the reaction rate (C) Enzymes are specific biological catalysts that are very specific in nature (D) Enzymes are specific biological catalysts with low molar masses

13. In which of the following transformation least energy is required ?

(A) g g

F F e (B) g g

P P e (C) g g

S S e (D) g g

Cl Cl e

14. The lowest O––O bond length in the following molecules is: (A)O2F2 (B)O2 (C) H2O2 (D) O3

15. Which of the following overlapping is not present in XeO3 molecule?

(A) 3

xsp p (B)3

ysp p (C) xz xd p (D) 3sp s

16. Which is not obtained when metal carbides react with H2O?

(A)4 3 2Al C H O CH CH (B)

2 2CaC H O CH CH

(C)4 3 2 3Mg C H O CH C CH (C)

2 2 4Be C H O CH

17. When a sample of NO2 is placed in a container, this equilibrium is rapidly established.

2 2 42NO g N O g

If this equilibrium mixture is a darker colour at high temperatures and at low pressure, which of these statements about the reaction is true? (A) The reaction is exothermic and NO2 is darker in colour than N2O4. (B) The reaction is exothermic and N2O4 is darker in colour than NO2. (C) The reaction is endothermic and NO2 is darker in colour than N2O4. (D) The reaction is endothermic and N2O4 is darker in colour than NO2.




18. What is the magnetic moment (spin only) and hybridization of the brown ring complex [Fe(H2O)5NO]SO4.?

(A) 3 23 ,BM sp d (B) 2 33 ,BM d sp (C) 3 215 ,BM sp d (D) 2 315 ,BM d sp

19. Salt (A) gives brick red fumes (B) with conc. H2SO4 and K2Cr2O7 which gives yellow solution (C)with NaOH and it gives yellow ppt. (D) with acetic acid and lead acetate. What is(C)? (A) Na2CrO4 (B)CrO2Cl2 (C)PbCrO4 (D)NaCl

20. The method of zone refining of metals is based on the principle of: (A)Greater mobility of the pure metal than that of impurity (B) Higher melting point of the impurity than that of the pure metal (C)Greater noble character of the solid metal than that of the impurity (D)Greater solubility of the impurity in the molten state than in the solid.

21. Among the following which is more reactive toward AgNO3?

(A)

(B)

(C)

(D)

22. Consider the following reactions,

(A)

(B)

(C)

(D)

23. Treatment of 2-bromobutane with hot alcoholic KOH gives a mixture of three isomeric butenes (A), (B) and (C). Ozonolysis of the minor product (A) gives HCHO and another aldehyde in equimolar amounts. Both (B) and (C) gave the same single product (D) on ozonolysis. Find structural formula of (D):

(A)

(B)

(C)

(D)




24.

The final product A is :

(A)

(B)

(C)

(D)

25.

S will be:

(A)

(B)

(C)

(D)

26. Which of the following is most reactive amine towards dilute aqueous hydrochloric acid?

(A) 3 3CH NH (B) 3 3CH NH CH (C)

(D)




27. Dinuclecotide is obtained by joining two nucleotides together by phosphodiester linkage . Between which

carbon atom of pentose sugar nucleotides are these linkages present? (A) 51 and 31 (B) 11 and 51 (C) 51 and 51 (D) 51 and 11

28. Which of the following polymers do not have vinylic monomer units? (A) Acrilan (B) Polystyrene (C) Nylon (D) Teflon

29. Which of the following in an example of liquid dishwashing (A) 3 2 2 310

CH CH CH OSO Na (B)

(C)

(D)

30. Which of the following statements is correct? (A) ozone hole is a hole formed in stratosphere from which ozone oozes out (B) Ozone hole is a hole formed in troposphere from which ozone oozes out (C)Ozone hole is thinning of ozone layer of stratosphere at some places (D)Ozone hole means vanishing of ozone layer around the earth completely




Section – 2 PHYSICS SINGLE CORRECT QUESTIONS:

1. A spherical shell of inner radius a and outer radius b is made of a material of resistivity ρ and negligible dielectric activity. A single point charge q0is located at the center of the shell. At time t = 0 all of the material of the shell is electrically neutral, including both the inner and outer surfaces. What is the total charge on the outer surface of the shell as a function of time for t > 0? Ignore any effects due to magnetism or radiation; do not assume that b − a is small.

