# JEE Main Sample Paper

**Questions:**

**PHYSICS:-**

**1. The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant t of this circuit lies between:**

a. 150s – 200s

b. 0s – 50s

c. 50s -100s

d. 150s – 200s

**2. In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the center. The graph that would correspond to the above will be**

**3. If x, v and a denote the displacement, velocity and the acceleration of a particle executing simple harmonic motion of a tie period t, then which of the following does not change with time?**

a. at + 2πv

b. at / v

c. at / x

d. (a^2 + t^2) + ( 4π^2 × v^2)

**4. In a optics experiment, with the position of the object fixed, a student varies the position of convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 45 degree with the x-axis meets the experimental curve at p. The coordinates of P will be**

a. ( f/2 , f/2)

b. 1.0 × 10^(-4)

c. Cp – Cv – 28R

d. ω

**5. A electromagnetic wave in vacuum has electric and magnetic field E and B, which are always perpendicular to each other. The direction of polarization is given by X and that of wave propagation by k. Then**

a. X || B AND k || B × E

b. X || E AND k || E × B

c. X || B AND k || E × B

d. X || E AND k || B × E

**6. If a simple pendulum has a significant amplitude ( up to a factor of 1/e of original) only in the period between T=0 sec to T= t sec, t may the average life of pendulum. When the spherical bob of pendulum suffers a retardation proportional to its velocity, with b as the constant of proportionality, the average life time of pendulum is**

a. 0.693 / b

b. B

c. 1 / b

d. 2 / b

**7. Hydrogen atom is excited from its ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be:**

a. 2

b. 3

c. 5

d. 6

**8. A thin uniform rod of length l and mass m is swinging freely about an horizontal axis passing through the end. Its angular speed is w. Its center of mass rise to a maximum height of:**

a. 1/6×( l^2 × w^2)/g

b. 1/6×(l^2 × w)/g

c. ½(l^2 × w^2)/g

d. 20%

**9. A coil is suspended in a uniform magnetic field, with the plane of coil parallel to magnetic lines of force. When a current is passed through the coil, it starts oscillating and it is very difficult to stop it. But if an aluminium plate is places near the coil so that it can be stopped. This is due to**

a. Development of air current when the plate is placed

b. Induction of electrical charge on plate

c. Shielding of magnetic fields as aluminium is a paramagnetic material

d. Electromagnetic in the aluminum plate gives rise to electromagnetic damping

**10. The mass of a spaceship is 1000kg. It is to be launched from the earth’s surface in to free space . the value of g and r( of earth) are 10m/s^2 and 6400km respectively. The required energy for this work will be**

a. 6.4 × 10^11 J

b. 6.4 × 10^8 J

c. 6.4 × 10^9 J

d. 6.4 × 10^10 J

11. Helium gas goes through a cycle ABCD as shown in figure. Efficiency of this cycle is nearly:

a. 15.4 %

b. 9.1 %

c. 10.5 %

d. 12.5 %

**12. Two electric bulbs marked 25W-220V and 100W-220V are connected in series to a 440V supply. Which of the bulbs will fuse?**

** **

a. 100W

b. 25W

c. Both of them

d.Neither of them

**13. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the currents and the voltage difference are 3% each, then error in the value of the resistance of the wire is**

a. 6%

b. 0%

c. 1%

d. 3%

**14. The transition from the state n=4 to n=3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:**

** **

a. r / 9

b. 5→4

c. 4→3

d. 45°

**15. A boy can throw a stone u to a maximum height of 10m.The maximum horizontal distance that the boy can throw the same stone up to will be:**

