jee mains test paper - 10 · 2019-07-25 · 8. a particle of mass 10 gram is executing simple...

JEE MAINS TEST PAPER - 10

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PHYSICS 1. Magnetic field produced by electrons in atoms and molecules is due to their

(a) spin motion only (b) orbital motion only

(c) spin and orbital motion both (d) neither spin nor orbital motion

2. The time period of a vibration magnetometer is . Its magnet is replaced by

another magnet whose moment of inertia is 3 times and magnetic moment is (1/3) of the initial magnet. The time period now will be :

(a) (b) (c) (d)

3. In an inductor of self-inductance L = 2 mH, current changes with time according to

relation . At what time e.m.f. is zero?

(a) 4 s (b) 3 s (c) 2 s (d) 1 s

4. The alternating current through an inductor is given by . Then the

magnetic field energy in the inductor changes from a minimum to a maximum value in a time equal to

(a) (b) (c) (d)

5. One milliwatt of light of wavelength 4560Å is incident on a caesium surface of work function 1.9 eV. Given that quantum efficiency of photoelectric emission is

0.5%, Planck constant J-sec, velocity of light m/s, the photoelectric current liberated is

(a) 1.84 × 10–6 amp (b) amp (c) amp (d) amp

6. Let v1 be the frequency of series limit of Lyman series, v2 the frequency of the first line of Lyman series and v3 the frequency of series limit of Balmer series. Then which of the following is correct?

(a) (b) (c) (d)

0T

03T 3/0T 0T 3/0T

tetI 2

ntII 2sin0

)/1( n )2/1( n )4/1( n )8/1( n

341062.6 h 8103C

71084.1 51084.1 41084.1

321 vvv 312 vvv )(2

1213 vvv 321 vvv


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7. The qualities best suited for a cooking utensil are

(a) high specific heat and low thermal conductivity.

(b) low specific heat and low thermal conductivity.

(c) high specific heat and high thermal conductivity.

(d) low specific heat and high thermal conductivity.

8. A particle of mass 10 gram is executing simple harmonic motion with an amplitude

of 0.5m and angular frequency of 10 rad/s. The maximum value of the force acting on the particle is

(a) 25 N (b) 2.5 N (c) 5 N (d) 0.5 N

9. Force between two co-axial identical bar magnets whose centres are r metre apart is 4.8 N. If separation is increased to 2r, the force between them is reduced to

(a) 2.4 N (b) 0.6 N (c) 1.2 N (d) 0.3 N

10. The current gain of a transistor is 0.95. In a common emitter arrangement change in collector current corresponding to a change of 0.4 mA in the base current will be

(a) 0.38 mA (b) 2.375 mA (c) 0.42 mA (d) 7.6 mA

11. The half-life period of a sample of radioactive substance is T. If we take a sample of 20 g, the amount of substance remain undecayed after time T/2 will be

(a) 16 g (b) 14 g (c) 12 g (d) 10.5 g

12. A flask containing air at 27°C is corked up at atmospheric pressure. The cork can be forced out by a pressure of 2.5 atmosphere. Then to force out the cork, flask should be heated to the temperature of

(a) 150 K (b) 300 K (c) 600 K (d) 750 K

)4.12(


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13. A copper wire and a steel wire of same diameter and length are connected end to end and a force is applied which stretches their combined length by 1 cm. The two wires will have

(a) same stress and strain (b) different stress and strain

(c) different stress and same strain (d) same stress and different strain

14. A force of 5 N acts on a body of 5 kg for 1 second and gives it a momentum p and kinetic energy E. If the same force accelerates the same body through 1 m, the

momentum and energy attained by the body are p and E respectively, then the correct relation is

(a) p > p, E > E (b) p < p, E < E (c) p > p, E < E (d) p < p, E > E

15. Two bodies are dropped from the windows of running trains on parallel tracks simultaneously. One of the trains is moving at constant velocity and the other is accelerating with initial velocity equal to that of former. Then (neglect air resistance)

(a) the body from accelerating train reaches ground first

(b) the body from uniformly moving train reaches ground first.

(c) both bodies reach ground simultaneously

(d) no conclusion can be drawn from the given data

16. The dimensionless physical quantity is

(a) universal gravitational constant (b) planck constant

(c) relative velocity (d) relative density

17. A nucleus of mass number A originally at rest, emits an alpha particle with speed v, the recoil speed of the daughter nucleus is

(a) (b) (c) (d)

18. A well cut diamond appears bright because

4

4

A

v

4

4

A

v

4A

v

4A

v


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(a) it is radioactive (b) it emits light

(c) it has high density (d)of total internal reflection

19. A cylindrical tube open at both ends has a fundamental frequency f in air. The tube is dipped vertically in water so that half of its length is in water. The fundamental frequency of the air column is now

(a) (b) (c) f (d)