(A) 𝑄 = 𝑞(1 − 𝑒−

(𝑏−𝑎)𝑡

4𝜋𝑎𝑏∈0) (B) 𝑄 = 𝑞(1 − 𝑒−

𝑏𝑡

𝑎∈0) (C) 𝑄 = 𝑞(1 − 𝑒−

(𝑏−𝑎)𝑡

𝑎𝑏∈0 ) (D) 𝑄 = 𝑞(1 − 𝑒−

𝑡

∈0)

2. A particle executing SHM in a straight line with amplitude A and time period T. What is the maximum average speed of the particle during a time interval T/6?

(A) 9𝐴

2𝑇 (B)

3√3𝐴

𝑇 (C)

3𝐴

𝑇 (D)

√3𝐴

2𝑇

3. A plane wave is incident on a lens of R.I. n=1.5 with one flat side (as shown in figure). The radius of the flat side is R. If all incoming rays are to be focused at the point P at a distance 3R from the flat side, calculate the thickness of the curved side of the middle of the lens. ( Do not assume the lens is thin)

(A) 2R (B) 2R (√6 − 2) (C) 2R (√10 − 3) (D) 2R (√3 + 1)

4. One end of a thread is connected at a point on a wall and other end is connected with a ring with is free to move over a vertical rod. In between the thread passes over another ring which is moved with a constant velocity 𝑣0. Then the speed of the other ring is n𝑣0. Find n.

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

5. Three capacitors having capacitance 4,12,6 micro farad and break down voltage of 10V, 6V and 8V respectively are connected in series. What will be the break down voltage of the combined system

(A) 12V (B) 20V (C) 22V (D) 4V

6. Point I (-6cm,-3cm) is the true image of a point source of light S (-18cm,9cm) in a spherical mirror whose optical axis is N1N2 as shown in figure.. Find the radius of curvature of the mirror (in cm.). (A) 6cm. (B) 8cm. (C) 9cm. (D) 10cm.




7. A light ray propagating along a =i+j−k

√3 is incident at Brewster’s angle at a boundary with normal direction given

by n =2i−j+2k

3. The electric field in the reflected light ray will be polarized along

(A) i+4j+3k

√26 (B)

i−4j−3k

√26 (C)

–i+4j−3k

√26 (D) none

8. Figure shows a small ball of mass m attached to one end of an inextensible thread

whose other end is connected to a fixed point O at a height2𝑙

3. Ball is brought to

horizontal level and released from rest. Length of the thread is l. Horizontal surface is smooth. The maximum height attained by the ball after striking the floor is (floor is smooth, and the collision is perfectly

inelastic)

(A) 32𝑙

243 (B)

23𝑙

43 (C)

64𝑙

243 (D)

32𝑙

27

9. A satellite is moving on a circular orbit around a planet. A sharp impulse is given

to the satellite such that it escapes from the gravitational field of the planet. The impulse can be given in two different ways as shown. The ratio of the impulse

given in the two different cases 𝑃1

𝑃2⁄ is

(A) 1 (B) 2 (C) √2 -1 (D) √2 +1 10. An equilateral prism ABC is placed in air with its base side BC lying horizontally along

X axis as shown in the figure. A ray given by 3 Z + X = 10 is incident at a point P on

face AB of the prism. The value of μ(of prism) for which the ray grazes the face AC is

(A) √2 (B) 2

√3 (C) √

3

2 (D) √3

11. An inextensible string connects two masses m and 4m and the system rests on a smooth horizontal floor. An impulse J is imparted to B as shown in figure. The tension in the string in the subsequent motion is (A) J2/mℓ (B) J2/5mℓ (C) 4J2/5mℓ (D) J2/20mℓ

12. A magnetic field, confined in a cylindrical region of radius R, is changing at the rate of 4 T/s.

A conducting rod PQ of length √3

2R and resistance r is placed in the region as shown. Ends

of the rod are joined to center C using straight wires PC & QC each of resistance r. The potential difference across the rod will be

(A) 𝑅2

9(𝜋 + 6)𝑉 (B)

𝑅2𝜋

18𝑉 C )

𝑅2𝜋

6𝑉 (D)

𝑅2

6(𝜋 + 6)𝑉




13. Three immiscible liquids are filled in a container as shown. The base area of the container is A and coefficient of cubical expansion of the material of the container is 3𝛾/2 while the coefficient of cubical expansion of the liquids are shown in the figure. The temperature of the system is increased by △T. The volume of the liquid flown out of the container is

(A) 𝐴𝐿𝛾△T

3 (B)

3𝐴𝐿𝛾△T

5 (C)

2𝐴𝐿𝛾△T

3 (D)

𝐴𝐿𝛾△T

2

14. Figure shows two concentric shells. The capacitance of the system when switch K is open is 𝐶1, capacitance on closing the switch is 𝐶2. The ratio 𝐶1/𝐶2 is (A) 1: 2 (B) 2: 1 (C) 1: 1 (D) none

15. A train is moving with constant acceleration along the x axis. A particle is projected inside the train in a vertical plane containing the motion of train as shown. Which of the following cannot be the trajectory of the particle be as observed from inside the train?