** **

a. 20√2 m

b. 10 m

c. 10√2 m

d. 20 m

**16. Choose the option that best describes the two statements given belo**

**StatemeNt 1: Davisson- Germer experiment established the wave nature of electrons.**

**Statement 2: if the electrons have wave nature value, they can interfere and show diffraction.**

a. Statement 1 is false, Statement 2 is true

b. Statement 1 is true, Statement 2 is true

c. Both the statements are true but statement 2 is the correct explanation of statement 1

d. Both the statements are false

**17. A thin liquid film formed between U-shaped wire and light slider supports a weight of 1.5 X 10^ (-2)N. The length of the slider is 20cm and weight is negligible. The surface tension of the liquid film is:**

a. 0.0125 N/m

b. 0.1 N/m

c. 0.025 N/m

d. 0.05 N/m

**18. A radar that has a power of 1kW and is operating at a frequency of 10GHz. It is located on a mountain top of height 500m. The maximum distance up to which it can be detect object located on the surface of the earth( radius of earth= 6.4 X 10^6m) is:**

a. 80 km

b. 16 km

c. 40 km

d. 64 km

**19. A Carnot engine whose efficiency is 40% takes in heat from a source maintained at a temperature at 500K. It is desired to have a efficiency 60%. Then the intake temperature for the same exhaust(sink) temperature must be:**

a. Efficiency cannot be more than 50%

b. 1200k

c. 750k

d. 600k

**20. A cylindrical tube, open at both the ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now:**

a. f

b. f / 2

c. 3f / 2

d. 2f

**21. Two cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is:**

a. m1r1 : m2r2

b. m1 : m2

c. r1 : r2

d. 1:1

**22. An object 2.4m in front of lens forms a sharp image on a film 12cm behind the lens. A glass plate 1cm thick, of refractive index 1.50 is interposed between the lens and the film with its plane faces parallel to film. At what distance ( from lens) should object be shifted to be in sharp focus on film?**

a. 7.2m

b. 2.4m

c. 3.2m

d. 5.6m

**23. A spectrometer gives the following reading when used to measure the angle of prism.**

**Main scale reading : 58.5 degree**

**Vernier scale reading : 09 divisions**

**Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale in 30 and match with 29 divisions of the main scale. The angle of prism from the above data:**

a. 58.59°

b. 58.77°

c. 58.65°

d. 59°

**24. Proton, deuteron and alpha particles of the same kinetic energy and moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively rp, rd and ra. Which of the following relations is correct?**

a. ra = rp = rd

b. ra = rp < rd

c. ra > rd > rp

d. ra = rd > rp

**25. A particle has an initial velocity of 2 tan^(-1) √(x + 100) and an acceleration of (CH3)2 C’ H. Its speed after 10s is:**

a. 2√2 units

b. 7 units

c. 8.5 units

d. 10 units

**26. A transparent solid cylindrical rod has a refractive index of 3.46. It is surrounded by air. A light ray is incident at the midpoint of one end of the rod as shown in the figure**

a. 3.46

b. sin^(-1) (1 / 1.73)

c. nπ – π/4

d. y` = y / 2

**27. Three sound waves of equal amplitudes have frequencies (v a 1), v, (v + 1). They superpose to give beats. The number of beats produced per second will be:**

a. 2

b. 1

c. 4

d. 3

**28. The question contains statement 1 and statement 2 .Of the four choices, choose the best option that describes the statement best.**

**Statement 1: for a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q.**

**Statement 2 : the net work done by a conservative force on an object moving along a closed loop is 0.**

a. Statement 1 is true, statement 2 is false

b. Both the statements are true and statement 2 is the correct explanation to statement 1.

c. Both the statements are true and statement 2 is not the correct explanation to statement 1.

d. Both the statements are false

**29. Ap – n junction shown in the figure can act as s rectifier. An alternating current source V is connected in the circuit. The current I in the resistor can be shown by:**

**30. The height at which the acceleration due to gravity becomes g/g, in terms of R, the radius of the earth, is:**

a. r / 2

b. r / √2

c. 2r

d. none of the above

**CHEMISTRY:-**

**31. Lithium forms body centered cubic structure. The length of the side of its unit cell is 351pm. Atomic radius of lithium will be:**

a. 75pm

b. 300pm

c. 240pm

d. 152pm

**32. Which method of purification is shown by the equation**

a. zone refining

b. cupellation

c. poling

d. van arkel

**33. The molecule having the smallest bond angle is**

a. N Cl3

b. As Cl3

c.Sb Cl3

d. P Cl3

**34. Which of the following compounds can not be detected by Molish’s test?**

a. nitro compounds

b. sugar

c. amines

d. primary alcohols

**35. The density of a solution prepared by dissolving 120gm of urea in 1000gm of water is 1.15 gm/ml. the molarity of this solution is( mol. mass of urea = 60u)**

