| Mathematics |
|
1. m[-3 4]+n[4 –3] = [10 –11]  3m+7n
=
|
| 1. 3 |
2. 5 |
| 3. 10 |
4. 1 |
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2. 
|
| 1. 110 |
2. 115 |
| 3. 120 |
4. 135 |
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3. The direction cosines of the line passing through (2,3-1) and the origin are:
|
1.  |
2.  |
3.  |
4.  |
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4. I: , , Two non-zero, non-collinera vectors are linearly dependent.
II: , , Any three coplanar vectors are linearly dependent.
Which of the above statements is true?
|
| 1. Only I |
2. Only II |
| 3. Both I and II |
4. Neither I nor II |
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5. If N
denotes the set all positive integers and if f: NŕN
is defined by f(n)=the sum of positive divisions of n then f(2k.3),where
k is a positive integers is:
|
| 1. 2k+1-1 |
2. 2(2k+1-1) |
| 3. 3(2k+1-1) |
4. 2(2k+1-1) |
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6. 
|
1.  |
2.  |
3.  |
4.  |
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7. If  are the roots of x3+2x2-3x-1=0,
then 
|
| 1. 12 |
2. 13 |
| 3. 14 |
4. 15 |
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8. 
|
1.  |
2.  |
3.  |
4.  |
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9. 
|
1.  1 |
2. 0 |
| 3. 2 |
4. 4 |
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10. The equation of the circle whose diameter is the common chord of the circles x2+y2+2x+3y+2=0
and x2+y2+2x+3y+2=0
|
| 1. x2+y2+2x+2y+2=0 |
2. x2+y2+2x+2y-1=0 |
| 3. x2+y2+2x+2y+1=0 |
4. x2+y2+2x+2y+3=0 |
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11. The Cartesian form of the polar equation  is:
|
| 1. x=2y |
2. y=2x |
| 3. x=4y |
4. y=4x |
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12. The parabola with directrix x+2y-1=0 and focus (1,0) is:
|
| 1. 4x2-4xy+y2-8x+4y+4=0 |
2. 4x2+4xy+y2-8x+4y+4=0 |
| 3. 4x2+4xy+y2+8x-4y+4=0 |
4. 4x2-4xy+y2-8x-4y+4=0 |
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13. If  is a non-real
root of x6=1, then 
|
1.  |
2. |
3.  |
4. |
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14. If PM is the perpendicular from P(2,3) onto the line x+y=3, then the coordinates of M are:
|
| 1. (2,1) |
2. (-1, 4) |
| 3. (1,2) |
4. (4,-1) |
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15. A tower, of x metres high, has flagstaff
at its top. The tower and the flagstaff subtend equal angles at a point distant y metres from the foot of the tower. Then the length of the flagstaff in metres is:
|
1.  |
2.  |
3.  |
4.  |
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16. The roots of the equation x3-3x-2=0
are:
|
| 1. -1, -1, 2 |
2. -1, -1, -2 |
| 3. -1, 2, -3 |
4. -1, -1, -2 |
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17. In a 
|
| 1. a |
2. b |
| 3. c |
4. 0 |
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18. 
|
| 1. 1 |
2. 2 |
| 3. 3 |
4.  |
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19. If  respectively
denote the moduli of the complex number –I,  and –1+I, then their increasing order is:
|
| 1. |
2.  |
| 3. |
4.  |
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20. If x-y+1=0 meets the circle x2+y2+y-1=0 at A and B, then the equation of the circle with AB as diameter is:
|
| 1. 2(x2+y2)+3x-y+1=0 |
2. 2(x2+y2)+3x-y+2=0 |
| 3. 2(x2+y2)+3x-y+3=0 |
4. x2+y2+3x-y+1=0 |
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| Chemistry |
|
21. 100 ml. Of 0.015 m HCl solution is mixed with 100 ml. Of 0.005 M HCl . What is the pH of the resultant solution ?
|
| 1. 2.5 |
2. 1.5 |
| 3. 2 |
4. 1 |
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22. pH of the aqueous solution of 0.1 MCH3COONa is
|
| 1. 0 |
2. 7 |
| 3. <7 |
4. >7 |
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23. Which of the following compounds possess zero dipolemoment?
|
| 1. CHCl3 |
2. CH2Cl2 |
| 3. CHCl |
4. CH4 |
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24. Enhanced green house effect is mainly due to the increase in the level of
|
| 1. CO2 |
2. NO |
| 3. N2 |
4. CO |
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25. The following equation represents the formation of carbon dioxide
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| 1. CO(g) + 1/2O2(g) -> CO2(g) |
2. C graphite + O2 (g) -> CO2 (g) |
| 3. CaCO3 (s) -> CaO(s)+ CO2(g) |
4. CO(g) + H2O (g) -> CO2 (g)+ H2 (g) |
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26. Ethylene chloro hydrine is the product obtained by the reaction between
|
| 1. CH2 = CH2 + HOCl |
2. CH2 = CH2 + H2 |
| 3. CH2 = CH2 + Cl2 |
4. CH2 = CH2 + HO Br |
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27. Which of the following possess acidic hydrogen?
