kerala model entrance exam repeaters – engineering...
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KKEERRAALLAA MMOODDEELL EENNTTRRAANNCCEE EEXXAAMM RREEPPEEAATTEERRSS –– EENNGGIINNEEEERRIINNGG ((MMOODDUULLEE –– VVII))
PPHHYYSSIICCAALL WWOORRLLDD,, UUNNIITTSS AANNDD MMEEAASSUURREEMMEENNTTSS,, MMOOTTIIOONN IINN AA SSTTRRAAIIGGHHTT LLIINNEE,, MMOOTTIIOONN IINN AA
PPLLAANNEE,, LLAAWWSS OOFF MMOOTTIIOONN,, GGRRAAVVIITTAATTIIOONN,,PPEERRIIOODDIICC TTAABBLLEE,, HHYYDDRROOGGEENN,, SS && PP BBLLOOCCKK
EELLEEMMEENNTTSS,,RREEDDOOXX RREEAACCTTIIOONNSS,,SSTTRRAAIIGGHHTT LLIINNEESS,,CCIIRRCCLLEESS,,CCOONNIICCSS,,CCOOMMPPLLEEXX NNUUMMBBEERRSS
1. It F denotes force and t time , then in equation
F=at-1+bt2, the dimensions of a and b, respectively are a) [LT-4]and [LT-1] b) [LT-1]and [LT-4] c) [MLT -4]and [MLT-1] d) [MLT -1]and [MLT-4] e) [MLT-3]and [MLT-2]
2. Dimensional formula of Stefan`s constant is a) [MT-3K-4] b) [ML2T-2K-4] c) [ML2T-2] d) [ML -2L0] e) [MT-4L0]
3. The physical quantity angular momentum has the same dimensions as that of a) work b) force c) momentum d) torque e) planck`s constant
4. Which of the following sets of quantities have same dimensional formula? a) Frequency , angular frequency and angular momentum b) Surface tension, stress and spring constant c) Accleration , momentum and retardation d) thermal capacity, specific heat and entropy e) Work, energy and torque
5. In a single pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time period is 3%. Then, the maximum percentage error in determination of the acceleration due to gravity g is a) 5% b) 6% c) 7% d) 8% e) 10%
6. The pitch and the number of circular scale divisions in a screw gauge with least count 0.02 mm are respectively a) 1mm and 100 b) 0.5 mm and 50 c) 1mm and 50 d) 0.5 mm and 100 e) 1mm and 200
7. A ball is dropped from the top of tower of height 100 m and at the same time another ball is projected vertically upward from ground with a velocity 25 ms-1 . Then , the distance from the top of the tower at which the two balls meet is a) 68.4 m b) 48.4 m c)18.4 m d) 28.4 m e) 78.4m
8. A particle starting with certain initial velocity and uniform acceleration covers a distance of 12m in first 3 s and a distance of 30m in next 3s. The initial velocity of the particle is a) 3 ms-1 b) 2.5ms-1 c) 2 ms-1 d) 1.5 ms-1 e) 1 ms-1
9. A particle is moving with constant acceleration from A to B in a straight line AB. If u and v are the velocities at A and B , respectively then, its velocity at the mid-point C will be
a) 22 2
2
u v
u
+
b) 2
u v+
c) 2
v u− d) 2 2
2
u v+
e) None of these
10. A particle crossing the origin of coordinates at time t=0, moves in the xy-plane with a constant acceleration a in a y-direction. If, its equation of motion is y=bx2(where , is b is a constant) its velocity component in the x-direction is
a) 2b
a b)
2
a
b
c) a
b d)
b
a e) ab
11. A ball A is thrown up vertically with a speed u and at the same instant another ball B is released from a height h. At time t, then the speed of A relative to B is a) u b) 2u c) u-gt
d) 2( )u gt− e) gt
12. A bullet fired into a fixed wooden block loses half of its velocity after penetrating 40cm. It comes to rest after penetrating a further distance of
