jee mains test paper - 6 · 2019-07-25 · jee mains test paper - 6 17. a 2 cm high object is...

JEE MAINS TEST PAPER - 6

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PHYSICS

1. A rocket of mass 1000 kg is exhaust gases at a rate of 4 kg/s with a velocity 3000 m/s. The thrust developed on the rocket is : (a) 12000 N (b) 120 N (c) 800 N (d) 200 N

2. Ampere-hour is the unit of : (a) quantity of charge (b) potential (c) energy (d) current

3. Water falls from a tap, down the streamline : (a) area decreases (b) area increases (c) velocity remains same (d) area remains same

5. Positively charged particles are projected into a magnetic field. If the direction of the magnetic field is along the direction of motion of the charge particles, the particles get :

6. (a) accelerated (b) decelerated (c) deflected (d) no changed in velocity

7. In Young’s double slit experiment a minima is observed when path difference between the interfering beam is:

(a) (b) 1.5 (c) 2 (d) 2.25

8. Calculate the energy released when three -particles combined to from a 12c

nucleus, the mass defect is : (atomic mass of 2He4 is )

(a) 0.007809 (b) 0.002603 (c) 4.002603 (d) 0.5

9. In a step-up transformer, if ratio of truns of primary and secondary is 1 : 10 and

primary voltage is 230 V. If the load current is 2A, then the current in primary is : (atomic mass of 2He4 is )

(a) 20 A (b) 10 A (c) 2 A (d) 1 A (b)

10. If the equation of transverse wave is , then the maximum particle velocity is :

4.002603

4.002603

2sin 2Y kx t


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(a) 4 unit (b) 2 unit (c) zero (d) 6 unit

11. Fusion reaction takes place at high temperature because :

(a) KE is high enough to overcome repulsion between nuclei (b) nuclei are most stable at this temperature (c) nuclei are unstable at this temperature (d) none of the above

12. An isotope decays to 1/16th of its mass in 1 h. what is the half-life period of the isotope?

(a) 15 min (b) 30 min (c) 12 min (d) 10 min

13. Converging rays are incident on a sphere of radius 10 cm (= 1.4). In the absence of sphere, the rays would have converged to 40 cm. Find the position of image

(a) 1.08 cm form P (b) 1.08 cm from O (c)1.8 cm from P (d) 1.18 cm from O

14. Two Nichol prisms are kept perpendicular, one of them is illuminated with a light intensity (natural) Io. Two more Nichol prisms are introduced in between symmetrically. Find the light intensity emitted from the last Nichol prism.

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

15. A student is studying a book placed at the edge of a circular table of radius R. A

point source of light is suspended directly above the centre of the table. What should be the height of the lamp so that maximum illuminance is produced at the position of the book?

(a) R (b) R/2 (c) (d)

16. The optical path of a monochromatic light is the same if it goes through 2 cm of glass or 2.25 cm of water. If the refractive index of water is 1.33, what is the refractive index of glass?

(a) 2.5 (b) 1.75 (c) 1.5 (d) 1.6

40 cm

O =1.4

P

o

27I

64o

27I

128o

9I

32o

9I

64

R/ 2 R/ 3


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17. A 2 cm high object is placed on the principal axis of a concave mirror at a distance of 12 cm from the pole. If the image is inverted, real and 5 cm high, find the focal length of mirror

(a) 7.6 cm (b) 9.6 cm (c) 8.6 cm (d) 12.6 cm

18. The refractive indices of flint glass for red and violet light are 1.613 and 1.632 respectively. Find the angular dispersion produced by a thin prism of flint glass having refracting angle 5o.

(a) 1o (b) 2o (c) 0.95o (d) 0.095o

19. A motor car is fitted with a convex driving mirror of focal length 20 cm. A second

motor car 2.1 m board and 1.05 m high is 4 m behind the first car. What is the size of the image of second car as seen in the mirror of the first?

