JEE Main

JEE MAIN (AIEEE) Past Exam Paper-2009

Physics

Part – A

1. This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

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 zero

(1)  Statement-1 is true, Statement-2 is false

(2)  Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

(3)  Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

(4)  Statement-1 is false, Statement-2 is true

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2. The above is a plot of binding energy per nucleon E_b, against the nuclear mass M; A, B, C, D, E, F correspond to different nuclei. Consider four reactions:

(i) A + B → C + ε             (ii) C → A + B + ε

(iii) D + E → F + ε and    (iv) F → D + E + ε

where ε is the energy released? In which reactions is ε positive?

(1)  (i) and (iv)

(2)  (i) and (iii)

(3)  (ii) and (iv)

(4)  (ii) and (iii)

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3. A p-n junction (4) shown in the figure can act as a rectifier. An alternating current source (V) is connected in the circuit.

(1) 

(2) 

(3) 

(4) 

Show Answer

4. The logic circuit shown below has the input waveforms ‘A’ and ‘B’ as shown. Pick out the correct output waveform.

(1) 

(2) 

(3) 

(4) 

Show Answer

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

(1)  a²T² + 4π²v²

(2)  aT/x

(3)  aT + 2πv

(4)  aT/v

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6. In an optics experiment, with the position of the object fixed, a student varies the position of a 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° with the x-axis meets the experimental curve at P. The coordinates of P will be

(1)  (2f, 2f)

(2)  (f/2, f/2)

(3)  (f, f)

(4)  (4f, 4f)

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7. A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to a maximum height of

(1) 

(2) 

(3) 

(4) 

Show Answer

8. Let  be the charge density distribution for a solid sphere of radius R and total charge Q. for a point ‘p’ inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is

(1)  0

(2) 

(3) 

(4) 

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9. 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

(1)  2 → 1

(2)  3 → 2

(3)  4 → 2

(4)  5 → 2

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10. One kg of a diatomic gas is at a pressure of 8 × 10⁴ N/m². The density of the gas is 4 kg/m⁻³. What is the energy of the gas due to its thermal motion?

(1)  3 × 10⁴ J

(2)  5 × 10⁴ J

(3)  6 × 10⁴ J

(4)  7 × 10⁴ J

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11. This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-1: The temperature dependence of resistance is usually given as R = R_o(1 + αΔt). The resistance of a wire changes from 100 Ω to 150 Ω when its temperature is increased from 27°C to 227°C. This implies that α = 2.5 ×10⁻³ /°C.

Statement 2: R = R_i (1 + αΔT) is valid only when the change in the temperature ΔT is small and ΔR = (R – R_o) << R_o.

(1)  Statement-1 is true, Statement-2 is false

(2)  Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

(3)  Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

(4)  Statement-1 is false, Statement-2 is true

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Directions: Question numbers 12 and 13 are based on the following paragraph.

A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB and CD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is 30°. Another straight thin wire with steady current I1 flowing out of the plane of the paper is kept at the origin.

12. The magnitude of the magnetic field (B) due to loop ABCD at the origin (O) is

(1)  zero

(2) 

(3) 

(4) 

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13. Due to the presence of the current I₁ at the origin

(1)  The forces on AB and DC are zero

(2)  The forces on AD and BC are zero

(3)  The magnitude of the net force on the loop is given by 

(4)  The magnitude of the net force on the loop is given by 

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14. A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young’s double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is

(1)  393.4 nm

(2)  885.0 nm

(3)  442.5 nm

(4)  776.8 nm

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15. Two points P and Q are maintained at the potentials of 10V and -4V respectively. The work done in moving 100 electrons from P to Q is

(1)  −19 × 10⁻¹⁷ J

(2)  9.60 × 10⁻¹⁷ J

(3)  −2.24 × 10⁻¹⁶ J

(4)  2.24 × 10⁻¹⁶ J

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16. The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc = 1240 eV nm)

(1)  3.09 eV

(2)  1.41 eV

(3)  151 eV

(4)  1.68 eV

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17. A particle has an initial velocity  and an acceleration of  Its speed after 10 s is

(1)  10 units

(2)  7√2 units

(3)  7 units

(4)  8.5 units

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18. A motor cycle starts from rest and accelerates along a straight path at 2 m/s². At the starting point of the motor cycle there is a stationary electric sire. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest? (speed of sound = 330 ms⁻¹).

(1)  49 m

(2)  98 m

(3)  17 m

(4)  196 m

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19. Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as function of time will be

(1) 

(2) 

(3) 

(4) 

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20. A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then the Q/q equals

(1)  −2√2

(2)  −1

(3)  1

(4)  −1/√2

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21. A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature θ along the length x of the bar from its hot end is best described by which of the following figure.

(1) 

(2) 

(3) 

(4) 

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22. A transparent solid cylindrical rod has a refractive index of 2/√ It is surrounded by air. A light ray is incident at the mid point of one end of the rod as shown in the figure.

The incident angle θ for which the light ray grazes along the wall of the rod is

(1)  sin⁻¹(1/2)

(2)  sin⁻¹(√3/2)

(3)  sin⁻¹(2/√3)

(4)  sin⁻¹(1/√3)

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

(1)  4

(2)  3

(3)  2

(4)  1

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24. The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth is

(1)  2R

(2)  R/√2

(3)  R/2

(4)  √2R

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25. Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire-2 has cross-sectional area 3A. If the length of wire 1 increases by Δx on applying force F, how much force is needed to stretch wire 2 by the same amount?

(1)  F

(2)  4F

(3)  6F

(4)  9F

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26. In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree(=0.5°), then the least count of the instrument is

(1)  one minute

(2)  half minute

(3)  one degree

(4)  half degree

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27. An inductor of inductance L = 400 mH and resistors of resistances R₁ = 2Ω and R2 = 2Ω are connected to a battery of emf 12V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is.

(1)  6e^−5tV

(2) 

(3)  6(1 – e^−t/0.2)V

(4)  12e^−5tV

Show Answer

Directions: Question numbers 28, 29 and 30 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the P – T diagram.

28. Assuming the gas to be ideal the work done on the gas in taking it from A to B is

(1)  200 R

(2)  300 R

(3)  400 R

(4)  500 R

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29. The work done on the gas in taking it from D to A is

(1)  −414 R

(2)  +414 R

(3)  −690 R

(4)  +690 R

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30. The net work done on the gas in the cycle ABCDA is

(1)  Zero

(2)  276 R

(3)  1076 R

(4)  1904 R

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CHEMISTRY

PART – B

31. Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the following statements in incorrect ?

(1)  Because of the large size of the Ln (III) ions the bonding in its compounds is predominantly ionic in character.

(2)  The ionic sizes of Ln (III) decrease in general with increasing atomic number.

(3)  Ln (III) compounds are generally colourless.

(4)  Ln (III) hydroxides are mainly basic in character.

Show Answer

32. A liquid was mixed with ethanol and a drop of concentrated H₂SO₄ was added. A compound with a fruity smell was formed. The liquid was :

(1)  CH₃OH

(2)  HCHO

(3)  CH₃COCH₃

(4)  CH₃COOH

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33. Arrange the carbanions,  in order of their decreasing stability :

(1) 

(2) 

(3) 

(4) 

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34. The alkene that exhibits geometrical isomerism is :

(1)  propene

(2)  2-methyl propene

(3)  2-butene

(4)  2-methyl-2-butene

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35. In which of the following arrangements, the sequence is not strictly according to the property written against it ?

(1)  CO₂ < SiO₂ < SnO₂ < PbO₂ : increasing oxidizing power

(2)  HF < HCl < HBr < HI : increasing acid strength

(3)  NH₃ < PH_­3 < AsH₃ < SbH₃ : increasing basic strength

(4)  B < C < O < N : increasing first ionization enthalpy.

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

(1)  benzoic acid

(2)  salicyladehyde

(3)  salicylic acid

(4)  phthalic acid

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37. Which of the following statements is incorrect regarding physissorptions ?

(1)  It occurs because of vander Waal’s forces.

(2)  More easily liquefiable gases are adsorbed readily.