a ) 22
cm3
b) 40
cm3
c) 20
cm3
d) 22
cm5
e) 26
cm5
13. A boat travels 50 km due to east, then 120 km due north and finally it comes back to the starting point through the shortest distance. The total time of journey is 3h. What is the average speed (in kmh-1) over the entire trip? a) Zero b) 100 c) 17 d) 33.33 e) 86.7
2211--33--1199 VVeerrssiioonn CCooddee:: AA Time : 2 ½ Hours
14. A cyclist starts from the centre O of a circular park of radius 1km , reaches the edge P of the park, then cycle along the circumference and returns to the point O as shown in figure. If the round trip takes 10 min, the net displacement and average speed of the cyclist (in metre and kilometer per hour) are
a) 0, 1 b) 4
, 02
π +
c) 4
21.4, 2
π + d) 0, 21.4 e) 0, 24.14
15. The coordinates of a particle moving in XY-plane at any instant of time t are x= 4t2, y=3t2. The speed of the particle at that instant is
a) 10t b) 5t c) 3t d) 2t e) 13t 16. The resultant of two vectors P and Q is R. If the
magnitude of Q is doubled, then the new resultant becomes perpendicular to P. Then, the magnitude of R is
a) P+Q b) Q c) P d) 2
P Q+ e) P-Q
17. A train of 150 m length is going towards North direction at a speed of 10 ms-1. A parrot flies at a speed of 5 ms-1 towards South direction parallel to the railway track. The time taken by the parrot to cross the train is equal to a) 12 s b) 8s c) 15s d) 10s e) 5s
18. A bridge is in the form of a semi-circle of radius 40m. The greatest speed with which a motor cycle can cross the bridge without leaving the ground at the highest point is (take , g=10ms-2 and frictional force is negligibly small ) a) 40ms-1 b) 20ms-1 c) 30ms-1 d) 15 ms-1 e) 25 ms-1
19. The time period f the second`s hand of a watch is a) 1 h b) 1s c) 12h d) 1 min e) 0.1h
20. Two projectiles A and B thrown with speeds in the ratio 1:√2 acquired the same heights. If A is thrown at an angle of 450 with the horizontal , the angle of projection of B will be a) 00 b) 600 c) 300 d) 450 e) 150
21. A ball is projected from the ground at a speed of 10 ms-1 making an angle of 300 with the horizontal. Another ball is simultaneously released from a point on the vertical line along the maximum height of the projectile. The initial height of the second ball is (take , g= 10ms-2) a) 6.25m b) 2.5 m c) 3.75 m d)5m e) 1.25m
22. An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground
observation point by the positions 10s apart is 300, then the speed of the aircraft is a) 19.63 ms-1 b) 1963 ms-1 c) 108ms-1 d) 196.3ms-1 e) 10.8 ms-1
23. An object of mass 5 kg is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift . The reading on the spring balance when the lift is going up with an acceleration of 0.25 m s-2 is (take , g= 10ms-2 ) a) 51.25N b) 48.75 N c) 52.75 N d) 47.25N e) 55N
24. A block of mass m is resting on a smooth horizontal surface. One end of the uniform rope of mass m/3 is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is
a) 8
6F b)
1
7F
c)
1
8F d)
1
5F e)
7
8F
25. A particle of mass 2kg is initially at rest. A force acts on it whose magnitude changes with the time. The force –time graph is shown below.