(A)

(B)

(C)

(D)

16. 8 identical spherical conducting droplets are charged to the same potential such that energy stored in the electric field of each is E0. When they are mixed to form a large drop, the new energy stored in electric field is: (A) 8 E0 (B) 16 E0 (C) 32 E0 (D) 64 E0

17. Two positive nuclei each having a charge q approach each other and electrons concentrate between the nuclei to create a bond. Assume that the electrons can be represented by a single point charge Q at the mid-point between the nuclei. Calculate the magnitude this charge must have to ensure that the potential energy is negative. (A) Q>2q (B) Q<q/2 (C) Q<q/4 (D) Q>q

18. For high principle quantum number (n) for hydrogen atom the spacing between the neighboring energy levels is

proportional to 1/𝑛𝑥. The value of x is: (A) 2 (B) 3 (C) 4 (D) 5

19. Find velocity of point C in the given figure. (A) 1m/s (B) 2m/s (C) 3m/s (D) 4m/s




20. An AM wave is represented by equation v = 5[1 + 0.6 cos(6280t)] sin(211 × 104t) V. If AM wave drives a

resistance of 2 kΩ, then (A) The carrier wave has a frequency 336 kHz with a bandwidth of 4 kHz. (B) The lower side band frequency is 335 kHz with modulation index of 0.3 (C) The power delivered to resistor by AM wave is approximately 7.5 mW (D) All are correct

21. The length of a rod is 5.88 cm (exact). It is measured by using a vernier calipers in which total length of 10 vernier space is equal to 8 main scale space. One division of a main scale is 1 mm. On putting the rod between the jaws of calipers, which line of vernier lies over any line of main scale. (A) 4th (B) 5th (C) 8th (D) 7th

22. In the given circuit, the Zener- diode has breakdown voltage Vz = 3 Volt and the maximum power limit Pmax = 18 mW. Choose the correct option.

(A) If VB= 12 Volt, the power dissipated in Zener diode will exceed the minimum power limit, specified for it.

(B) If VB = 12 volt, the power dissipated in Zener diode will not exceed the maximum power limit, specified for it.

(C) If VB = 15 volt, the power dissipated in zener diode will exceed the maximum power limit, specified for it.

(D) If VB = 20 volt, the power dissipated in zener diode will not exceed the maximum power limit, specified it.

23. Two physical pendulums perform small oscillations about the same horiiontal axis with angular frequencies ω1 and ω2. Their moments of inertia relative to the given axis are equal to I1 and I2respectively. In a state of stable equilibrium the pendulums were fastened rigidly together. What will be the angular frequency of small oscillations of the compound pendulum?

(A) √I1ω1+I2ω2

I1+I2 (B) √

I12ω1+I2

2ω2

I1+I2 (C) √

I1ω12+I2ω2

2

I1+I2 (D) ω1 + ω2

24. A rod of length 1 m and 10 cm2 cross – sectional area for a portion of its length and 5 cm2 for remaining length. It is pulled from both ends to develop stress in it. The strain energy in this stepped rod is 40% of that of the rod of 1 m length and uniform area of 10 cm2 when subjected to same maximum stress in stepped rod. Find the length of portion of 10 cm2 area in stepped bar. (A) 0.1 m (B) 0.2 m (C) 0.3 m (D) 0.4 m

25. a solid hemisphere of weight W rests with its curved surface in contact with a rough inclined plane. A weight P is placed at some point on the rim of the hemisphere (refer diagram) to keep its plane surface horizontal. Find the friction coefficient between the hemisphere and the inclined plane, if the hemisphere is just in equlibrium.

(A) P

√W(2P+W) (B)

W

√W(2P+W) (C)

P

√W(P+W) (D)

W

√W(P+W)




26. A graph of potential energy (U) and displacement (x) of a particle which is constrained to move along the x – axis (x >0) is shown in figure. The particle is in motion and its total energy is E0. The graph between kinetic energy and displacement of the particle is given by

(A)

(B)

(C)

(D)

27. If P represents radiation pressure, c represent speed of light and Q represent radiation energy striking a unit area per second, then non – zero integers x, y and z such that PxQycz is dimensionless, may be (A) x = 1, y = 1, z = 1 (B) x = 1, y = −1, z = 1 (C) x = −1, y = 1, z = 1 (D) x = 1, y = 1, z = −1

28. a bar magnet with its north pole up is placed along the axis of symmetry of a horizontal conducting ring carrying current I, as shown in the figure. At the location of the ring, the magnetic field makes an angle θ with the vertical. The mass of the ring is ‘m’ and gravity acts vertically downwards. The ring stays in equilibrium, then the current passing through the ring is?