|
| 1. C2H6 |
2. C2H4 |
| 3. C2H2 |
4. CH4 |
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28. In which of the following reactions, the concentration of reactant is equal to concentration of product at equilibrium (K = equilibrium constant)
|
| 1. A =B ; K = 0.01 |
2. R = P ; K = 1 |
| 3. X = Y ; K = 10 |
4. L =J ; K = 0.025. |
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29. F2when heated with conc. NaOH liberates
|
| 1. O2 |
2. H2 |
| 3. OF2 |
4. PH3 |
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30. Which one of the following series of lines is found in ultraviolet region of the atomic spectrum of hydrogen
|
| 1. Balmer series |
2. Paschen series |
| 3. Brackeet series |
4. Lyman series |
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31. 0.1 kg sample of hard water contains 22.2 mg CaCl2. the degree of hardness in ppm is
|
| 1. 10ppm |
2. 75ppm |
| 3. 200ppm |
4. 100ppm |
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32. The value of kc for AB(g) *** 1/2 A2(g) + B2(g) *** 2AB (g) is
|
| 1. 4 x 10-2 |
2. 2 x 10-5 |
| 3. 50 |
4. 25 |
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33. Chloroform is stored in dark coloured bottle filled up to the neck and kept in a dark place. This is to avoid its
|
| 1. Oxidation |
2. Reduction |
| 3. Hydrolysis |
4. Dehalogenation |
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34. (CH3)2 CH - CH2Cl is
|
| 1. A primary alkyl halide |
2. A secondary alkyl halide |
| 3. A tertiary alkyl halide |
4. A halogen derivative of Straight chain alkane |
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35. Assertion: A1F3 is ionic compound where as BF3 is a covalent compund.
Reason: BF3 involves back it bonding
|
| 1. Both A and R are correct and R is the correct explanation of A |
2. Both A and R are correct but R is not correct explanation of A |
| 3. A is correct but R is wrong |
4. A is wrong but R is correct |
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36. Sulphur reacts with chlorine in 1 : 2 ratio and forms X. Hydrolysis of X gives a sulphur compound Y. What is the hybridization state of central atom in the anion of Y ?
|
| 1. sp3 |
2. sp |
| 3. sp2 |
4. sp3d |
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37. In which one of the following compound Fe has least oxidation state?
|
| 1. FeSO4 |
2. K4 [Fe(CN)6] |
| 3. Fe2O3 |
4. Fe(CO)5 |
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38. The elctrolyte used in Castners process of sodium extraction is
|
| 1. Aqueous Na2CO3 |
2. Aqueous NaOH |
| 3. NaCl + CaCl2 |
4. Fusd anhydrous NaOH |
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39. Aspirin is formed when p – aminophenol undergoes
|
| 1. Acetylation |
2. Benzoylation |
| 3. Oxidation |
4. Sulphonation |
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40. One of the elements present in Carnalite shows flame coouration. The colour of the flame is
|
| 1. Orange |
2. Green |
| 3. Yellow |
4. Lilac |
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| Physics |
|
41. An
inductance 1H is connected in series with an A.C. source of 220 V and 50 Hz.
The inductive reactance (in ohms) is:
|
1. 2 |
2. 50 |
| 3. 100 |
4. 1000 |
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42. Consider
the following statements (A) and (B) and identify the correct answer:
(A):In
an elastic collision, if a body suffers a head on collision with another of
same mass at rest, the first body comes to rest while the other starts moving with the velocity of the first one.
(B):Two
bodies of equal masses suffering a head-on elastic collision merely exchanges their velocities.
|
| 1. Both (A) and (B) are true |
2. (A) is true but (B) is false |
| 3. (A) is true but (B) is false |
4. (A) is false but (B) is true |
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43. If two
identical bar magnets, each of length l pole strength m and magnetic moment
M are placed perpendicular to each other with their unlike poles in contact,
the magnetic moment of the combination is:
|
1.  |
2.  |
3.  |
4. 2M |
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44. The tyre of a motor car contains air at 150C. if the temperature increases to 350C, the approximate percentage increase in pressure
is (ignore the expansion of tyre)
|
| 1. 7 |
2. 9 |
| 3. 11 |
4. 13 |
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45. Assertion
(A):Propagation of light through an optical fibre is due to total internal
reflection taking place at the core-clad interface.