The velocity of the particle after 10s is a) 20 ms-1 b) 10 ms-1
c) 75ms-1 d) 26 ms-1 e) 50 ms-1
26. Two masses m1 =1 kg and m2=2 kg are connected by a tight inextensible string and suspended by means of a weightless pulley as shown in figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in 2s is (take , g=10m/s2)
a) 20
m9
b)40
m9
c) 2
m3
d) 1
m3
e) 4m
27. A uniform metal chain is placed on a rough table such that one end of it hangs down over the edge of the table. When one –third of its length hangs over the edge, the chain starts sliding. Then, the coefficient of static friction is a) 3/4 b) 1/4 c) 2/3 d) 1/3 e) 1/2
28. A block at rest slides down a smooth inclined plane which makes an angle 600 with the vertical and it reaches the ground in t1 second. Another block is dropped vertically from the same point and reaches the ground in t2 second. Then the ratio of t1:t2 is a) 1:2 b) 2:1 c) 1:3 d) 1:√2 e) 3:1
29. A block of mass m is placed on a surface with a vertical cross –section given by y=x3/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is
a) 1
m6
b) 2
m3
c) 1
m3
d) 1
m2
30. A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off in two mutually perpendicular directions, one with a
velocity of -13̂i ms and the other with a velocity of
-14̂j ms . If the explosion occurs in 10-4 s, the average
force acting on the third piece in newton is
a) 4(3 4 ) 10i j −+ × ) b) 4(3 4 ) 10i j −− ×
c) 4(3 4 ) 10i j+ × d) 4(3 4 ) 10i j− + ×
e) 4(4 3 ) 10i j− × 31. A monkey climbs up and another monkey climbs
down a rope hanging from a tree with same uniform acceleration separately. If the respective masses of monkeys are in the ratio 2:3, the common acceleration must be a) g/5 b) 6g c) g/2 d) g e) g/3
32. Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle . Their orbital velocity is
a) GM
L b)
3
2
GM
L
c) 3GM
L d)
2
3
GM
L e)
3
GM
L
33. The ratio of radii of the earth to another planet is
2
3and the ratio of their mean densities is
4
5. If an
astronaut can jump to a maximum height of 1.5 m on the earth, with the same effort, the maximum height he can jump on the planet is a) 1m b) 0.8 m c) 0.5 m d) 1.25 m e) 2 m
34. At what depth below the surface of the earth, the value of g is the same as that height of 5 km? a) 1.25km b) 2.5 km c) 5 km d) 7.5 km e) 10km
35. If a body of mass has to be taken from the surface to the earth to a height h=R , then the amount of energy required is (R=radius of the earth)
a) mgR b) 3
mgR
c) 2
mgR d)
12
mgR
e) 9
mgR
36. A body is projected with a velocity of 2×11.2 km/s from the surface of earth. The velocity of the body when it escapes the gravitational pull of the earth is
a) 3×11.2 km/s b) 11.2 km/s
c) 3×11.2 km/s d) 0.5 × 11.2 km/s e) 2 ×11.2 km/s
37. If an object of mass m is taken from the surface of earth(radius R) to a height 2R, then the work done is
a) 2mgR b) mgR c) 2
3mgR
d) 3
2mgR e)
1
3mgR
38. Infinite number of masses each 1 kg are placed along the X-axis at x =±1m, ±2m, ±4m, ±8m, ±16m….The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin (x=0) is a) G/2 b) G c) 2G d) 4G e) 8G
39. A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R. The ratio of their respective periods is a) 4:1 b) 1:8 c) 8:1 d) 1:4 e) 1:2
40. A satellite is revolving around the earth with a kinetic energy E. The minimum addition of kinetic energy needed to make it escape from its orbit is a) 2E b) √E c) E/2 d) √E/2 e) E
41. The correct order of standard reduction potentials a) Li < Na < K < Ca < Mg b) Li < K < Ca< Na < Mg c) Li < Mg < K < Ca < Na d) Mg < Na < K < Ca < Li e) Mg < Li < Ca < K < Na
42. MgCl2.8H2O on heating undergoes a) Hydrolysis b) Dehydration c) Dehydration takes place when heated in presence of HCl d) a and c e) None of these
43. Alkali metals reacts with ethyne and forms ethynide except a) Rb b) K c) Li d) Na
44. Alkali metals can liberate H2 gas from which of the following a) H2O b) Alcohol c) Ethyne d) All of the above