(3)  Under high pressure it results into multi molecular layer on adsorbent surface.

(4)  Enthalpy of adsorption (∆H_adsorption) is low and positive.

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38. Which of the following on heating with aqueous KOH, produces acetaldehyde ?

(1)  CH₃COCl

(2)  CH₃CH₂Cl

(3)  CH₂ClCH₂Cl

(4)  CH_­3CHCl₂

Show Answer

39. In an atom, an electron is moving with a speed of 600m/s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is (h = 6.6 × 10⁻³⁴ kg m²s⁻¹, mass of electron e_m = 9.1 × 10⁻³¹ kg)

(1)  1.52 × 10⁻⁴ m

(2)  5.10 × 10⁻³ m

(3)  1.92 × 10⁻³ m

(4)  3.84 × 10⁻³ m

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40. In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction  is At 298 K standard Gibb’s energies of formation for CH₃OH(ℓ), H₂O(ℓ) and CO₂(g) are −2, −237.2 and −394.4 kJ mol⁻¹ respectively. If standard enthalpy of combustion of methanol is −726 kJ mol⁻¹, efficiency of the fuel cell will be

(1)  80%

(2)  87%

(3)  90%

(4)  97%

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41. Two liquids X and Y form an ideal solution. At 300K, vapour pressure of the solution containing 1 mol of X and 3 mol of Y is 550 mm Hg. At the same temperature, if 1 mol of Y is further added to this solution, vapour pressure of the solution increases by 10 mm Hg. Vapour pressure (in mmHg) of X and Y in their pure states will be, respectively :

(1)  200 and 300

(2)  300 and 400

(3)  400 and 600

(4)  500 and 600

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42. The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log 2=0.301) :

(1)  230.3 minutes

(2)  23.03 minutes

(3)  46.06 minutes

(4)  460.6 minutes

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43. Given :  The value of standard electrode potential for the change,  will be :

(1)  −0.072 V

(2)  0.385 V

(3)  0.770 V

(4)  −0.270

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44. On the basis of the following thermochemical data : (∆FG°H_(aq)⁺ = 0)

H₂O(ℓ) → H⁺ (aq) + OH⁻(aq); ∆H = 57.32 kJ

The value of enthalpy of formation of OH⁻ ion at 25°C is :

(1)  −22.88 kJ

(2)  −228.88 kJ

(3)  +228.88 kJ

(4)  −343.52 kJ

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45. Copper crystallizes in fcc with a unit cell length of 361 pm. What is the radius of copper atom ?

(1)  108 pm

(2)  127 pm

(3)  157 pm

(4)  181 pm

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46. Which of the following has an optical isomer?

(1)  [CO(NH₃)₃Cl]⁺

(2)  [CO(en)(NH₃)₂]²⁺

(3)  [CO(H₂O)₄ (en)]³⁺

(4)  [CO(en)₂(NH₃)₂]³⁺

Show Answer

47. Solid Ba (NO₃)₂ is gradually dissolved in a 1.0 × 10⁻⁴ M Na_­2CO₃ At what concentration of Ba²⁺ will a precipitate begin to form ? (K_sp for BaCO₃ = 5.1 × 10⁻⁹).

(1)  4.1 × 10⁻⁵ M

(2)  5.1 × 10⁻⁵ M

(3)  8.1 × 10⁻⁵ M

(4)  8.1 × 10⁻⁷ M

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48. Which one of t he following reactions of Xenon compounds is not feasible?

(1)  XeO₃ + 6HF → XeF₆ + 3H₂O

(2)  3XeF₄ + 6H₂O → 2Xe + XeO₃ + 12HF + 1.5O₂

(3)  2XeF_4­ + 2H₂O → 2Xe + 4HF + O₂

(4)  XeF₆ + RbF → Rb(XeF₇]

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49. Using MO theory predict which of the following species has the shortest bond length ?

(1)  O₂²⁺

(2)  O₂⁺

(3)  O₂⁻

(4)  O₂²⁻

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50. In context with the transition elements, which of the following statements is incorrect ?

(1)  In addition to the normal oxidation states, the zero oxidation state is also shown by these elements in complexes.

(2)  In the highest oxidation states, the transition metal show basic character and form cationic complexes.

(3)  In the highest oxidation states of the first five transition elements (Sc to Mn), all the 4s and 3d electrons are used for bonding.

(4)  Once the d⁵ configuration is exceeded, the tendency to involve all the 3d electrons in bonding decreases.

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51. Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 ×10³ ms⁻¹ (Mass of proton = 1.67 ×10⁻²⁷ kg and h = 6.63 ×10⁻³⁴ Js ) :

(1)  0.032 nm

(2)  0.40 nm

(3)  2.5 nm

(4)  14.0 nm

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52. A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statements is correct regarding the behaviour of the solution ?

(1)  The solution formed is an ideal solution

(2)  The solution is non-ideal, showing +ve deviation from Raoult’s law.

(3)  The solution is non-ideal, showing –ve deviation from Raoult’s law.

(4)  n-heptane shows +ve deviation while ethanol shows –ve deviation from Raoult’s law.

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53. The number of stereoisomers possible for a compound of the molecular formula CH₃ − CH = CH − CH OH −Me is :

(1)  3

(2)  2

(3)  4

(4)  6

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54. The IUPAC name of neopentane is

(1)  2-methylbutane

(2)  2, 2-dimethylpropane

(3)  2-methylpropane

(4)  2, 2-dimethylbutane

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55. The set representing the correct order of ionic radius is :

(1)  Li⁺ > Be²⁺ > Na⁺ > Mg²⁺

(2)  Na⁺ > Li⁺ > Mg²⁺ > Be²⁺

(3)  Li⁺ > Na⁺ > Mg²⁺ > Be²⁺

(4)  Mg²⁺ > Be²⁺ > Li⁺ > Na⁺

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56. The two functional groups present in a typical carbohydrate are :

(1)  −OH and −COOH

(2)  −CHO and −COOH

(3)  > C = O and −OH

(4)  −OH and −CHO

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57. The bond dissociation energy of B – F in BF₃ is 646 kJ mol⁻¹ whereas that of C-F in CF₄ is 515kJ mol⁻¹ . The correct reason for higher B-F bond dissociation energy as compared to that of C- F is :

(1)  smaller size of B-atom as compared to that of C- atom

(2)  stronger σ bond between B and F in BF₃ as compared to that between C and F in CF₄

(3)  significant pπ – pπ interaction between B and F in BF₃ whereas there is no possibility of such interaction between C and F in CF₄.

(4)  lower degree of pπ – pπ interaction between B and F in BF₃ than that between C and F in CF₄.

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58. In Cannizzaro reaction given below

the slowest step is :

(1)  the attack of :  at the carboxyl group

(2)  the transfer of hybride to the carbonyl group

(3)  the abstraction of proton from the carboxylic group

(4)  the deprotonation of Ph CH₂OH

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59. Which of the following pairs represents linkage isomers ?