20. A series LCR circuit is tuned to resonance. The impedance of the circuit at resonance is

(a) (b)

(c) (d) R

21. A sphere, a cube and a thin circular plate, all made of same material and having the same mass are initially heated to the same temperature of 200°C, the body which will cool fastest when left in air at room temperature is a

(a) sphere (b) cube (c) circular plate (d) all at the same rate

22. Roads are banked on turns so that

(a) the weight of the vehicle may be decreased

(b) the frictional force between the road and vehicle may be decreased

(c) the wear and tear of tyres may be avoided

(d) to provide necessary centripetal force

23. The rms speed of the particles of fume of mass 5 × 10–17 kg executing Brownian

motion in air at N.T.P. is (Boltzmann constant, k = 1.4 × 10–23 J/K )

(a) 1.5 m/s (b) 3.0 m/s (c) 1.5 cm/s (d) 3 cm/s

2

f

4

3 ff2

2/12

2 1

CLR

2/12

22 1)(

CLR

2/12

2 1

L

CR


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24. Surface area of a soap bubble is 1.3 × 10–4 m2. The work done to double the surface area will be (Surface tension for soap solution, T = 3 × 10–3 N/m)

(a) 23 J (b) 7.8 × 10–7 J (c) 2.6 × 10–4 J (d) 3.9 × 10–7 J

24. A particle moving in one dimension with a constant acceleration of 2 m/s2 is observed to cover a distance of 5 m during a particular interval of one second. The distance covered by particle in the next one second interval is (in metres)

(a) 12 (b) 6 (c) 7 (d) 10

26. At large distance from an electric dipole, the electric field strength varies with the distance r as

(a) (b) (c) (d)

27. An object is placed at a distance of 30 cm from a concave mirror and its real image is formed at a distance of 30 cm from the mirror. The focal length of the mirror is

(a) 15 cm (b) 45 cm (c) 30 cm (d) 20 cm

28. A plane electromagnetic wave travels in vacuum along direction, where

are unit vectors along the x, y and z axis respectively. The direction

along which the electric field and the magnetic field vectors point may be respectively

(a) and (b) and (c) and (d) and

29. A source of sound produces waves of wavelength 60 cm when it is stationary. If the speed of sound in air is 320 m/s and the source moves with speed 20 m/s, the wavelength of sound in the direction of motion will be nearly

(a) 56 cm (b) 60 cm (c) 64 cm (d) 68 cm

30. A motor cyclist moving with a velocity of 72 km/h on a flat road takes a turn where the radius of curvature is 20 m. In order to avoid skidding, he must not bend with

respect to the vertical plane by an angle greater than (g = 10 m/s2)

6

1

r 2

1

r 3

1

r 4

1

r

k

kji ˆandˆ,ˆ

k j i j k i i j


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(a) (b) (c) (d)

)6(tan 1 )2(tan 1 )92.25(tan 1 )4(tan 1


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CHEMISTRY

1. Which of the following elements has the smallest atomic size?

(a) Cs (b) F (c) Na (d) Cl

2. Which disproportionates on heating?

(a) H3PO4 (b) H3PO3 (c) Both (a) and (b) (d) None

3. Tungsten carbide is which kind of compound?

(a) Covalent (b) Ionic (c) Interstitial (d) Metallic

4. Chocolate brown precipitate formed during the detection of the ion using

Nessler’s reagent is of:

(a) (b)

(c) (d) Iodine

5. A silver salt of a monobasic acid on ignition gave 60% of Ag. The molecular weight of the acid is

(a) 37 (b) 33 (c) 73 (d) 77

6. Pyrolusite is a/an:

(a) oxide ore (b) sulphide ore (c) carbide ore (d) not an ore

7. Chloroform is slowly oxidised by air in the presence of light to form:

(a) formyl chloride (b) phosgene

(c) trichloroacetic acid (d) formic acid

8. 1,3-Butadiene + Acrolein

The product for the reaction is:

4NH

IHgHgNH2 INHHg 4

HgIOHgNH2

oductPr


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(a) (b) (c) (d)

9. Monomer of Nylon–6 is :

(a) Adipic acid (b) Hexamethylenediaminec

(c) Caprolactam (d) All of these

10. Tautomerism is not exhibited by

(a) C6H5CH=CHOH (b) (c) (d)

11. The product of the reaction is CH3CH2OH + Cu

(a) C2H6 (b) CH3COCH3 (c) CH3CHO (d) CH3COOH

12. The number of optical isomers observed in 2,3 dichlorobutane is:

(a) 0 (b) 2 (c) 3 (d) 4

13. Electrolysis of a concentrated aqueous solution of NaCl between two Pt electrodes, gives at cathode and anode, respectively.