(A) mg

2πrB sin θ (B)

mg

πrB sin θ (C)

2mg

πrB sin θ (D)

3mg

2πrB sin θ

29. A person of mass M is standing on a railroad car, which is rounding an unbanked turn of radius R at a speed v. His centre of mass is at a height L above the car midway between his feet, which are separated by a distance d. The man is standing in the direction of motion. Two statements are given below regarding the magnitude of normal reaction on foot A & B, and the maximum possible speed allowed for turning. (i): Magnitude of normal reaction on the foot A is less than the magnitude of normal reaction on the foot B.

(ii): Maximum speed possible such that the man does not fall over is √Rgd

2L

Find the correct option regarding which statement is correct. (A) only (i) is correct (B) only (ii) is correct (C) both statements are correct (D) none of these

30. Two Point coherent sources of power P0 and 4P0 emitting sound of frequency

150Hz are kept at point A and B respectively. Both sources are in same phase. A detector is kept at C as shown in figure. The distance of point A and B is r and 4r from detector respectively. The speed of sound in medium is 300 m/s. given P0 = 64 watt and r = 1m. The intensity observed by detector is

(A) 25 watt/m2 (B) 4 watt/m2 (C) 9 watt/m2 (D)0




Section – 3 MATHEMATICS

1. If the derivative of a everywhere continuous function f(x) w.r.t. x is xf

xsin2

1 2, then the period of f(x), if f(x) is a

periodic function, is

(A) (B) 2 (C) /2 (D) none of these.

2. The total number of terms in the expansion of (x + y)100 + (x – y)100 after simplification is (A) 50 (B) 51 (C) 202 (D) none of these

3. The equation of the circle having its centre on the line x + 2y –3 = 0 and passing through the point of intersection of the circles x2 + y2 –2x –4y + 1= 0 and x2 + y2 –4x –2y + 1 = 0 is

(A) x2 + y2 –6x + 1 = 0 (B) x2 + y2 –3x + 4 = 0 (C) x2 + y2 –4x – 2y + 1= 0 (D) x2 + y2 + 2x –4y + 4 = 0

4. Let g(x) be a continuous function for all x, and f(x) = f() + (x - ).g(x) x R. Then;

(A) f(x) is necessarily differentiable at x = (B)f(x) is not necessarily differentiable at x =

(C) f(x) is not necessarily continuos at x = (D)none of these

5. The value of x such that

1 0 2 1

1 1 0 2 1 1 0

2 1 0 1

x

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

6. Let f(x) = ln(2x – x2) + sin2

x , then which of the following is NOT true?

(A) Graph of y=f(x) is symmetrical about the line x = 1 (B) g(x) = f(x) – ln(2x – x2) is an odd function. (C) maximum value of y = f(x) is 1 (D) minimum value of y=f(x) does not exist . 7. The diagram shows the graph of y = ax2 + bx + c, then (A) a < 0, b > 0 (B) c < 0, a < 0

(C) b < 0, c > 0 (D) none of these

(x1, 0)

(x2, 0)

y

x

8. Let f be a oneone function with domain {2, 1, 0} and range {1, 2, 3} such that exactly one of the following

statements is true. f (2) = 1, f (1) 1, f (0) 2 and the remaining two are false. The distance between points

A(2, 1, 0) and B( f (2), f (1), f (0) ) is (A) 2 (B) 3 (C) 4 (D) 5




9. The area bounded by y =f(x), the lines x=1, x = b and the x-axis is (b-1) cos (3b + 4), b > 1, then f(x) is (A) (x-5) sin (3x+4) (B) (x-1) sin (x+1)+ (x+1) cos (x-1) (C) cos (3x+4) –3(x-1) sin (3x+4) (D) (x-5) cos (3x+4)

10. If banda

are two unit vectors and is the angle between them, then a unit vector along the angular

bisector of banda

will be given by

(A)

2cos2

ba

(B)

2cos2

ba

(C)

2sin2

ba

(D)

2sin2

a b

11. If in a triangle ABC, C = 1350, then value of tan A + tan B + tan A tan B equals (A) 0 (B) 1 (C) –1 (D) none of these