(1)  [Cu(NH₃)₄] [PtCl₄] and [Pt(NH₃)₄] [CuCl₄]

(2)  [Pd(P Ph₃)₂ (NCS)₂] and [Pd(P Ph₃)₂ (SCN)₂]

(3)  [CO (NH₃)₅ NO₃] SO₄ and [CO(NH₃)₅SO₄] NO₃

(4)  [Pt Cl₂(NH₃)₄]Br₂ and [PtBr₂(NH₃)₄]Cl₂

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60. Buna-N synthetic rubber is a copolymer of :

(1)   and H₂C = CH – CH = CH₂

(2)  H₂C = CH – CH = CH₂ and H₅C₆ – CH = CH₂

(3)  H₂C = CH – CN and H₂C = CH – CH = CH₂

(4)  H₂C = CH – CN and 

Show Answer

Mathematics

PART – C

61. Let a, b, c be such that b(a + c) ≠ 0 . If  , then the value of ‘n’ is

(1)  zero

(2)  any even integer

(3)  any odd integer

(4)  any integer

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62. If the mean deviation of number 1, 1 + d, 1 + 2d, ….. , 1 + 100d from their mean is 255, then the d is equal to

(1)  10.0

(2)  20.0

(3)  10.1

(4)  20.2

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63. If the roots of the equation bx² + cx + a = 0 be imaginary, then for all real values of x, the expression 3b²x² + 6bcx + 2c² is

(1)  greater than 4ab

(2)  less than 4ab

(3)  greater than −4ab

(4)  less than −4ab

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64. Let A and B denote the statements

A: cos α + cos β + cos γ = 0

B: sin α + sin β + sin γ = 0

If cos(β – γ) + cos(γ – α) + cos(α – β) = −3/2, then

(1)  A is true and B is false

(2)  A is false and B is true

(3)  both A and B are true

(4)  both A and B are false

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65. The lines p(p² + 1) x – y + q =0 and (p² + 1)² x + (p² + 1)y + 2q = 0 are perpendicular to a common line for

(1)  no value of p

(2)  exactly one value of p

(3)  exactly two values of p

(4)  more than two values of p

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66. If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then

(1)  A = B

(2)  A = C

(3)  B = C

(4)  A ∩ B = ϕ

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67. If  are non-coplanar vectors and p, q are real numbers, then the equality  holds for

(1)  exactly one value of (p, q)

(2)  exactly two values of (p, q)

(3)  more than two but not all values of (p , q)

(4)  all values of (p, q)

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68. Let the line  lies in the plane x + 3y – αz + β = 0. Then (α, β) equals

(1)  (6, −17)

(2)  (−6, 7)

(3)  (5, −15)

(4)  (−5, 15)

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69. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is

(1)  less than 500

(2)  at least 500 but less than 750

(3)  at least 750 but less than 1000

(4)  at least 1000

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70. denotes the greatest integer function, is equal to

(1)  π/2

(2)  1

(3)  −1

(4)  −π/2

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71. For real x, let f (x) = x³ + 5x + 1, then

(1)  f is one-one but not onto R

(2)  f is onto R but not one-one

(3)  f is one-one and onto R

(4)  f is neither one-one nor onto R

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72. In a binomial distribution  if the probability of at least one success is greater than or equal to 9/10, then n is greater than

(1) 

(2) 

(3) 

(4) 

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73. If P and Q are the points of intersection of the circles x² + y² + 3x + 7y + 2p − 5 = 0 and x² + y² + 2x + 2y − p² = 0 , then there is a circle passing through P, Q and (1, 1) for

(1)  all values of p

(2)  all except one value of p

(3)  all except two values of p

(4)  exactly one value of p

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74. The projections of a vector on the three coordinate axis are 6, −3, 2 respectively. The direction cosines of the vector are

(1)  6, −3, 2

(2)  6/5, −3/5, 2/5

(3)  6/7, −3/7, 2/7

(4)  −6/7, −3/7, 2/7

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75. If  then the maximum value of |z| is equal to

(1)  √3 + 1

(2)  √5 + 1

(3)  2

(4)  2 + √2

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76. Three distinct points A, B and C are given in the 2 – dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point ( – 1, 0) is equal to 1/3. Then the circumcentre of the triangle ABC is at the point

(1)  (0, 0)

(2)  (5/4, 0)

(3)  (5/2, 0)

(4)  (5/3, 0)

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77. The remainder left out when 8²ⁿ – (62)^{2n + 1} is divided by 9 is

(1)  0

(2)  2

(3)  7

(4)  8

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78. The ellipse x² + 4y² = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

(1)  x² + 16y² = 16

(2)  x² + 12y² = 16

(3)  4x² + 48y² = 48

(4)  4x² + 64y² = 48

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79. The sum to the infinity of the series  is

(1)  2

(2)  3

(3)  4

(4)  6

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80. The differential equation which represents the family of curves  where c₁ and c₂ are arbitrary constants is

(1)  y’ = y²

(2)  y” = y’y

(3)  yy” = y’

(4)  yy”=(y’)²

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81. One ticket is selected at random from 50 tickets numbered 00, 01, 02, …., 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals

(1)  1/14

(2)  1/7

(3)  5/14

(4)  1/50

Show Answer

82. Let y be an implicit function of x defined by x^2x − 2x^x cot y −1= 0 . Then y'(1) equals

(1)  −1

(2)  1

(3)  log 2

(4)  −log 2

Show Answer

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

(1)  3

(2)  6

(3)  9

(4)  12

Show Answer

84. Given P(x) = x⁴ + ax³ + bx² + cx + d such that x = 0 is the only real root of P'(x) = 0 . If P(−1) < P(1) , then in the interval [−1, 1]

(1)  P(−1) is the minimum and P(1) is the maximum of P

(2)  P(−1) is not minimum but P(1) is the maximum of P

(3)  P(−1) is the minimum and P(1) is not the maximum of P

(4)  neither P(−1) is the minimum nor P(1) is the maximum of P

Show Answer

85. The shortest distance between the line y − x = 1 and the curve x = y² is

(1) 

(2) 

(3) 

(4) 

Show Answer

Directions: Question number 86 to 90 are Assertion – Reason type questions. Each of these questions contains two statements

Directions: Question number 86 to 90 are Assertion – Reason type questions. Each of these questions

contains two statements

Statement-1 (Assertion) and Statement-2 (Reason).

Each of these questions also have four alternative choices, only one of which is the correct answer. You have to select the correct choice

86. Let f(x) = (x + 1)² – 1, x ≥ −1

Statement-1 : The set {x : f(x) = f⁻¹(x)} = {0, −1}

Statement-2 : f is a bijection.

(1)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

(2)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

(3)  Statement-1 is true, Statement-2 is false

(4)  Statement-1 is false, Statement-2 is true

Show Answer

87. Let f (x) = x |x| and g(x) = sinx .

Statement-1 : gof is differentiable at x = 0 and its derivative is continuous at that point.

Statement-2 : gof is twice differentiable at x = 0.

(1)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

(2)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

(3)  Statement-1 is true, Statement-2 is false

(4)  Statement-1 is false, Statement-2 is true

Show Answer

88. Statement-1 : The variance of first n even natural numbers is 

Statement-2 : The sum of first n natural numbers is  and the sum of squares of first n natural numbers is 

(1)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

(2)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

(3)  Statement-1 is true, Statement-2 is false

(4)  Statement-1 is false, Statement-2 is true

Show Answer

89. Statement-1 : ~ (p ↔~ q) is equivalent to p ↔ q.

Statement-2 : ~ (p ↔~ q) is a tautology.

(1)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

(2)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

(3)  Statement-1 is true, Statement-2 is false

(4)  Statement-1 is false, Statement-2 is true

Show Answer

90. Let A be a 2 × 2 matrix

Statement-1 : adj(adj A) = A

Statement-2 : |adj A| = |A|

(1)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

(2)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

(3)  Statement-1 is true, Statement-2 is false

(4)  Statement-1 is false, Statement-2 is true

Show Answer

JEE MAIN (AIEEE) Past Exam Paper-2008

Mathematics

PART-A

1. AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45°. Then the height of the pole is

(1) 

(2) 

(3) 

(4) 

Show Answer

2. It is given that the events A and B are such that 

Then P(B) is

(1)  1/6

(2)  1/3

(3)  2/3

(4)  1/2

Show Answer

3. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is

(1)  3/5

(2)  0

(3)  1

(4)  2/5

Show Answer

4. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi−major axis is

(1)  8/3

(2)  2/3

(3)  4/3

(4)  5/3

Show Answer

5. A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

(1)  (0, 2)

(2)  (1, 0)

(3)  (0, 1)

(4)  (2, 0)

Show Answer

6. The point diametrically opposite to the point P (1, 0) on the circle x² + y² + 2x + 4y − 3 = 0 is

(1)  (3, −4)

(2)  (−3, 4)

(3)  (−3, −4)

(4)  (3, 4)

Show Answer

7. Let f : N → Y be a function defined as f (x) = 4x + 3, where Y = {y ∈ N : y = 4x + 3 for some x ∈ N}. Show that f is invertible and its inverse is

(1) 

(2) 

(3) 

(4) 

Show Answer

8. The conjugate of a complex number is  Then the complex number is

(1) 

(2) 

(3) 

(4) 

Show Answer

9. Let R be the real line. Consider the following subsets of the plane R × R.

S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x − y is an integer}. Which one of the following is true?