a. 0.50M

b. 1.78M

c.1.02M

d. 2.05M

**36. The species that can be best serve as a initiator for the cationic polymerization is**

a. Li Al H4

b. H N O3

c. Al Cl3

d. Bu Li

**37. Which of the following on thermal decompostion yields a basic as well as a acidic oxide?**

a. Na N O3

b. K Cl O3

c. Ca C O3

d. N H4 N O3

**38. The compressibility factor for a real gas at high temperature is**

a. 1 + RT / pb

b. 1

c. 1 + pb / RT

d. 1 – pb / RT

**39. Which of the following statement is correct?**

a.all amino acids except lysine are optically active

b. all amino acids are optically active

c. all amino acids except glycine are optically active

d. all amino acids except glutamic acids are optically active

**40. Aspirin is also known as**

a.acetyl salicylic acid

b. phenyl salicylate

c. acetyl salicylate

d. methyl salicyclic acid

**41. Ortho- Nitrophenol is less soluble in water than p- and m- Nitrophenols because**

a. O- Nitrophenol is more volatile in steam

b. o- Nitrophenol shows intra-molecular H-bonding

c. o- Nitrophenol shows inter- molecular H-bonding

d. melting point of o- Nitrophenol is less than m- and p- Nitrphenol

**42. How many chiral compounds are possible on mono-chlorination of 2-methyl butane?**

a. 8

b. 2

c. 4

d. 6

**43. Very pure Hydrogen can be made by which of the following processes?**

a. reaction of methane with steam

b. mixing natural hydrocarbons of high molecular weight

c. electrolysis of water

d. reaction of salt like hydrides with water

**44. The electrons defined by quantum number n and i are**

1)n=4 i=1

2)n=4 i=0

3)n=3 i=2

4)n=3 i=1

can be placed in increasing order of their energy as:

a. 3<4<2<1

b. 4<2<3<1

c. 2<4<1<3

d. 1<3<2<4

**45. Iron exhibits +2 and +3 oxidant states. Which of the following statement about iron is not correct?**

a. ferrous oxide is more basic in nature than ferric oxide

b. ferrous compounds are comparatively more ionic than ferric compounds

c. ferrous compounds are more volatile than ferric compounds

d. ferrous compounds are more easily hydrolysed than corresponding to ferric compounds.

**46. The pH of a 0.1 molar solution of the acid HQ is 3. The value of ionization constant Ka of the acid is**

a. 3 × 10^(-1)

b. 1 × 10^(-3)

c.1 × 10^(-5)

d. 1 × 10^(-7)

**48. Which branched chain isomer of the hydrocarbon with molecular mass 72u gives only one isomer of mono substituted alkyl halide?**

a. tertiary butyl chloride

b. neopentane

c. isohexane

d. neohexane

**49. What is DDT among the following**

a. greenhouse gas

b. a fertilizer

c. biodegradable pollutant

d. non- biodegradable pollutant

**50. Iodoform can be prepared from all except**

a. ethyl methyl ketone

b. isopropyl alcohol

c.3-methyl-2-butanone

d. isobutyl alcohol

**51. In the given transformation, which of the following is most appropriate reagent?**

a. NH2NH2 OH

b. Zn- Hg/Cl

c.Na LiqNH3

d. Na B H4

**52. The alkene that exhibits geometrical isomerism is:**

a. 2-methyl propane

b. 2-methyl-2-butane

c. 2-butene

d. propene

**53. The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is:**

a.benzoic acid

b. phthalic acid

c. salicyladehyde

d. salicylic acid

**54. Which of the following statements are incorrect about physisorptions?**

a.under high pressure it results in multi molecular layer on adsorbent surface

b. enthalpy of adsorption is low and positive

c. It occurs because of vander waal’s force

d. more easily liquefiable gases are adsorbed readily

**55. The half life period of the first order chemical reaction is 6.99min. the time required for the completion of 99% of the chemical reaction will be( log 2=0.301):**

a.46.06min

b. 230.3min

c. 23.03min

d. 460.6min

**56. copper crystallises in fcc with a unit length of 361pm. What is the radius of copper atom?**

a. 157pm

b. 108pm

c. 127pm

d. 181pm

**57. In the context with transition elements, which of the following is incorrect?**

a. in addition to normal oxidation states, the zero oxidation states is also shown by these elements in complexes.