(a) Breadth = 8 cm, height = 4 cm (b) Breadth = 10 cm, height = 5 cm (c) Breadth = 12 cm, height = 6 cm (d) Breadth = 14 cm, height = 7 cm

20. A giant telescope in an observatory has an objective of focal length 19 m and an eye piece of focal length 1 cm. In normal adjustment, the telescope is used to view the moon. What is the diameter of the image of moon formed by objective? The

diameter of moon is 3.5 106 m and radius of lunar orbit round the earth is 3.8

108 m

(a) 10 cm (b) 12.5 cm (c) 15 cm (d) 17.5 cm

21. In Young’s double slit experiment, the intensity of light at a point on the screen

where the path difference is is K units. What is the intensity of light at a point

where the path difference is /3; being the wavelength of light used?

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

22. The two slits in Young’s double slit experiment have widths in the ratio of 1 : 25.

The ratio of the intensities of maxima and minima in the interference pattern is

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

23. Suppose energy liberated in the recombination of a hole electron pair is converted

to EM radiation. If the maximum wavelength emitted is 660 nm, what is band gap?

(a) 2.875 eV (b) 3.875 eV (c) 4.875 eV (d) 1.875 eV

K

4

K

3

K

2

5

3

7

5

9

4

3

2


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24. A semiconductor is known to have an electron concentration of 5 1012 cm3 and

a hole concentration of 8 1013 cm3. What is the resistivity of sample if electron

mobility is 23000 cm2 v1 s1 and hole mobility is 100 cm2 v1 s1?

(a) 0.808 m (b) 0.708 m (c) 0.608 m (d) 0.508 m

25. The mean free path of conduction electron in copper is about 4 108 m. Find the electric field which can give an average, 2 eV energy to a conduction electron in a block of copper

(a) 5 107 V/m (b) 6 107 V/m (c) 7 107 V/m (d) 8 107 V/m

26. A common emitter circuit has an input resistance of 0.6 k and output resistance

of 51 k. If the current given is 65, find power gain

(a) 4.591 105 (b) 3.591 105 (c) 2.591 105 (d) 1.591 105

27. An input resistance of a silicon transistor is 665 . Its base current in changed by

15 A which results in the change in collector current by 2 mA. This transistor in

used as a common emitter amplifier with a load resistance of 5 k. What is the voltage gain of the amplifier

(a) 1000 (b) 2000 (c) 3000 (d) 4000

28. Simplify the Boolean expression

A.B + A.B.C + .B + A. .C (a) A . C + B (b) A+ C . B (c) (A + B) . C (d) AC

29. Simplify the expression:

(a) A. + .B (b) . + A.B (c) A + B (d) +

30. An AM transmitter records an antenna current of 10.5 A. The antenna current drops to 10 A when only carrier is transmitted. What is the percentage modulation ?

(a) 55.3% (b) 65.3% (c) 45.3% (d) 75.3%

31. An optical fibre has a numerical aperture of 0.2 and a cladding refractive index of 1.59. Determine the critical angle at core cladding interface

(a) 83.0o (b) 82.9o (c) 81.9o (d) 80.9o

A B

A.B . A.B

B A A B A B


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32. When modulation percentage is 75, an AM transmitter produces 10 kw. What would be % power saving if carrier and one of side bands were suppressed before transmission took place?

(a) 90.1% (b) 89.1% (c) 88.1% (d) 87.1%


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CHEMISTRY

1. For a first order reaction with rate constant ‘k’ and initial concentration ‘a’, the half-life period is given by :

(a) ln 2

k (b) 1

ka (c)

2

3

2ka (d) none of the above

2. Aldol condensation will not take place in :

(a) HCHO (b) CH3CH2CHO (c) CH3CHO (d) CH3COCH3

3. Which of the following is called Berthelot’s salt?

(a) (NaPO3)6 (b) NaOCl (c) KClO3 (d) KHF2

4. Which of the following is a Boyle plot at very low pressure ?

(a) (b)