(1)  neither S nor T is an equivalence relation on R

(2)  both S and T are equivalence relations on R

(3)  S is an equivalence relation on R but T is not

(4)  T is an equivalence relation on R but S is not

Show Answer

10. The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y−intercept − 4. Then a possible value of k is

(1)  1

(2)  2

(3)  −2

(4)  −4

Show Answer

11. The solution of the differential equation  satisfying the condition y(1) = 1 is

(1)  y = ln x + x

(2)  y = x ln x + x²

(3)  y = xe^{(x – 1)}

(4)  y = x ln x + x

Show Answer

12. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

(1)  a = 0, b =7

(2)  a = 5, b = 2

(3)  a = 1, b = 6

(4)  a = 3, b = 4

Show Answer

13. The vector  lies in the plane of the vectors  and bisects the angle between  Then which one of the following possible values of α and β?

(1)  α = 2, β = 2

(2)  α = 1, β = 2

(3)  α = 2, β = 1

(4)  α = 1, β = 1

Show Answer

14. The non-zero vectors  are related by   Then the angle between  is

(1)  0

(2)  π/4

(3)  π/2

(4)  π

Show Answer

15. The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the point  Then

(1)  a = 2, b= 8

(2)  a = 4, b = 6

(3)  a = 6, b = 4

(4)  a = 8, b = 2

Show Answer

16. If the straight lines  and  intersect at a point, then the integer k is equal to

(1)  −5

(2)  5

(3)  2

(4)  −2

Show Answer

Directions: Questions number 17 to 21 are Assertion−Reason type questions. Each of these questions contains two statements : Statement − 1 (Assertion) and Statement−2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

17. Statement -1 : For every natural number n ≥ 2, 

Statement-2 : For every natural number n ≥ 2, 

(1)  Statement −1 is false, Statement −2 is true

(2)  Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

(3)  Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

(4)  Statement − 1 is true, Statement − 2 is false.

Show Answer

18. Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A² = I.

Statement −1: If A ≠ I and A ≠ − I, then det A = − 1.

Statement −2: If A ≠ I and A ≠ − I, then tr (A) ≠ 0.

(1)  Statement −1 is false, Statement −2 is true

(2)  Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

(3)  Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

(4)  Statement − 1 is true, Statement − 2 is false.

Show Answer

19. Statement – 1: 

Statement – 2: 

(1)  Statement −1 is false, Statement −2 is true

(2)  Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

(3)  Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

(4)  Statement − 1 is true, Statement − 2 is false.

Show Answer

20. Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”.

Statement –1: r is equivalent to either q or p

Statement –2: r is equivalent to ∼ (p ↔ ∼ q).

(1)  Statement −1 is false, Statement −2 is true

(2)  Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

(3)  Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

(4)  Statement − 1 is true, Statement − 2 is false.

Show Answer

21. In a shop there are five types of ice-creams available. A child buys six ice-creams.

Statement -1: The number of different ways the child can buy the six ice-creams is ¹⁰C₅.

Statement -2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row.

(1)  Statement −1 is false, Statement −2 is true

(2)  Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

(3)  Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

(4)  Statement − 1 is true, Statement − 2 is false.

Show Answer

22. Let  Then which one of the following is true?

(1)  f is neither differentiable at x = 0 nor at x = 1

(2)  f is differentiable at x = 0 and at x = 1

(3)  f is differentiable at x = 0 but not at x = 1

(4)  f is differentiable at x = 1 but not at x = 0

Show Answer

23. The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

(1)  −4

(2)  −12

(3)  12

(4)  4

Show Answer

24. Suppose the cube x³ – px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

(1)  The cubic has minima at  and maxima at 

(2)  The cubic has minima at  and maxima at

(3)  The cubic has minima at both  and

(4)  The cubic has maxima at both  and 

Show Answer

25. How many real solutions does the equation x⁷ + 14x⁵ + 16x³ + 30x – 560 = 0 have?

(1)  7

(2)  1

(3)  3

(4)  5

Show Answer

26. The statement p → (q → p) is equivalent to

(1)  p → (p → q)

(2)  p → (p ∨ q)

(3)  p → (p ∧ q)

(4)  p → (p ↔ q)

Show Answer

27. The value of  is

(1)  6/17

(2)  3/17

(3)  4/17

(4)  5/17

Show Answer

28. The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

(1)  (x – 2)y′² = 25 – (y – 2)²

(2)  (y – 2)y′² = 25 – (y – 2)²

(3)  (y – 2)2y′² = 25 – (y – 2)²

(4)  (x – 2)2y′² = 25 – (y – 2)²

Show Answer

29. Let  Then which one of the following is true?

(1) 

(2) 

(3) 

(4) 

Show Answer

30. The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1 is equal to

(1)  5/3

(2)  1/3

(3)  2/3

(4)  4/3

Show Answer

31. The value of  is

(1) 

(2) 

(3) 

(4) 

Show Answer

32. How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

(1)  8 . ⁶C₄ . ⁷C₄

(2)  6 . 7 . ⁸C₄

(3)  6 . 8 . ⁷C₄

(4)  7 . ⁶C₄ . ⁸C₄

Show Answer

33. Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then a² + b² + c² + 2abc is equal to

(1)  2

(2)  −1

(3)  0

(4)  1

Show Answer

34. Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

(1)  If detA = ± 1, then A^–1 exists but all its entries are not necessarily integers

(2)  If detA ≠ ± 1, then A^–1 exists and all its entries are non-integers

(3)  If detA = ± 1, then A^–1 exists and all its entries are integers

(4)  If detA = ± 1, then A^–1 need not exist

Show Answer

35. The quadratic equations x² – 6x + a = 0 and x² – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

(1)  1

(2)  4

(3)  3

(4)  2

Show Answer

Chemistry

PART – B

36. The organic chloro compound, which shows complete stereochemical inversion during a S_N2 reaction, is

(1)  (C₂H₅)₂CHCl

(2)  (CH₃)₃CCl

(3)  (CH₃)₂CHCl

(4)  CH₃Cl

Show Answer

37. Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains

(1)  mixture of o− and p−bromotoluenes

(2)  mixture of o− and p−dibromobenzenes

(3)  mixture of o− and p−bromoanilines

(4)  mixture of o− and m−bromotoluenes

Show Answer

38. The coordination number and the oxidation state of the element ‘E’ in the complex [E(en)₂(C₂O₄)]NO₂ (where (en) is ethylene diamine) are, respectively,

(1)  6 and 2

(2)  4 and 2

(3)  4 and 3

(4)  6 and 3

Show Answer

39. Identify the wrong statements in the following:

(1)  Chlorofluorocarbons are responsible for ozone layer depletion

(2)  Greenhouse effect is responsible for global warming

(3)  Ozone layer does not permit infrared radiation from the sun to reach the earth

(4)  Acid rains is mostly because of oxides of nitrogen and sulphur

Show Answer

40. Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives

(1)  2,4,6-trinitrobenzene

(2)  o-nitrophenol

(3)  p-nitrophenol

(4)  nitrobenzene

Show Answer

41. In the following sequence of reactions, the alkene affords the compound ‘B’

The compound B is

(1) 

(2) 

(3) 

(4) 

Show Answer

42. Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being

(1)  4f orbitals more diffused than the 5f orbitals

(2)  lesser energy difference between 5f and 6d than between 4f and 5d orbitals

(3)  more energy difference between 5f and 6d than between 4f and 5d orbitals

(4)  more reactive nature of the actinoids than the lanthanoids

Show Answer

43. In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of Δ_o be the highest?

(1)  [Co(CN)₆]³⁻

(2)  [Co(C₂O₄)₃]³⁻

(3)  [Co(H₂O)₆]³⁺

(4)  [Co(NH₃)₆]³⁺

Show Answer

44. At 80°C, the vapour pressure of pure liquid ‘A’ is 520 mm Hg and that of pure liquid ‘B’ is 1000 mm Hg. If a mixture solution of ‘A’ and ‘B’ boils at 80°C and 1 atm pressure, the amount of ‘A’ in the mixture is (1 atm = 760 mm Hg)

(1)  52 mol percent

(2)  31 mol percent

(3)  48 mol percent

(4)  50 mol percent

Show Answer

45. For a reaction  rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the expression

(1) 

(2) 

(3) 

(4) 

Show Answer

46. The equilibrium constants  for the reactions X⇌ 2Y and Z ⇌ P +Q, respectively are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total pressure at these equilibria is

(1)  1 : 36

(2)  1 : 1

(3)  1 : 3

(4)  1 : 9

Show Answer

47. Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below:

The energy involved in the conversion of 

(using the data, 

(1)  +152 kJmol⁻¹

(2)  −610 kJmol⁻¹

(3)  −850 kJmol⁻¹

(4)  +120 kJmol⁻¹

Show Answer

48. Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?