Reason
(R):Refractive index of the material of the core of the optical fibre is greater than that of air.
|
| 1. Both (A) and (R) are true and (R) is the correct explanation of (A) |
2. Both (A) and (R) are true but (R) is not the correct explanation of (A) |
| 3. (A) is true but (R) is false |
4. (A) is false but (R) is true |
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46. An
iron sphere of mass 20 x 10-3kg falls through a viscous liquid with
terminal celocity 0.5 ms-1. the terminal velocity (in ms-1)
of another iron sphere of mass 54 x 10-2 kg is:
|
| 1. 4.5 |
2. 3.5 |
| 3. 2.5 |
4. 1.5 |
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47. With a
standard rectangular bar magnet of length (l), breadth (b; b<<l) and magnetic
moment. M, the time period of the magnet in a vibration magnetometer is 4s. if
the magnet is cut normal to its length into four equal pieces, the time period
(in seconds) with one of the pieces is:
|
| 1. 16 |
2. 2 |
| 3. 1 |
4. 1/4 |
| |
48. Identify
the increasing order of the angular velocities of the following
a)earth rotating about its own axis
b)hours hand of a clock
c)seconds hand of a clock
d)flywheel of radius 2m making 300 r.p.m.
|
| 1. (a),(b), (c), (d) |
2. (b), (c), (d), (a) |
| 3. (c),(d), (a), (b) |
4. (d), (a), (b), (c) |
| |
49. A
particle of mass 1x10-26 kg and charge 1.6x10-19C traveling with a velocity 1.28x106ms-1 along the postive
X-axis enters a region in which a uniform electric field  and a uniform magnetic
field of induction  are present. If  , the direction of motion
of the particles is:
|
| 1. Along the positive X-axis |
2. Along the negative X-axis |
| 3. At 450 to the positive X-axis |
4. At 1350 to the positive X-axis |
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50. Magnetic
field induction at the center of a circular coil of radius 5 cm and carrying a current 0.9A is (in S.I. units) ( =absolute permittivity of air in S.I.units, velocity of light = 3x 108 ms-1)
|
1.  |
2.  |
3.  |
4.  |
| |
51. In a
meter bridge a 30  resistance is connected in the left
gap a pair of resistances P and Q in the right gap. Measured from the left, the
balance point is 37.5 cm when P and Q are in series and 7.14 cm when they are
parallel. The value of P and Q (in ) are:
|
| 1. 40,10 |
2. 35,15 |
| 3. 30,20 |
4. 25,25 |
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52. A
thin wire ring of 3 cm radius rests flat on the surface of a liquid. The pull
required to raise the ring before the film breaks is 30.14 X 10-3N
more than it is after. The surface tension of the liquid (in Nm-1)
is:
|
| 1. 80 x 10-3 |
2. 87 x 10-3 |
| 3. 90 x 10-3 |
4. 98 x 10-3 |
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53. Degenereate electron pressure will not be sufficient to prevent core collapse of white dwarf if its mass becomes n times of our solar mass. Value of ‘n’ is:
|
| 1. 0.5 |
2. 0.8 |
| 3. 1 |
4. 1.4 |
| |
54. The
difference between volume and pressure coefficients of an ideal gas is:
|
| 1. 1/273 |
2. 273 |
| 3. 2/273 |
4. Zero |
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55. A
vehicle sounding a whistle of frequency 256 Hz is moving on a straight road,
towards a hill with a velocity of 10ms-1. The number of beats per
second observed a person traveling in the vehicle is : (velocity of sound = 330
ms-1).
|
| 1. Zero |
2. 10 |
| 3. 14 |
4. 16 |
| |
56. The
equation of trajectory of a projectile is  .If
we assume g=10 ms-2, the range of projectile (in meters) is:
|
| 1. 36 |
2. 24 |
| 3. 18 |
4. 9 |
| |
57. Two
parallel rails of a railway track insulated from each other and with the ground
are connected to a millivoltmeter. The distance between the rails is one meter.
A train is traveling with a velocity of 72 kmph along the track. The reading of
the millivoltemetr (in mV) is: (Vertical component of the earth’s magnetic
induction is 2x10-5T)
|
| 1. 1.44 |
2. 0.72 |
| 3. 0.4 |
4. 0.2 |
| |
58. The
focal length of an equi-convex lens is greater than the radius of curvature of
any of the surfaces. Then the refractive index of the material of the lens is:
|
| 1. Greater than zero but less tthan 1.5 |
2. Greater than 1.5 but less than 2.0 |
| 3. Greater then 2.0 but less than 2.5 |
4. Greater than but less than 3.0 |
| |
59. The center of mass of three particles of masses ikg, 2kg and 3kg is at (2, 2, 2). The position of the fourth mass of 4 kg to be placed in the system so that the new center of mass is at (0, 0 , 0) is:
|
| 1. (-3,-3,-3) |
2. (-3,3,-3) |
| 3. (2,3,-3) |
4. (2,-2,3) |
| |
60. The
radii and Youngs moduli of two uniform wires A and B are in the ratio 2: 1 and
1:2 respectively. Both wires are subjected to the same longitudinal force. If
the increase the percentage of the wire A is one per cent, the percentage
increase in length of the wire B is:
|
| 1. 1.0 |
2. 1.5 |
| 3. 2.0 |
4. 3.0 |
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