(a) Na and Cl2(g) (b) H2(g) and Cl2(g) (c) H2(g) and O2(g) (d) O2(g) and H2(g)

14. Which of the following will have the highest coagulating power for As2S3 colloid?

(a) (b) (c) (d)

15. Hinsberg’s reagent is

(a) phenyl isocyanide (b)benzenesulphonyl chloride

(c) p-toluenesulphonic acid (d) o-dichlorobenzene

CHO CHO CHO CHO

O O

O

O

O

O

C300

3

4PO3Al 2

4SONa


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16. For the reaction PCl5(g) PCl3(g) + Cl2(g), the forward reaction at constant temperature is favoured by

(a) Introducing an inert gas at constant volume

(b) Introducing Cl2 gas at constant volume

(c) Introducing an inert gas at constant pressure

(d) Decreasing the volume of the container

17. The coordination number of a metal crystallising in a hcp structure is

(a) 12 (b) 10 (c) 8 (d) 6

18. Cyanohydrin of a compound on hydrolysis gives lactic acid (CH3CHOHCOOH). The compound is

(a) Formaldehyde (b) Acetaldehyde (c) Ethyl cyanide (d) Ethyl alcohol

19. Mutation in DNA occurs due to change in the sequence of

(a) nitrogenous base (b)ribose unit (c) phosphate unit (d) none of the above

20. Which of the following pair will diffuse at the same rate in the porous plug under same condition of temperature?

(a) CO, N2 (b) NO2, CO2 (c) NH3, PH3 (d) NO2, C2H6

21. Which ion has the maximum magnetic moment?

(a) Mn3+ (b) Cu2+ (c) Fe3+ (d) V3+

22. When SO2 is passed in an acidified K2Cr2O7 solution, the oxidation state of S is changed from

(a) +4 to +6 (b) + 4 to +2 (c) + 4 to 0 (d) + 6 to +4

23. Zinc reacts with very dilute nitric acid to produce

(a) NO (b) NH4NO3 (c) NO2 (d) N2O


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24. A is

(a) (b)

(c) (d)

25. Compound that is both paramagnetic and coloured is

(a) (b) (c) (d)

25. With rise in temperature, viscosity; of a liquid

(a) increases (b) decreases

(c) remains constant (d)may increase or decrease

26. Resonance structures can be written for

(a) O3 (b) NH3 (c) CH4 (d) H2O

28. The difference between heats of reaction at constant pressure and constant

volume of the following reaction would be 2C6H6(l) + 15O2(g) 12CO2(g) +

6H2O(l) at 25°C in kJ mol1 is

(a) 7.43 (b) +3.72 (c) 3.72 (d) +7.43

29. The passage of current liberates H2 at cathode and Cl2 at anode. The solution is

(a) copper chloride in water (b) NaCl in water

(c) ferric chloride in water (d) AuCl3 in water

30. Which is the correct order of acidic strength of the following acids?

(a) CH3CH2COOH > CH2=CHCOOH > CHCCOOH

(b) CH3CH2COOH < CH2=CHCOOH < CHCCOOH

(c) CH3CH2COOH < CH2=CHCOOH > CHCCOOH

(d) CH3CH2COOH > CH2=CHCOOH < CHCCOOH

.AproductCHOCHCHaldol

,NaOH

23

CHOCHCHCHCHCH 223

CH3CH2CH=C–CHO

CH3

CH3CH2CH–CH2CH2CHO

OH

CH3CH2CH–CH–CHO

OH

CH3

722 OCrK 624 TiCl)NH( 4VOSO ])CN(Cu[K 43


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MATHEMATICS 1. Two finite sets have m and n elements. The total number of subsets of the first set

is 56 more than the total number of subsets of the second set. The values of m and n are

(a) 7, 6 (b) 6, 3 (c) 5, 1 (d) 8, 7

2. If , then

(a) , where n is any positive integer

(b) , where n is any positive integer

(c) , where n is any positive integer

(d) , where n is any positive integer

3. If and , then is equal to

(a) – 2 (b) – 1 (c) 2 (d) 1

4. If and are different complex numbers with , then is equal to

(a) 0 (b) 1/2 (c) 1 (d) 2

5. If a, b, c are in A.P., then the straight line will always pass through

the point

(a) (–1, –2) (b) (1, –2) (c) (–1, 2) (d) (1, 2)

6. If (where Sk is the sum of first k terms of an A.P., ), then the

value of in terms of m and n will be

11

1

x

i

i

nx 4

nx 2

14 nx

12 nx

iyxz iqpz 3/1 )/( 22 qpq

y

p

x

1||

1

0 cbyax

2

2

m

n

S

S

m

n ,....,, 321 aaa

1

1

n

m

a

a


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(a) (b) (c) (d)

7. If , then the values of x are

(a) – 2, 2, –4 (b) – 2, 2, 4 (c) 3, 2, –2 (d) 4, 4, 3

8. The solution of the equation is given by

(a) (b) (c) (d)