(1)  Metal sulphides are thermodynamically more stable than CS₂

(2)  CO₂ is thermodynamically more stable than CS₂

(3)  Metal sulphides are less stable than the corresponding oxides

(4)  CO₂ is more volatile than CS₂

Show Answer

49. Bakelite is obtained from phenol by reacting with

(1)  (CH₂OH)₂

(2)  CH₃CHO

(3)  CH₃COCH₃

(4)  HCHO

Show Answer

50. For the following three reactions a, b and c, equilibrium constants are given:

(a) CO(g) + H₂O(g) ⇋ CO₂(g) + H₂(g); K₁

(b) CH₄(g) + H₂O(g) ⇌ CO (g) + 3H₂(g); K₂

(c) CH₄(g) + 2H₂O(g) ⇌ CO₂(g) + 4H₂(g); K₃

Which of the following relations is correct?

(1) 

(2)  K₂K₃ = K₁

(3)  K₃ = K₁K₂

(4)  K₃K₂³ = K₁²

Show Answer

51. The absolute configuration of

is

(1)  S, S

(2)  R, R

(3)  R, S

(4)  S, R

Show Answer

52. The electrophile, E^⊕ attacks the benzene ring to generate the intermediate σ-complex. Of the following, which σ-complex is of lowest energy?

(1) 

(2) 

(3) 

(4) 

Show Answer

53. α-D-(+)-glucose and β-D-(+)-glucose are

(1)  conformers

(2)  epimers

(3)  anomers

(4)  enantiomers

Show Answer

54. Standard entropy of X₂, Y₂ and XY₃ are 60, 40 and 50 JK⁻¹ mol⁻¹, respectively. For the reaction,  ∆H = −30 kJ, to be at equilibrium, the temperature will be

(1)  1250 K

(2)  500 K

(3)  750 K

(4)  1000 K

Show Answer

55. Four species are listed below

Which one of the following is the correct sequence is their acid strength?

(1)  iv < ii < iii < i

(2)  ii < iii < i < iv

(3)  i < iii < ii < iv

(4)  iii < i < iv < ii

Show Answer

56. Which one of the following constitutes a group of the isoelectronic species?

(1) 

(2) 

(3) 

(4) 

Show Answer

57. Which one of the following pairs of species have the same bond order?

(1)  CN⁻ and NO⁺

(2)  CN⁻ and CN⁺

(3) 

(4)  NO⁺ and CN⁺

Show Answer

58. The ionization enthalpy of hydrogen atom is 1.312 × 10⁶ Jmol⁻¹. The energy required to excite the electron in the atom from n = 1 to n = 2 is

(1)  8.51 × 10⁵ Jmol⁻¹

(2)  6.56 × 10⁵ Jmol⁻¹

(3)  7.56 × 10⁵ Jmol⁻¹

(4)  9.84 × 10⁵ Jmol⁻¹

Show Answer

59. Which one of the following is the correct statement?

(1)  Boric acid is a protonic acid

(2)  Beryllium exhibits coordination number of six

(3)  Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase

(4)  B₂H₆ . 2NH₃ is known as ‘inorganic benzene’

Show Answer

60. Given  The potential for the cell Cr | Cr³⁺ (0.1 M)| | Fe²⁺(0.01 M)| Fe is

(1)  0.26 V

(2)  0.399 V

(3)  −0.339 V

(4)  −0.26 V

Show Answer

61. Amount of oxalic acid present in a solution can be determined by its titration with KMnO₄ solution in the presence of H₂SO₄. The titration gives unsatisfactory result when carried out in the presence of HCl, because HCl

(1)  gets oxidised by oxalic acid to chlorine

(2)  furnishes H⁺ ions in addition to those from oxalic acid

(3)  reduces permanganate to Mn²⁺

(4)  oxidises oxalic acid to carbon dioxide and water

Show Answer

62. The vapour pressure of water at 20°C is 17.5 mm Hg. If 18 g of glucose (C₆H₁₂O₆) is added to 178.2 g of water at 20°C, the vapour pressure of the resulting solution will be

(1)  17.675 mm Hg

(2)  15.750 mm Hg

(3)  16.500 mm Hg

(4)  17.325 mm Hg

Show Answer

63. Among the following substituted silanes the one which will give rise to cross linked silicone polymer on hydrolysis is

(1)  R₄Si

(2)  RSiCl₃

(3)  R₂SiCl₂

(4)  R₃SiCl

Show Answer

64. In context with the industrial preparation of hydrogen from water gas (CO + H₂), which of the following is the correct statement?

(1)  CO and H₂ are fractionally separated using differences in their densities

(2)  CO is removed by absorption in aqueous Cu₂Cl₂ solution

(3)  H₂ is removed through occlusion with Pd

(4)  CO is oxidized to CO₂ with steam in the presence of a catalyst followed by absorption of CO₂ in alkali

Show Answer

65. In a compound atoms of element Y from ccp lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of the compound will be

(1)  X₄Y₃

(2)  X₂Y₃

(3)  X₂Y

(4)  X₃Y₄

Show Answer

66. Gold numbers of protective colloids A, B, C and D are 0.50, 0.01, 0.10 and 0.005, respectively. The correct order of their protective powers is

(1)  D < A < C < B

(2)  C < B < D < A

(3)  A < C < B < D

(4)  B < D < A < C

Show Answer

67. The hydrocarbon which can react with sodium in liquid ammonia is

(1)  CH₃CH₂CH₂C ≡ CCH₂CH₂CH₃

(2)  CH₃CH₂C ≡ CH

(3)  CH₃CH = CHCH₃

(4)  CH₃CH₂C ≡ CCH₂­CH₃

Show Answer

68. The treatment of CH₃MgX with CH₃C≡C−H produces

(1)  CH₃ – CH = CH₂

(2)  CH₃C ≡ C – CH₃

(3) 

(4)  CH₄

Show Answer

69. The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is

(1)  −COOH, −SO₃H, −CONH₂, −CHO

(2)  −SO₃H, −COOH, −CONH₂, −CHO

(3)  −CHO, −COOH, −SO₃H, −CONH₂

(4)  −CONH₂, −CHO, −SO₃H, −COOH

Show Answer

70. The pK_a of a weak acid, HA, is 4.80. The pK_b of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be

(1)  9.58

(2)  4.79

(3)  7.01

(4)  9.22

Show Answer

Physics

PART – C

Directions: Questions No. 71, 72 and 73 are based on the following paragraph.

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by

requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in figure).

71. Electrons accelerated by potential V are diffracted from a crystal. If d = 1Å and i = 30°, V should be about (h = 6.6 × 10⁻³⁴ Js, me = 9.1 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C)

(1)  2000 V

(2)  50 V

(3)  500 V

(4)  1000 V

Show Answer

72. If a strong diffraction peak is observed when electrons are incident at an angle ‘i’ from the normal to the crystal planes with distance ‘d’ between them (see figure), de Broglie wavelength λ_dB of electrons can be calculated by the relationship (n is an integer)

(1)  d sin i = nλ_dB

(2)  2d cos i = nλ_dB

(3)  2d sin i = nλ_dB

(4)  d cos i = nλ_dB

Show Answer

73. In an experiment, electrons are made to pass through a narrow slit of width ‘d’ comparable to their de Broglie wavelength. They are detected on a screen at a distance ‘D’ from the slit (see figure).