45. The coordination number of alkaline earth metals in their complexes with liq. NH3 a) 4 b) 5 c) 6 d) They do not form complexes e) 3
46. Water soluble compound is a) BeF2 b) BeO c) Be(OH)2 d) BaSO4 e) None of these
47. To a piece of charcoal, sulphuric acid is added. Then: a)there is no reaction b) water gas is formed c) SO2 and CO2 are evolved d) CO and SO2 are evolved e) SO2 and CO are evolved
48. When Sn is treated with conc. HNO3 a) It is converted into stannous nitrate b) It is converted into stannic nitrate c) It is converted into metastannic acid d) It becomes passive e) None of these
49. BeCO3 is always kept in an atmosphere of CO2. The reason is that… a) It is unstable and may react with other air components b) It is unstable at room temperature and decomposes c) It is stable to heat d) The given statement is false e) H evaporates
50. In castnerkellner cell for the manufacture of NaOH, a) Aq. NaCl is used as electrolyte and NaOH formed in the middle compartment of the cell b) Cl2 gas formed at anode of outer compartment and H2 gas formed at the cathode of middle compartment c) Compartment separation is used to prevent the disproportion of Cl2 with NaOH d) Hg act as anode in outer compartment and as cathode in middle compartment e) Hg act as cathode in outer compartment and as anode in middle compartment
51. Gypsum is added to cement to slows down setting of a) Tricalcium aluminate b) Tricalcium silicate c) Dicalcium silicate d)Dicalcium aluminate e) All of them
52. The compound that do not react with caustic soda a) NaHCO3 b) Na2CO3 c) Be(OH)2 d) Both a and b e) All of these
53. H2 gas is not released when a) Sn reacts with acid b) Sn reacts with alkali c) Ba reacts with water d) Ca reacts with alkali
54. Electrolysis of aqueous solution of sodium salt of formic acid liberates H2 gas a) At cathode b) At anode c) At cathode and anode d) No H2 gas formed
55. Which of the following methods of removal hardness involves precipitation a) By using EDTA b) By using slaked lime c) By using polyphosphates d) All of the above
56. Calculate the volume strength of H2O2 sample containing 3g H2O2 in 100 ml. a) 3 volume b) 30 volume c) 10 volume d) 100 volume e) 15 volume
57. Correct statement a) On mass by mass consideration, hydrogen is better fuel than LPG and CH4 b) LPG is more efficient fuel than H2 and CH4 per mole or per litre consideration c) Energy released by 1g H2 is lesser than 1 mol H2 or 1L H2 d) All are correct
58. Which of the following reaction do not involve redox change a) CH2 = CH2(g) + H2(g) →H3C –CH3(g) b) 3Fe2O3 +CO→2Fe3O4 +CO2 c) Na2[Zn(CN)4] +Cu2+ →Na[Cu(CN)4]+Zn2+ d) Dissolving chlorine in lime water
59. The maximum oxidation state of an element is given by a) 8 b) Valance electrons c) 8 – valance electrons d) 6
60. True about KMnO4 a) Always acts as oxidising agent irrespective of the medium of reaction b) Always acts as reducing agent irrespective of the medium of reaction c) Can act both as oxidising or reducing agent with respect to medium d) Can act as oxidising agent only in acidic medium. e) Can act as oxidising agent only in basic medium.
61. The equivalent weight of K2Cr2O7 in acidic medium is M/6, calculate the weight of CO2 that formed by the reaction 6 equivalent of K2Cr2O7 with oxalic acid. (Where M is the molecular weight of K2Cr2O7) a) 6 g b) 44g c) 7.33g d) 264 g e) 50g
62. Steam reforming is the preparation of H2 gas from a) Carbon and steam b) Water gas c) CH4 and Steam d) Iron and steam e) None of these
63. Which of the following property H2O has higher value than D2O a) Enthalpy of formation b) Temperature of maximum density c) Dielectric constant d) Viscocity e) None of these
64. Incorrect statement among the following a) Urea retards decomposition of H2O2 b) Metals like Ag, PT accelerate decomposition of H2O2 c) Dust cant induce explosive decomposition on H2O2 d) H2O2 do not react with glass bottle.