9. The value of a for which the quadratic equation

possesses roots with opposite sign, lies in

(a) (b) (c) (1, 2) (d)

10. The number of ways in which five identical balls can be distributed among ten different boxes such that no box contains more than one ball, is

(a) 10 ! (b) (c) (d) none of these

11. Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then men select the chairs from amongst the remaining. The number of possible arrangements is

(a) (b) (c) (d) none of these

12. If in the expansion of and in the expansion of are equal,

then n =

(a) 3 (b) 4 (c) 5 (d) 6

2

2

)12(

)12(

n

m2

2

)12(

)12(

m

n2

2

)12(

)12(

n

m2

2

)12(

)12(

m

n

2|6| 2 xxx

0932 2 xx

32

3 x

2

33 x 33 x 2

2

3 x

0)23()1(23 222 aaxax

)1,( )0,(

2,

2

3

!5

!102)!5(

!10

2

4

3

6 CC 3

4

3

4 CC 3

4

2

4 PP

3

2

T

T nba )( 4

3

T

T3)( nba


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13. If n is a positive integer and , then the value of =

(a) (b) (c) (d) none of these

14. If , then x =

(a) (b)

(c) (d) none of these

15. If , are the roots of the equation , then =

(a)

(b)

(c)

(d) none of these

16. If , then

(a) for all (b) A is an odd Function of

(c) A = 0 for = + + (d) A is independent of

k

n

k CC

2

11

3

k

kn

k C

Ck

12

)2)(1( nnn

12

)1( 2nn

12

)1()2( 2 nnn

....32

32 xxxy

....32

32 yyy ....

!3!2

32 yyy

....!3!2

132 yy

y

02 qpxx )1(log 2qxpxe

...32

)( 333

222

xxx

...3

)(

2

)()( 3

32

2

xxx

...32

)( 333

222

xxx

1)cos()sin(

1)cos()sin(

1)cos()sin(

A

0A


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17. The number of distinct real roots of in the internal

is

(a) 0 (b) 2 (c) 1 (d) 3

18. Matrix A is such that , where I is the identity matrix. Then for

=

(a) (b) (c) (d)

19. The value of k, for which is an identity, is

(a) – 1 (b) – 2 (c) 1 (d) 0

20. If , , then the smallest positive value of B is

(a) (b) (c) (d)

21. The solution of the equation is

(a) (b) (c) (d) None of these

22. Let , then which of the following is true

(a) is periodic with period

(b) is periodic with period

(c) is periodic with period

(d) is not a periodic function

0

sincoscos

cossincos

coscossin

xxx

xxx

xxx

44

x

IAA 22 nAn ,2

InnA )1( InA InAn )1(2 1 IAn 12

01cossin)sin(cos 2 xxkxx

1)tan( BA3

2)sec( BA

24

25

24

19

24

13

24

11

)0(,2sinsin4cos2cos2 xxxxx

2

1cot 1 2tan 1

2

1tan 1

xxf cos)(

)(xf 2

)(xf

)(xf 24

)(xf


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23. In a triangle ABC, and and D divides BC internally in the ratio 1 :

3. Then is equal to

(a) (b) (c) (d)

24. If , then the smallest interval in which lies is given

by

(a) (b) (c) (d)

25. If , then the value of is

equal to

(a) 0 (b) 3 (c) – 3 (d) 9

26. Three vertices of parallelogram taken in order, are (1, 3), (2, 0) and (5, 1). Then its fourth vertex is

(a) (3, 3) (b) (4, 4) (c) (4, 0) (d) (0, –4)

27. The line joining two points and is rotated about A in anti-clockwise

direction through an angle of 15°. The equation of the line in the new position, is

(a) (b)

(c) (d)

28. In the equation if m and x1 are fixed and different lines are drawn

for different values of y1, then

(a) the lines will pass through a single point

(b) there will be a set of parallel lines

3

B

4

C

CAD

BAD

sin

sin

3

1

3

1

6

1

3

2

0,tancossin 111 xxxx

4

3

4

0 0

4

24

2

3sinsinsin 111

zyx 101101101

100100100 9

zyxzyx

)0,2(A )1,3(B

0323 yx 023 yx

0323 yx 023 yx

)( 11 xxmyy


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(c) there will be one line only

(d) none of these

29. The intercept of a line between the coordinate axes is divided by point (– 5, 4) in the ratio 1 : 2. The equation of the line will be

(a) (b) (c) (d) None of these

30. The equation represents a

(a) circle (b) pair of straight lines

(c) parabola (d) ellipse

06085 yx 06058 yx 03052 yx

4)2()2( 2222 yxyx

jee mains test paper - 10 · 2019-07-25 · 8. a particle of mass 10 gram is executing simple...

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