Which of the following graph can be expected to represent the number of electrons ‘N’ detected as a function of the detector position ‘y’(y = 0 corresponds to the middle of the slit)?

(1) 

(2) 

(3) 

(4) 

Show Answer

74. A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 kms⁻¹, the escape velocity from the surface of the planet would be

(1)  1.1 kms⁻¹

(2)  11 kms⁻¹

(3)  110 kms⁻¹

(4)  0.11 kms⁻¹

Show Answer

75. A spherical solid ball of volume V is made of a material of density ρ₁. It is falling through a liquid of density ρ₂(ρ₂ <ρ₁). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e. F_viscous = −kv²(k > 0). The terminal speed of the ball is

(1) 

(2) 

(3) 

(4) 

Show Answer

76. Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.

The value of the unknown resistor R is

(1)  13.75 Ω

(2)  220 Ω

(3)  110 Ω

(4)  55 Ω

Show Answer

77. A thin rod of length ‘L’ is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as k(x/L)ⁿ, where n can be zero or any positive number. If the position x_CM of the centre of mass of the rod is plotted against ‘n’, which of the following graphs best approximates the dependence of x_CM on n?

(1) 

(2) 

(3) 

(4) 

Show Answer

78. While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then

(1)  18 > x

(2)  x > 54

(3)  54 > x > 36

(4)  36 > x > 18

Show Answer

79. The dimension of magnetic field in M, L, ,T and C (Coulomb) is given as

(1)  MLT⁻¹C⁻¹

(2)  MT²C⁻²

(3)  MT⁻¹C⁻¹

(4)  MT⁻²C⁻¹

Show Answer

80. Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

(1) 

(2) 

(3) 

(4) 

Show Answer

81. A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms⁻¹. The magnitude of its momentum is recorded as

(1)  17.6 kg ms⁻¹

(2)  17.565 kg ms⁻¹

(3)  17.56 kg ms⁻¹

(4)  17.57 kg ms⁻¹

Show Answer

82. An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

(1)  200 J − 500 J

(2)  2 × 10⁵ J − 3 × 10⁵ J

(3)  20,000 J – 50,000 J

(4)  2,000 J – 5,000 J

Show Answer

83. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is ‘d’. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k₁ = 3 and thickness d/3 while the other one has dielectric constant k₂ = 6 and thickness 2d/3. Capacitance of the capacitor is now

(1)  1.8 pF

(2)  45 pF

(3)  40.5 pF

(4)  20.25 pF

Show Answer

84. The speed of sound in oxygen (O₂) at a certain temperature is 460 ms⁻¹. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

(1)  460 ms⁻¹

(2)  500 ms⁻¹

(3)  650 ms⁻¹

(4)  330 ms⁻¹

Show Answer

85. This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement – I:

Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.

and

Statement – II

For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decrease with increasing Z.

(1)  Statement – 1is false, Statement – 2 is true.

(2)  Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.

(3)  Statement – 1is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.

(4)  Statement – 1 is true, Statement – 2 is False.

Show Answer

86. This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement – I:

For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides is 4π GM.

and

Statement – II

If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ for the source is given as 1/r², its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface

(1)  Statement – 1is false, Statement – 2 is true.

(2)  Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.

(3)  Statement – 1is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.

(4)  Statement – 1 is true, Statement – 2 is False.

Show Answer

87. A jar filled with two non mixing liquids 1 and 2 having densities ρ₁ and ρ₂ A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.

Which of the following is true for ρ₁, ρ₂ and ρ₃?

(1)  ρ₃ < ρ₁ < ρ₂

(2)  ρ₁ < ρ₃ < ρ₂

(3)  ρ₁ < ρ₂ < ρ₃

(4)  ρ₁ < ρ₃ < ρ₂

Show Answer

88. A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following is true for the transistor?

(1)  It is an npn transistor with R as base

(2)  It is a pnp transistor with R as collector

(3)  It is a pnp transistor with R as emitter

(4)  It is an npn transistor with R as collector

Show Answer

Directions: Question No. 89 and 90 are based on the following paragraph.

Consider a block of conducting material of resistivity ‘ρ’ shown in the figure. Current ‘I’ enters at ‘A’ and leaves from ‘D’. We apply superposition principle to find voltage ‘ΔV’ developed between ‘B’ and ‘C’. The calculation is done in the following steps:

(i) Take current ‘I’ entering from ‘A’ and assume it to spread over a hemispherical surface in the block.

(ii) Calculate field E(r) at distance ‘r’ from A by using Ohm’s law E = ρj, where j is the current per unit area at ‘r’.

(iii) From the ‘r’ dependence of E(r), obtain the potential V(r) at r.

(iv) Repeat (i), (ii) and (iii) for current ‘I’ leaving ‘D’ and superpose results for ‘A’ and ‘D’.

89. ∆V measured between B and C is

(1) 

(2) 

(3) 

(4) 

Show Answer

90. For current entering at A, the electric field at a distance ‘r’ from A is

(1) 

(2) 

(3) 

(4) 

Show Answer

91. A student measures the focal length of convex lens by putting an object pin at a distance ‘u’ from the lens and measuring the distance ‘v’ of the image pin. The graph between ‘u’ and ‘v’ plotted by the student should look like

(1) 

(2) 

(3) 

(4) 

Show Answer

92. A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

(1)  0.16 J

(2)  1.00 J

(3)  0.67 J

(4)  0.34 J

Show Answer

93. A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

(1) 

(2) 

(3) 

(4) 

Show Answer

94. Suppose an electron is attracted towards the origin by a force k/r where ‘k’ is a constant and ‘r’ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be ‘r_n’ and the kinetic energy of the electron to be T_n. Then which of the following is true?

(1)  T_n ∝ 1/n², r_n ∝ n²

(2)  T_n independent of n, r_n ∝ n

(3)  T_n ∝ 1/n, r_n ∝ n

(4)  T_n ∝ 1/n, r_n ∝ n²

Show Answer

95. A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos (αx −βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are

(1)  α = 25.00 π, β = π

(2) 

(3) 

(4)  α = 12.50 π, β = π/2.0

Show Answer

96. Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area A = 10 cm² and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is (μ₀ = 4π × 10⁻⁷ Tm A⁻¹)

(1)  2.4 π × 10⁻⁵ H

(2)  4.8 π × 10⁻⁴ H

(3)  4.8 π × 10⁻⁵ H

(4)  2.4 π × 10⁻⁴ H

Show Answer

97. In the circuit below, A and B represent two inputs and C represents the output.

The circuit represents

(1)  NOR gate

(2)  AND gate

(3)  NAND gate

(4)  OR gate

Show Answer

98. A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x-direction with a constant speed. The position of the first body is given by x₁(t) after time ‘t’ and that of the second body by x₂(t) after the same time interval. Which of the following graphs correctly describes (x₁ – x₂)as a function of time ‘t’?

(1) 

(2) 

(3) 

(4) 

Show Answer

99. An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by

(1)  a vernier scale provided on the microscope

(2)  a standard laboratory scale

(3)  a meter scale provided on the microscope

(4)  a screw gauage provided on the microscope

Show Answer

100. A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0 ≤ r < ∞ , where r is the distance from the centre of the shell?