65. In which of the following cases, the central atoms have different oxidation states a) Br3O8 b) C3O2 c) Fe3O4 d) All of these
66. Cl2O7(g) + H2O2(aq) →ClO 2(aq)− +O2(g) +H+
Find coefficients of oxidising and reducing agent in balanced equation . a) 4,2 b) 2,4 c) 2,1 d) 1,4 e)1,2
67. The formula of the stable binary compounds that would be formed by the combination of element 71 (X) and fluorine is a) XF b) XF2 c) XF3 d) XF4 d) XF5
68. The stability of +1 oxidation state increases in the sequence a) Tl < In < Ga< Al b) In< Tl < Ga < Al c) Ga < Ln < Al < Tl d) Al < Ga <In < Tl e) Al < In < Ga < Tl
69. Glass reacts with HF to produce a) SiF4 b) H2SiF6 c) H2SiO3 d) Na3AlF6 e) H2SiF8
70. The electron gain enthalpy and electron affinity can be related at any temperature as
a) eg AH E∆ = −
b) eg AH E∆ = −
c) eg A
5RT
2H E∆ = − +
d) eg A
5RT
2H E∆ = − −
71. Energy of an electron in the ground state of the
hydrogen atom is - 2.18 ×10-18J. What the ionization enthalpy of atomic hydrogen in terms of J mol-1. a) 2.18×10-18J mol-1 b) 1.31 ×106 J mol-1 c) 1.31 ×10-6 J mol-1 d) 2.18×106 J mol-1
e) 2.18×10-6 J mol-1 72. Select correct statement
a) IE1 of Ne(inert gas) is larger than IE2 b) IE2 of Ca(2nd group ) is lesser than IE1 c) The first ionization enthalpies for two isotopes of the same element should be same d) All are correct
73. Anhydrous AlCl3 cannot be obtained from which of the following reactions? a) Heating AlCl3, 6H2O b) By passing dry HCl over hot aluminium power c) By passing dry Cl2 over hot aluminium power d) By passing dry Cl2 over a hot mixture of alumina and coke.
74. In diborane a) 4 – bridged hydrogens and two terminal hydrogens are present b) 2 – bridged hydrogens and four terminal hydrogens are present c) 3 – bridged and three terminal hydrogens are present d) None of these
75. Which does not exist a) [SnCl6]
2- b) [GeCl6]2-
c) [SiCl6]2- d) [CCl6]
2- 76. On addition of excess of sodium hydroxide solution
to stannous chloride solution, we obtain a) Sn (OH)2 b) SnO2. H2O c) Na2SnO2 d)NaSnO2 e)None of these
77. Which of the following noble gas are found in minerals of radioactive origin? a) He & Ne b) Ne & Ar c) Ar &Kr d) Kr & Xe e) He & Kr
78. In an acidic medium reaction, H2O2 acts oxidising agent and reducing agent, the number of electrons involved in the reduction and oxidation half separately are a) 1,1 b) 1,2 c) 2,2 d) 2,1 e) 3,2
79. A compound with low coordination number of cation and anion show Frenkel defect because the compound have a) cation and anion of the same size
b) cation and anion of same coordination number c) A highly polarizing cation and an easily polarisable anion d) A highly polarizing anion and easily polarisable cation. e) None of these