PV

p

PV

p (c) (d)

PV

p

PV

p 5. Calgon used as water softener is :

(a) Na2[Na4(PO3)6] (b) Na4[Na2(PO3)6] (c) Na2[Na4(PO4)5] (d) none of these

6. How many asymmetric carbon atoms are presnet in : (i) 1,2-dimethylcyclohexene (ii) 3-methylcyclopentene and (iii) 3-dimethyl-5-cyclohexene (a) two, one, one (b) one, one, one (c) two, none, two (d) two, none, one

7. For which order half-life period is independent of initial concentration?

(a) zero (b) first (c) second (d) third


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8. In the reaction CH3CN + 2H HCl

SnCl2 X Boiling H2O

SnCl2 Y

The term Y is (a) acetone (b) ethanamine (c) acetaldehyde (d) dimethyl amine

9. The spices that undergoes disproportionation in an alkaline medium is :

(a) 24MnO (b) 4ClO (c) NO2 (d) all of these

10. On shaking H2O2 with acidified potassium dichromate and ether, etheral layer

becomes:

(a) green (b) red (c) blue (d) brown 11.

alc. KOH Pr oduct

H

Cl

H

H

H

CH3 The product is an alkene which is mainly. (a) (b)

CH3 CH3

H

(c) (d) No elimination reaction is possible

CH3

H

12. Which of the following reactions are regioselective.

(a) Dehydration of alcohols by conc. H2SO4 at 443 k (b) Dehydrohalogenation of alkyl halides by using alcoholic KOH. (c) Addition of unsymmetrical addendum molecules like HX to alkenes (d) Addition of H2O in the presence of acids to alkenes.


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13. Reduction of But-2-yne with Na and liquid NH3 gives an alkene which upon catalytic hydrogenation with D2/Pt gives an alkane. The alkene and alkane formed respectively are:

(a) cis-but-2-ene and racemic-2, 3-dideuterobutane (b) trans-but-2-ene and meso-2-, 3-dideuterobutane (c) trans-but-2-ene and racemic-2, 3-dideuterobutane (d) cis-but-2-ene and meso-2, 3-dideuterobutane

14. Which of the following has maximum Baeyer’s angle of strain and is most reactive.

(a) cyclopropane (b) Cyclobutane (c) cyclopentane (d) Cyclohexane

15. The number of geometrical isomers possible in the compound CH3 – CH = CH – CH = CH – CH3 is

(a) 4 (b) 4 (c) 2 (d) 5

16. Which of the following cyanocyclohexanes conformatons will have high keq value. (a) (b)

H

CN

CN

H

CN

H

H

CN

(c) Both of these have same Keq values (d) none of these

17. Which of the following would be optically active. (a) CH2 = C = CH2 (b)

F F

(c) CH3 – CH = C = CH – CH3 (d)

H

Me

OH

H OH

Me

18. Sorrel’s cement is a mixture of

(a) CaO and MgO (b) MgO and MgCl2 (c) CaO and CaCl2 (d) MgCl2 and CaCl2

19. Identify the correct statement


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(a) Gypsum contains a lower percentage of calcium than plaster of pairs. (b) Gypsum is obtained by heating plaster of pairs (c) Plaster of pairs can be obtained by hydration of gypsum (d) Plaster of paris is obtained by partial oxidation of gypsum

20. The decreasing order of acidic strength

2 3 2IIII II

CH CH COOH CH CH COOH CH C COOH

(a) I II III (b) II I III (c) III I II (d) I III II

21. Which of the process is used in the extractive metallurgy of Mg

(a) Fused salt electrolysis (b)Self reduction (c) Aqueous solution electrolysis (d) Thermite reduction