(1) 

(2) 

(3) 

(4) 

Show Answer

101. A 5V battery with internal resistance 2Ω and a 2V battery with internal resistance 1Ω are connected to a 10Ω resistor as shown in the figure. The current in the 10 Ω resistor is

(1)  0.27 A P₂ to P₁

(2)  0.03 A P₁ to P₂

(3)  0.03 A P₂ to P₁

(4)  0.27 A P₁ to P₂

Show Answer

102. A horizontal overhead power line is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is (μ0 = 4π × 10⁻⁷T m A⁻¹)

(1)  2.5 × 10⁻⁷ T southward

(2)  5 × 10⁻⁶ T northward

(3)  5 × 10⁻⁶ T southward

(4)  2.5 × 10⁻⁷ T northward

Show Answer

103. Relative permittivity and permeability of a material are ε_r and μ_r, respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

(1)  ε_r = 0.5, μ_r = 1.5

(2)  ε_r = 1.5, μ_r = 0.5

(3)  ε_r = 0.5, μ_r = 0.5

(4)  ε_r = 1.5, μ_r = 1.5

Show Answer

104. Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

(1)  3.32 mm

(2)  3.73 mm

(3)  3.67 mm

(4)  3.38 mm

Show Answer

105. An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V₁ and contains ideal gas at pressure P₁ and temperature T₁. The other chamber has volume V₂ and contains ideal gas at pressure P₂ and temperature T₂. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

(1) 

(2) 

(3) 

(4) 

Show Answer

Physics		Chemistry		Maths
Q 1	1	Q 1	4	Q 1	2
Q 2	1	Q 2	4	Q 2	3
Q 3	2	Q 3	2	Q 3	1
Q 4	4	Q 4	4	Q 4	3
Q 5	3	Q 5	3	Q 5	4
Q 6	4	Q 6	3	Q 6	1
Q 7	4	Q 7	3	Q 7	2
Q 8	2	Q 8	4	Q 8	3
Q 9	2	Q 9	2	Q 9	3
Q 10	4	Q 10	3	Q 10	1
Q 11	4	Q 11	1	Q 11	1
Q 12	1	Q 12	1	Q 12	3
Q 13	3	Q 13	4	Q 13	2
Q 14	2	Q 14	1	Q 14	2
Q 15	2	Q 15	4	Q 15	1
Q 16	2	Q 16	4	Q 16	4
Q 17	2	Q 17	4	Q 17	1
Q 18	4	Q 18	2	Q 18	4
Q 19	4	Q 19	1	Q 19	1
Q 20	1	Q 20	3	Q 20	3
Q 21	2	Q 21	1	Q 21	2
Q 22	4	Q 22	3	Q 22	4
Q 23	1	Q 23	2	Q 23	1
Q 24	4	Q 24	1	Q 24	3
Q 25	3	Q 25	1	Q 25	4
Q 26	1	Q 26	3	Q 26	4
Q 27	1	Q 27	1	Q 27	2
Q 28	4	Q 28	1	Q 28	3
Q 29	3	Q 29	2	Q 29	2
Q 30	2	Q 30	4	Q 30	4

 

Physics		Chemistry		Maths
Q 1	1	Q 1	4	Q 1	2
Q 2	1	Q 2	4	Q 2	3
Q 3	2	Q 3	2	Q 3	1
Q 4	4	Q 4	4	Q 4	3
Q 5	3	Q 5	3	Q 5	4
Q 6	4	Q 6	3	Q 6	1
Q 7	4	Q 7	3	Q 7	2
Q 8	2	Q 8	4	Q 8	3
Q 9	2	Q 9	2	Q 9	3
Q 10	4	Q 10	3	Q 10	1
Q 11	4	Q 11	1	Q 11	1
Q 12	1	Q 12	1	Q 12	3
Q 13	3	Q 13	4	Q 13	2
Q 14	2	Q 14	1	Q 14	2
Q 15	2	Q 15	4	Q 15	1
Q 16	2	Q 16	4	Q 16	4
Q 17	2	Q 17	4	Q 17	1
Q 18	4	Q 18	2	Q 18	4
Q 19	4	Q 19	1	Q 19	1
Q 20	1	Q 20	3	Q 20	3
Q 21	2	Q 21	1	Q 21	2
Q 22	4	Q 22	3	Q 22	4
Q 23	1	Q 23	2	Q 23	1
Q 24	4	Q 24	1	Q 24	3
Q 25	3	Q 25	1	Q 25	4
Q 26	1	Q 26	3	Q 26	4
Q 27	1	Q 27	1	Q 27	2
Q 28	4	Q 28	1	Q 28	3
Q 29	3	Q 29	2	Q 29	2
Q 30	2	Q 30	4	Q 30	4

Physics		Chemistry		Maths
Q 1	1	Q 1	4	Q 1	2
Q 2	1	Q 2	4	Q 2	3
Q 3	2	Q 3	2	Q 3	1
Q 4	4	Q 4	4	Q 4	3
Q 5	3	Q 5	3	Q 5	4
Q 6	4	Q 6	3	Q 6	1
Q 7	4	Q 7	3	Q 7	2
Q 8	2	Q 8	4	Q 8	3
Q 9	2	Q 9	2	Q 9	3
Q 10	4	Q 10	3	Q 10	1
Q 11	4	Q 11	1	Q 11	1
Q 12	1	Q 12	1	Q 12	3
Q 13	3	Q 13	4	Q 13	2
Q 14	2	Q 14	1	Q 14	2
Q 15	2	Q 15	4	Q 15	1
Q 16	2	Q 16	4	Q 16	4
Q 17	2	Q 17	4	Q 17	1
Q 18	4	Q 18	2	Q 18	4
Q 19	4	Q 19	1	Q 19	1
Q 20	1	Q 20	3	Q 20	3
Q 21	2	Q 21	1	Q 21	2
Q 22	4	Q 22	3	Q 22	4
Q 23	1	Q 23	2	Q 23	1
Q 24	4	Q 24	1	Q 24	3
Q 25	3	Q 25	1	Q 25	4
Q 26	1	Q 26	3	Q 26	4
Q 27	1	Q 27	1	Q 27	2
Q 28	4	Q 28	1	Q 28	3
Q 29	3	Q 29	2	Q 29	2
Q 30	2	Q 30	4	Q 30	4

 

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Q 1	1	Q 1	4	Q 1	2
Q 2	1	Q 2	4	Q 2	3
Q 3	2	Q 3	2	Q 3	1
Q 4	4	Q 4	4	Q 4	3
Q 5	3	Q 5	3	Q 5	4
Q 6	4	Q 6	3	Q 6	1
Q 7	4	Q 7	3	Q 7	2
Q 8	2	Q 8	4	Q 8	3
Q 9	2	Q 9	2	Q 9	3
Q 10	4	Q 10	3	Q 10	1
Q 11	4	Q 11	1	Q 11	1
Q 12	1	Q 12	1	Q 12	3
Q 13	3	Q 13	4	Q 13	2
Q 14	2	Q 14	1	Q 14	2
Q 15	2	Q 15	4	Q 15	1
Q 16	2	Q 16	4	Q 16	4
Q 17	2	Q 17	4	Q 17	1
Q 18	4	Q 18	2	Q 18	4
Q 19	4	Q 19	1	Q 19	1
Q 20	1	Q 20	3	Q 20	3
Q 21	2	Q 21	1	Q 21	2
Q 22	4	Q 22	3	Q 22	4
Q 23	1	Q 23	2	Q 23	1
Q 24	4	Q 24	1	Q 24	3
Q 25	3	Q 25	1	Q 25	4
Q 26	1	Q 26	3	Q 26	4
Q 27	1	Q 27	1	Q 27	2
Q 28	4	Q 28	1	Q 28	3
Q 29	3	Q 29	2	Q 29	2
Q 30	2	Q 30	4	Q 30	4

Physics		Chemistry		Maths
Q 1	1	Q 1	4	Q 1	2
Q 2	1	Q 2	4	Q 2	3
Q 3	2	Q 3	2	Q 3	1
Q 4	4	Q 4	4	Q 4	3
Q 5	3	Q 5	3	Q 5	4
Q 6	4	Q 6	3	Q 6	1
Q 7	4	Q 7	3	Q 7	2
Q 8	2	Q 8	4	Q 8	3
Q 9	2	Q 9	2	Q 9	3
Q 10	4	Q 10	3	Q 10	1
Q 11	4	Q 11	1	Q 11	1
Q 12	1	Q 12	1	Q 12	3
Q 13	3	Q 13	4	Q 13	2
Q 14	2	Q 14	1	Q 14	2
Q 15	2	Q 15	4	Q 15	1
Q 16	2	Q 16	4	Q 16	4
Q 17	2	Q 17	4	Q 17	1
Q 18	4	Q 18	2	Q 18	4
Q 19	4	Q 19	1	Q 19	1
Q 20	1	Q 20	3	Q 20	3
Q 21	2	Q 21	1	Q 21	2
Q 22	4	Q 22	3	Q 22	4
Q 23	1	Q 23	2	Q 23	1
Q 24	4	Q 24	1	Q 24	3
Q 25	3	Q 25	1	Q 25	4
Q 26	1	Q 26	3	Q 26	4
Q 27	1	Q 27	1	Q 27	2
Q 28	4	Q 28	1	Q 28	3
Q 29	3	Q 29	2	Q 29	2
Q 30	2	Q 30	4	Q 30	4