80. Na2B4O7. 10 H2O is correctly represented as a) 2 NaBO2. Na2B2O2.10 H2O b) Na2[B4O5(OH)4].8 H2O c) Na2[B4(H2O)4O7].6H2O d) Na2[B4(H2O)7O4].5H2O e) All of the above
81. The area of the triangle with vertices at the points (a , b+ c), (b, c+ a), (c, a + b) is a) 0 b) a+ b+ c c) ab+ bc +ca d) none of them
82. The equation of the line passing through (1,2) and perpendicular to x+ y + 1 = 0 is a) y –x + 1 = 0 b) y –x − 1 = 0 c) y –x + 2 = 0 d) y –x − 2 = 0
83. The line segment joining the points (1,2) and (−2,1) is divided b y the line 3x+4y = 7 in the ratio a) 3: 4 b) 4: 3 c) 9:4 d) 4:9
84. The distance between the lines 3x+ 4y = 9 and 6x+ 8y = 15 is a) 3/2 b) 3/10 c) 6 d) none of these
85. The distance of the line 5x+ y + 3 = 0 from the point (1,2) measured parallel to the line 5x – 12y +1 = 0 is a) 5 b) 1 c) 10 d) 2
86. The locus of mid – point of the portion intercepted between the axes by the line x cos α + y sin α = p. where p is a constant is
a) x2+ y2 = 4p2 b) 2 2 2
1 1 4
x y p+ =
c) x2+ y2 = 2
4
p d)
2 2 2
1 1 2
x y p+ =
87. The number of lines that can be drawn
through the point (4, 13) at a distance of 3 units from the point ( −2, 0) is a) 0 b) 1 c) 2 d) infinite
88. In a rhombus ABCD, the diagonals AC and BD intersect at the point (3,4) . If the point A is (1,2), the diagonal BD has the equation a) x – y – 1 = 0 b) x + y – 1 = 0 c) x – y + 1 = 0 d) x+ y – 7 = 0
89. The ratio in which the line 3x + 4y + 2 = 0 divides the distance between 3x+4y+ 5 = 0 and 3x+ 4y− 5 = 0 is a) 7:3 b) 3: 7 c) 2: 3 d) none of these
90. In non – zero numbers a, b, c are in H.P., then
the straight line 1
0x y
a b c+ + = always passes
through a fixed point, that point is
a) (1, - 2) b) 11,
2 −
c) ( - 1, 2) d) (-1, -2)
91. If the equation ax2 + by2 + 2hxy + 2gx +2fy + c = 0 represents a circle , the condition will be a) a = b and c = 0 b) f = g and h = 0 c) a = b and h = 0 d) f = g and c = 0
92. The angle between two tangents from the origin to the circle ( x – 7) 2 + ( y+ 1) 2 = 25 is a) π/3 b) π/6 c) π/2 d) 0
93. The equation of the circle orthogonal to both the circles x2+ y2 + 3x - 5y + 6 = 0 and 4x2 + 4y2 - 28x + 29 = 0 and whose centre lies on 3x+ 4y + 1 = 0 is
a) 2 2 29
2 4
yx y+ + = −
b) 2 2 3 50
2 4
xx y+ + + =
c) 2 2 7 35 0
2 2
y xx y+ + + + =
d) none of these 94. If the line y = x+ 3 meets the circle x2+ y2 = a2
at A and B , then the equation of the circle on AB as diameter is a) x2 + y2 + 3x – 3y – a2+ 9 = 0 b) x2 + y2 − 3x + 3y – a2+ 9 = 0 c) x2 + y2 + 3x + 3y – a2+ 9 = 0 d) none of these
95. The equation of the circumcircle of the triangle formed by the lines
3 6, 3 6y x y x+ = − = and y = 0 is a) x2+ y2 – 4y = 0 b) x2+ y2 + 4x = 0 c) x2+ y2 – 4y = 12 d) x2+ y2 + 4x = 12
96. The tangent to the circle x2+ y2 = 169 at (5, 12) and ( 12 , −5) are a) parallel b) perpendicular c) coincide d) none of these