b. in the highest oxidation states, transition metal shows basic character and form cationic complexes.

c. in the highest oxidation states of !st five transition elements, all 4s and 3d electrons are used for bonding.

d. once the 5d configuration is exceeded, the tendency to involve all 3d electrons in bonding decreases

**58. A binary liquid solution is prepared by mixing n-heptane and ethanol. Which of the following statement does not depict the behaviour of the solution?**

a. solution is non-ideal and shows positive deviation from Roult’s law.

b. solution is non-ideal and shows negative deviation from Roult’s law.

c. its a ideal solution

d. n-heptane shows positive deviation while ethanol shows negative deviation form Roult’s law.

**59. the number of stereo isomers possible for a compound of molecular formula**

a. 3

b. 2

c. 6

d. 4

**60. The IUPAC name of neo-pentane is:**

a. 2-methylpropane

b. 2,2-dimethylbutane

c.2,2-dimethylpropane

d. 2-methylbutane

**MATHEMATICS:-
**

**61. The equation e^(sinx ) – e^(-sinx) -4 = 0 has**

a. infinite number of real roots

b. no real roots

c. exactly one real root

d. exactly four real roots

**62. a spherical balloon is filled with 4500π cubic meters of helium gas. If a leak in balloon gas causes the gas to escape at the rate of 72π cubic meters per minute.Then the rate at which the radius of the balloon decreases in 49minutes after the leakage began is**

a. 9/7

b. 7/9

c.2/9

d. 9/2

**63. Statement 1: the sum of the series**

**1 + ( 1+2+4) + (4+6+9) + (9+12+16)+………+(361+380+400) is 8000.**

**Statement 2: ∑( k^3 – (k-1)^3) = n^3 for any natural number n**

a. Statement 1 is false, statement 2 is true

b. both the statements are true and statement 2 is the correct explanation of statement 1

c. both the statements are true and statement 2 is not the correct explanation of statement 1

d. both the statements are false

**64. if the integral**

then n is equal to

a. -1

b. -2

c. 1

d. 2

**65. If n is a positive integer then (√3 + 1)^ 2n – (√3 – 1)^2n is**

a. irrational number

b.odd positive number

c. even positive number

d. rational number other than positive integer

**66. if 100 times the 100th term of A.P with non-zero common difference equals 50times its 50th term , then 15th term of A.P is**

a. -150

b. 150

c. 0

d. none of the above

**67. In a ΔPQR, if 3sin p + 4cos Q=6 and 4sin Q + 3cos p=1, then the angle R is equal to**

a.5π/6

b. π/6

c. π/4

d. 3π/4

**68. A equation of a plane parallel to the plane x-2y+2z-5=0 and from the unit distance from the origin is**

a. x-2y+2z-3=0

b. x-2y+2z+1=0

c. x-2y-2z-1=0

d. x-2y-2z-5=0

**69. If the line 2x+y=k passes through the point that divides the line segment that joins the point (1,1) and (2,4) in the ratio 3:2, then k equals**

a. 29/5

b.5

c. 6

d. 11/5

**70. let x1,x2……xN be n observations and let x` be the arithmetic mean and σ^2 be its variance.**

**Statement 1: 2×1, 2×2, 2×3……2xN is 4σ^2**

**Statement 2: arithmetic mean of 2×1, 2×2,……..2xN is 4x`.**

a. Statement 1 is false. statement 2 is true

b. Both the statements are true and statement 2 is the correct explanation of statement 1

c. Both the statements are true but statement 2 is not the correct explanation of statement 1