 

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Q 3	2	Q 3	2	Q 3	1
Q 4	4	Q 4	4	Q 4	3
Q 5	3	Q 5	3	Q 5	4
Q 6	4	Q 6	3	Q 6	1
Q 7	4	Q 7	3	Q 7	2
Q 8	2	Q 8	4	Q 8	3
Q 9	2	Q 9	2	Q 9	3
Q 10	4	Q 10	3	Q 10	1
Q 11	4	Q 11	1	Q 11	1
Q 12	1	Q 12	1	Q 12	3
Q 13	3	Q 13	4	Q 13	2
Q 14	2	Q 14	1	Q 14	2
Q 15	2	Q 15	4	Q 15	1
Q 16	2	Q 16	4	Q 16	4
Q 17	2	Q 17	4	Q 17	1
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Q 20	1	Q 20	3	Q 20	3
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Q 22	4	Q 22	3	Q 22	4
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Q 24	4	Q 24	1	Q 24	3
Q 25	3	Q 25	1	Q 25	4
Q 26	1	Q 26	3	Q 26	4
Q 27	1	Q 27	1	Q 27	2
Q 28	4	Q 28	1	Q 28	3
Q 29	3	Q 29	2	Q 29	2
Q 30	2	Q 30	4	Q 30	4

Physics		Chemistry		Maths
Q 1	3	Q 1	3	Q 1	2
Q 2	4	Q 2	1	Q 2	4
Q 3	3	Q 3	4	Q 3	1
Q 4	3	Q 4	2	Q 4	2
Q 5	1	Q 5	1	Q 5	1
Q 6	2	Q 6	3	Q 6	2
Q 7	3	Q 7	4	Q 7	3
Q 8	2	Q 8	2	Q 8	2
Q 9	3	Q 9	2	Q 9	4
Q 10	3	Q 10	2	Q 10	3
Q 11	2	Q 11	2	Q 11	3
Q 12	4	Q 12	1	Q 12	3
Q 13	2	Q 13	2	Q 13	4
Q 14	4	Q 14	3	Q 14	1
Q 15	1	Q 15	3	Q 15	3
Q 16	1	Q 16	3	Q 16	3
Q 17	4	Q 17	4	Q 17	1
Q 18	4	Q 18	1	Q 18	1
Q 19	4	Q 19	2	Q 19	1
Q 20	3	Q 20	2	Q 20	3
Q 21	3	Q 21	3	Q 21	1
Q 22	1	Q 22	1	Q 22	2
Q 23	4	Q 23	3	Q 23	1
Q 24	1	Q 24	1	Q 24	2
Q 25	1	Q 25	3	Q 25	3
Q 26	4	Q 26	1	Q 26	3
Q 27	1	Q 27	2	Q 27	3
Q 28	2	Q 28	2	Q 28	4
Q 29	2	Q 29	1	Q 29	2
Q 30	1	Q 30	4	Q 30	4

 

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Q 1	3	Q 1	3	Q 1	2
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Q 3	3	Q 3	4	Q 3	1
Q 4	3	Q 4	2	Q 4	2
Q 5	1	Q 5	1	Q 5	1
Q 6	2	Q 6	3	Q 6	2
Q 7	3	Q 7	4	Q 7	3
Q 8	2	Q 8	2	Q 8	2
Q 9	3	Q 9	2	Q 9	4
Q 10	3	Q 10	2	Q 10	3
Q 11	2	Q 11	2	Q 11	3
Q 12	4	Q 12	1	Q 12	3
Q 13	2	Q 13	2	Q 13	4
Q 14	4	Q 14	3	Q 14	1
Q 15	1	Q 15	3	Q 15	3
Q 16	1	Q 16	3	Q 16	3
Q 17	4	Q 17	4	Q 17	1
Q 18	4	Q 18	1	Q 18	1
Q 19	4	Q 19	2	Q 19	1
Q 20	3	Q 20	2	Q 20	3
Q 21	3	Q 21	3	Q 21	1
Q 22	1	Q 22	1	Q 22	2
Q 23	4	Q 23	3	Q 23	1
Q 24	1	Q 24	1	Q 24	2
Q 25	1	Q 25	3	Q 25	3
Q 26	4	Q 26	1	Q 26	3
Q 27	1	Q 27	2	Q 27	3
Q 28	2	Q 28	2	Q 28	4
Q 29	2	Q 29	1	Q 29	2
Q 30	1	Q 30	4	Q 30	4

Physics		Chemistry		Maths
Q 1	3	Q 1	3	Q 1	2
Q 2	4	Q 2	1	Q 2	4
Q 3	3	Q 3	4	Q 3	1
Q 4	3	Q 4	2	Q 4	2
Q 5	1	Q 5	1	Q 5	1
Q 6	2	Q 6	3	Q 6	2
Q 7	3	Q 7	4	Q 7	3
Q 8	2	Q 8	2	Q 8	2
Q 9	3	Q 9	2	Q 9	4
Q 10	3	Q 10	2	Q 10	3
Q 11	2	Q 11	2	Q 11	3
Q 12	4	Q 12	1	Q 12	3
Q 13	2	Q 13	2	Q 13	4
Q 14	4	Q 14	3	Q 14	1
Q 15	1	Q 15	3	Q 15	3
Q 16	1	Q 16	3	Q 16	3
Q 17	4	Q 17	4	Q 17	1
Q 18	4	Q 18	1	Q 18	1
Q 19	4	Q 19	2	Q 19	1
Q 20	3	Q 20	2	Q 20	3
Q 21	3	Q 21	3	Q 21	1
Q 22	1	Q 22	1	Q 22	2
Q 23	4	Q 23	3	Q 23	1
Q 24	1	Q 24	1	Q 24	2
Q 25	1	Q 25	3	Q 25	3
Q 26	4	Q 26	1	Q 26	3
Q 27	1	Q 27	2	Q 27	3
Q 28	2	Q 28	2	Q 28	4
Q 29	2	Q 29	1	Q 29	2
Q 30	1	Q 30	4	Q 30	4

 

Physics		Chemistry		Maths
Q 1	3	Q 1	3	Q 1	2
Q 2	4	Q 2	1	Q 2	4
Q 3	3	Q 3	4	Q 3	1
Q 4	3	Q 4	2	Q 4	2
Q 5	1	Q 5	1	Q 5	1
Q 6	2	Q 6	3	Q 6	2
Q 7	3	Q 7	4	Q 7	3
Q 8	2	Q 8	2	Q 8	2
Q 9	3	Q 9	2	Q 9	4
Q 10	3	Q 10	2	Q 10	3
Q 11	2	Q 11	2	Q 11	3
Q 12	4	Q 12	1	Q 12	3
Q 13	2	Q 13	2	Q 13	4
Q 14	4	Q 14	3	Q 14	1
Q 15	1	Q 15	3	Q 15	3
Q 16	1	Q 16	3	Q 16	3
Q 17	4	Q 17	4	Q 17	1
Q 18	4	Q 18	1	Q 18	1
Q 19	4	Q 19	2	Q 19	1
Q 20	3	Q 20	2	Q 20	3
Q 21	3	Q 21	3	Q 21	1
Q 22	1	Q 22	1	Q 22	2
Q 23	4	Q 23	3	Q 23	1
Q 24	1	Q 24	1	Q 24	2
Q 25	1	Q 25	3	Q 25	3
Q 26	4	Q 26	1	Q 26	3
Q 27	1	Q 27	2	Q 27	3
Q 28	2	Q 28	2	Q 28	4
Q 29	2	Q 29	1	Q 29	2
Q 30	1	Q 30	4	Q 30	4