12. The number of digits in 530 is, (log102 = 0.3010) (A) 30 (B) 22 (C) 21 (D) none of these

13. If 1t and 2t be the parameters of extremities of a focal chord of the parabola 2 4y ax , a > 0, then the

equation 2

1 2 0t x ax t has

(A) imaginary roots, (B) both roots positive (C) one positive and one negative roots (D) both roots negative

14. Let 'E' and 'F' be two independent events. The probability that both 'E’ and 'F’ happen is 1/12 and the probability that neither 'E' nor 'F' happens is 1/2, then ,

(A) 1/ 3, 1/ 4 P E P F (B) 1/ 2, 1/ 6 P E P F

(C) 1/ 6, 1/ 2P E P F (D) 1/ 4, 1/ 3P E P F

15. The general solution of the equation 2

2

1 sin sin ..... 1 cos2

1 cos21 sin sin .....

x x x

xx x

if x =

(A) n

1 n3

(B)

n1 n

6

(C)

n 11 n

6

(D)

n 11 n n I

3

16. A rod of steel is fixed at (1, 0) and toy is fixed at (2, 1) on it. The rod is rotated through an angle 15 in clockwise direction, the new position of the toy will be

(A)

2

1,61 (B) 2,61 (C) 2,61 (D) none of these

17. If and are the roots at ax2 + bx + c = 0 then

x/12

xcbxax1lim is

(A) a ( – ) (B) ln|a( – )| (C) ea( – ) (D) ea| – |




18. If 6 3 1

4 3 1

20 3

i i

i

i

= x + iy, then

(A) x = 3, y = 1 (B) x = 1, y = 3 (C) x = 0, y = 3 (D) x = 0, y = 0

19. The mean and variance of n observations 1 2 3, , ,........, nx x x x are 5 and 0 respectively. If 2

1

400n

i

i

x

, then n is

(A) 16 (B) 20 (C) 25 (D) 36

20. The value of

4/

4/

2 )xsin1(xsec

dx is

(A) 4

(B) (C)

2

(D) 2

21. The equation 1 1 22cos x sin 2x 1 x is valid for all values of x satisfying

(A) –1 x 1 (B) 0 x 1 (C) 10 x

2 (D)

1x 1

2

22. If the equation 3x2 + xy – y2 – 3x + 6y + 2 = 0 represents hyperbola then equation of the asymptotes is given by (A) 3x2 + xy – y2 – 3x + 6y – 9 = 0 (B) 3x2 + xy – y2 – 3x + 6y – 7 = 0 (C) 3x2 + xy – y2 – 3x + 6y = 0 (D) none of these

23. If 2 ; 0

( )2 ; 0

x xf x

x x

; then f(f(x)) is given by

(A) 2 , 0

2 , 0

x x

x x

(B)

4 , 0

4 , 0

x x

x x

(C)

4 , 0

4 , 0

x x

x x

(D)

2 , 0

2 , 0

x x

x x

24. The minimum value of 6xcos32xsin2

1

is equal to

(A) - 110

(B) - 13

(C) 110

(D) 16

25. If 1 2 3z , z , z be the vertices of ABC such that AB

2AC

and A3

, then which of the following is always true.

(A) 2 1

3 1

z z1 i 3

z z

(B) 2 1

3 1

z z1 3 i

z z

(C) 2 1

3 1

z z2

z z

(D) None of these




26. The family whose x and y intercepts of a tangent at any point are respectively double of the x and y coordinates of that point is

(A) x2 + y2 = c (B) x2 – y2= c (C) xy = c (D) None of these

27. If Sn = nP + Q

2

1nn , where Sn denotes the sum of the first ‘n’ terms of an A.P. then the common difference is

(A) P + Q (B) 2P + 3Q (C) 2Q (D) Q

28.

n2

1r22n rn

r

n

1lim equals

(A) 5 1 (B) 5 1 (C) 2 1 (D) 2 1

29. A ellipse has OB as semiminor axis, F and F are its foci and FBF is a right angle then eccentricity of the ellipse is

(A) 2

1 (B)

2

1 (C)

3

2 (D)

3

1

30. 10 IIT and 2 NIT students sit at random in a row, and then number of ways in which exactly 3 IIT students sit

between 2 NIT students is

(A) 16 10! (B) 15 10! (C) 10 16! (D) none of these




Answer Key – JEE Main Mock Test Paper 4 – JEE 2018 a FIITJEE team initiative

CHEMISTRY

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

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

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

PHYSICS

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

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

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

MATHEMATICS

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

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

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


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