22. The process of zone refining is used for (a) Silicon (b) Germanium (c) Gallium (d) All the above

23. The oxidation state of iron in pyrites, FeS2 is :

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

24. Californium undergoes spontaneous fission as follows : 252 142 106 1

98 56 42 0Cf Ba Mo 4 n

The binding energies per nucleon are 7.50, 8.25 and 8.50 MeV respectively. The energy released in the process is : (a) 180 MeV (b) 215 MeV (c) 235 MeV (d) 240 MeV

25. The number of geometrical isomers of [Rh(Py)3 Cl3] are :

(a) 2 (b) 3 (c) 4 (d) 5x

26. Which of the following has the greatest affinity for water

(a) P4O10 (b) Cl2O7 (c) Cl2O5 (d) All have same

27. Metals which are not extracted by smelting process

(a) Pb (b) Fe (c) Zn (d) Mg

28. Wolframite ore is separated from tinstone ore by the process of


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(a) Roasting (b) Electromagnetic (c) Smetting (d) Calcination

29. Compounds (A) and (B) are treated with dil. HCl separately. The gases liberated are Y and Z respectively. Y turns acidified K2Cr2O7 paper green while Z turns lead acetate paper black. The compounds (A) and (B) are respectively :

(a) Na2S and Na2SO3 (b) Na2SO3 and Na2S (c) NaCl and Na2CO3 (d) Na2SO3 and Na2SO4

30. HNO2 acts as

(a) Oxidising agent (b) Reducing agent (c) Both (a) and (b) (d) Its solution is stable


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MATHEMATICS

1. For a first order reaction with rate constant ‘k’ and initial concentration ‘a’, the half-life period is given by :

(a) log 28

e

(b) 2log4

e (c) log 2

4e

(d) 1log

8 2e

2. The modulus and amplitude of 2

1 2

1 (1 )

i

i

are

(a) 2 and 6

(b) 1 and 0 (c) 1 and 3

(d) 1 and 4

3. 30

tan sinlimx

x x

x

is equal to

(a) 1

2 (b) 1

2 (c) 0 (d) 1

4. If 2

sin5, 0

2( )

1, 0

2

xx

x xf x

k x

is continuous at x = 0, then the value of k is :

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

5

5. The area bounded by the parabola y2 = 4ax and the line x = a and x = 4a is

(a) 235

3

a (b)

24

3

a (c)

27

3

a (d)

256

3

a

6. A population p(t) of 1000 bacteria introduced into nutrient medium grows according

to the relation 2

1000tp(t) =1000 +

100 + t. The maximum size of this bacterial population is:

(a) 1100 (b) 1250 (c) 1050 (d) 5250

7. The differential equation representing a family of circles touching the y-axis at the origin is :

(a) 2 2 2 0dy

x y xydx

(b) 2 2 2 0dy

x y xydx

(c) 2 2 2 0dy

x y xydx

(d) 2 2 2 0dy

x y xydx


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8. The general solution of the differential equation (2x – y + 1) dx + (2y – x + 1) dy = 0 is :

(a) x2 + y2 + xy – x + y = c (b) x2 + y2 – xy + x + y = c (c) x2 – y2 + 2xy – x + y = c (d) x2 – y2 – 2xy + x – y = c

9. If 2 2

1

2 2

1 1tan

1 1

x xy

x x

, then dy

dxis equal to

(a) 2

41

x

x (b)

2

41

x

x (c)

41

x

x (d)

41

x

x

10. If x = sin t, y = cos pt, then

(a) (1 – x2) y2 + xy1 + p2y = 0 (b) (1 – x2) y2 + xy1 – p2y = 0 (c) (1 + x2) y2 – xy1 + p2y = 0 (d) (1 – x2) y2 – xy1 + p2y = 0

11. If ST and SN are the lengths of the subtangent and the subnormal at the point

2

on the curve x = a(θ + sinθ) , y = a(1 - cosθ) , 1a then :

(a) ST = SN (b) ST = 2SN (c) ST2 = a SN3 (d) ST3 = a SN

12. If is the acute angle of intersection at a real point of intersection of the circle x2

+ y2 = 5 and the parabola y2 = 4x, then = tan is equal to :

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

3

13. Universal set,

5 4 3 2

2

2

6 11 6 0

5 6 0

3 2 0

U x x x x x

A x x x

B x x x

what is 'A B equal to?