d. Both the statements are false

**71. The population p(t) of time t of a certain mouse species satisfies the differential equation**

**d p(t) / dt = 0.5p(t) – 450**

**If p(0)= 850 then the time at which the population becomes zero as**

a. 2 ln 18

b. 9

c. ½ ln 18

d. ln 18

**72. The area bounded between the parabolas x^2 = y/4 and x^2 = 9y and the straight line y=2 is**

a. 20√2

b. 10√2 / 3

c. 20√2 / 3

d. 10√2

**73. Assuming the balls to be identical except for the difference in colors , the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black ball is**

a. 880

b. 629

c. 630

d. 879

**74. Three numbers are chosen at random without replacement from 1, 2……8. The probability that their minimum is**

a. 3/8

b. 1/5

c. 1/4

d. 2/5

**75. If the mean deviation of the numbers 1, 1+d, 1+2d… 1+100d is 1/x , then d is equal to**

a. 20.2

b. 10.1

c. 10.0

d. 20.0

**76. If the roots of the equation 2.0 × 10^(-5)be imaginary, then for all real values of x,the expression (α,β ) is**

a. greater than 4ab

b. less than 4ab

c. less than equal to 4ab

d. greater than equal to 4ab

**77. The lines p(p^2 +1)x -y +q=0 and (p^2 + 1)^2x + (p^2 +1)^2y + 2q =0 are perpendicular to the common line for**

a. exactly one value of p

b. no value of p

c. more than 2 values of p

d. exactly 2 values of p

**78. From 6 different novels and 3 different dictionaries , 4 novels and 1 dictionary is to be selected**

**and arranged in a row on a shelf in such a way that the dictionary is always in the middle.. then the number of such arrangement is**

a. >=750 and <1000

b. >=500 and <750

c. <500

d.>=1000

**79. the remainder left out when 8^2n – 62^(2n+1) is divided by 9 is**

a. 7

b. 0

c. 2

d. 8

**80. The ellipse x^2 + 4y^2 = 4 is inscribed in a rectangle aligned by the coordinate axes, which in turn is inscribed in an ellipse that passes through the point (4,0). then the equation of the ellipse is**

a. 4x^2 + 48y^2 = 48

b. 4x^2 + 64y^2 = 48

c. x^2 + 16y^2 = 16

d. none of the above

**81.The sum to the infinity of the series 1+ 2/3 +6/3^2…. is**

a. 3

b. 2

c. 4

d. 6

**82. The area of the region bounded by parabola (y-2)^2 = x-1.The tangent to the parabola at the point (2,3) and x-axis is**

a. 12

b. 6

c. 9

d. 3

**83. A triangle with vertices (4,0), (-1,-1) and (3,5) is**

a. isosceles and right angled

b. only isosceles

c. only right angled

d. neither of them

**84. A problem in mathematics is given to 3 students A,B,C. and their respective probability of solving the problem is 1/2 , 1/3, 1/4. probability that the problem is solved**

a. 3/4

b. 1/2

c. 2/3

d. 1/3

**85. A parallelopipe is formed by planes drawn through the points (2,3,5) and (5,9,7) parallel to the coordinate planes. the length of the diagonal of parallelopipe is**

a. 7

b. √38

c.√155

d. none

**86. The equation of the directrix of the parabola y^2 + 4y + 4x + 2=0 is**

a. x=-1

b. x=1

c. x=-3/2

d. x= 3/2

**87. The value of 2^1/4 , 4^1/8, 8^1/6………..∞ is**

a. 1

b. 2

c. 4

d. 3/2

**88. The area bounded by the curve y= 2x – x^2 and the straight line y= -x is**

a.9/2

b. 43/6

c. 35/6

d. none of the above

**89. In a triangle ABC, 2ca sin((A-B+C)/2) =**

a. a^2 + b^2 – c^2

b. c^2 + a^2 – b^2

c. b^2 – c^2 – a^1

d. c^2 – a^2 – b^2

**90. the period of sin^2 Θ is**

a. π^2

b. π

c. 2π

d. π/2

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**JEE Main Entrance Exam 2013 Physics Question Papers**

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