(a) {1, 3} (b) {1, 2, 3} (c) {0, 1, 3} (d) {0, 1, , 2, 3}

14. Which of the following statements is not correct for the relations R defined by aRb, if and only, if b lives within on kilometre from a “ (a) R is reflexive (b) R is symmetric (c) R is not anti-symmetric (d) None of the above


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15. What is the value of

2 2

2 2 2 2

11 11

2 2

10 01 01 10

2 2 2 2

1001 101

1001 1001 101 101

?

(a) (1001)2 (b) (101)2 (c) (110)2 (d) (100)2

16. If a + b + c = 0, the line 3ax + by + 2c = 0 passes through the fixed point

(a) 1

,13

(b) 2

2,3

(c) 2

,23

(d) 1

1,3

17. The incentre of the triangle with vertices (1, 3), (0,0) and (2,0) is

(a) 1

1,3

(b) 1

,13

(c) (1, 0) (d) 1

, 23

18. The vertices of a triangle are (0, 3), (–3, 0) and (3, 0). The co-ordinates of the

orthocentre are

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

19. If x

y2

and 3y + x = 0 are the equations of a pair of conjugate diameters of the

ellipse 2 2

2 2

x y1

a b , then its eccentricity is

(a) 2

3 (b)

1

6 (c)

1

5 (d)

5

6

20. A point P on the ellipse 2 2x y

116 9

has the eccentric angle 8

. the sum of the

distance of P from the two foci is (a) 4 (b) 8 (c) 9 (d) 16

21. Let f(x) be a differentiable function and f(1) = 3. If f (x)

3x 2

2 dtlim 6

x 2

, then the value of

f(2) is (a) 4 (b) 3 (c) 1 (d) 2

22. If y = 0

sinx dx

, then the value of dy

dx at x =

2

is


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(a) 2 (b) 3 (c) 1 (d) ½ 23. Let f(x) be a continuous function such that the area bounded by the curve y = f(x),

the x-axis and the two ordinates x = 0 and x = a is 2a 3a

sina cosa4 2 4

. Then f() is

(a) 2

(b)

2

(c) (d) –

24. If f(x) and g(x) be continuous function over the closed interval [0, a] such that f(x)

= f(–x) and g(x) + g(b – x) = 2. Then b

0f(x) g(x) dx is equal to

(a) b

0

bf(x) dx

2 (b)

b

0f(x) dx (c) 0 (d)

b

02 f(x) dx

b

0

bf(x) dx

2

25. a

2

ealog (x 1 x )dx

is equal to

(a) logea (b) e

3log a

2 (c) 0 (d) 2logea

26. The number of solutions of 2 2sin cos16 16 10, 0 2 is

(a) 4 (b) 1 (c) 8 (d) 2

27. The most general solutions of the equation sec - 1 = ( 2 1)tan are given by

(a) n4

(b) nn ( 1) .

4

(c) 2n, 2n +

4

(d) 2n

4

28. If 1

6 sinx, cos x and tan x are in GP, then the general value of x is

(a) 2n (b) 2n 2

(c) 2n

3

(d) 2n

6

29. The number of solutions of the equation tan + sec = 2cos lying in the interval

[0,2] is (a) 0 (b) 3 (c) 1 (d) 2

30. The most general values of x satisfying the equation (1 + 2 sinx)2 + ( 23 tanx 1) =

0 are given by


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(a) 7

2n6

(b)

7n

6

(c)

52n

6

(d)

5n

6

jee mains test paper - 6 · 2019-07-25 · jee mains test paper - 6 17. a 2 cm high object is...

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