97. The equation of the common tangent to the circle x2+ y2 – 4x – 6y – 12 = 0 and x2+ y2 + 6x + 18 y + 26 = 0 at their point of contract is a) 12x + 5y + 19 = 0 b) 5x+ 12y + 19= 0 c) 5x – 12y + 19 = 0 d) 12x – 5y + 19 = 0
98. The normal at the point (3,4) on a circle cuts the circle at the point ( −1, −2). Then the equation of the circle is a) x2+ y2 −2x – 2y – 11 = 0 b) x2+ y2 −2x – 2y + 14 = 0 c) x2+ y2 −2x – 2y – 13 = 0 d) x2+ y2 −2x + 2y +12 = 0
99. If a circle passes through the point A (a,b) and cuts the circle x2+ y2 = 4 orthogonally , then locus of its centre is a) 2ax + 2by + (a2 + b2 + 4) = 0 b) 2ax + 2by - (a2 + b2 + 4) = 0 c) 2ax−2by + (a2 + b2 + 4) = 0 d) 2ax − 2by + (a2 + b2 + 4) = 0
100. The intercept on the line y = x by the circle x2+ y2 – 2x = 0 is AB. The equation of circle on AB as a diameter is a) x2+ y2 – x – y = 0 b) x2+ y2 – x + y = 0 c) x2+ y2 + x + y = 0 d) x2+ y2 − x − y = 0
101. Any point on the parabola whose focus is (0,1) and the directrix is x + 2 = 0 is given by a) ( t2 + 1 , 2t – 1) b) (t2 + 1, 2t +1) c) (t2, 2t) d) (t2−1, 2t +1)
102. The tangents from the origin to the parabola y2+ 4 = 4x are inclined at a) π/6 b) π/4 c) π/3 d) π/2
103. The length of the common chord of the parabola 2y2 = 3( x+ 1) and the circle x2+ y2 + 2x = 0 is
a) 3 b) 2 3
c) 3 / 2 d) none of these 104. P is a point. Two tangents are drawn from it to
the parabola y2 = 4x such that the slope of one tangent is three times the slope of the other. The locus of P is a) an ellipse b) a circle c) parabola d) a straight line
105. The eccentricity of ellipse 9x2 + 5y2 – 30 y =0 is
a) 1/3 b) 2/3 c) 3
4 d) none of these
106. If the straight line y = 4x + c is a tangent to
the ellipse 2 2
18 4
x y+ = , then c will be equal to
a) ± 4 b) ± 6
c) ± 8 d) 132± 107. The minimum area of triangle formed by the
tangent to the ellipse 2 2
2 21
x y
a b+ = coordinates
axes is
a) ab sq. units b) 2 2
.2
a bsq units
+
c) ( )2
.2
a bsq units
+ d) 2 2
.3
a ab bsq units
+ +
108. Equation of the hyperbola with eccentricity 3/2 and foci at ( ±2,0) is
a) 2 2 4
4 5 9
x y− = b) 2 2 4
9 9 9
x y− =
c) 2 2
14 9
x y− = d) none of these
109. If e and e ′ be the eccentricities of a hyperbola
and its conjugate, then 2 2
1 1
'e e+ is equal to
a)0 b) 1 c) 2 d) none of these 110. The angle between line joining the origin to
the points of intersection of the line
3 2x y+ = and the curve y2 - x2 =4 is
a) 1 2tan
3−
b) 6
π
c) 1 3tan
2−
d) 2
π
111. The complex number 1 2
1
i
i
+−
lies in
a) first quadrant b) second quadrant c) third quadrant d) fourth quadrant
112. The square root of 5+ 12 i is a) 3+ 2i b) 3− 2i c) ± (3+ 2i) d) none of these
113. If 2
1
5
7
z
zis a purely imaginary number, then
1 2
1 2
2 3
2 3
z z
z z
+−
is equal toe
a) 5/7 b) 7/5 c) 25/49 d) none of these
114. 100
1 3
2
− + −
+100
1 3
2
− − −
is equal to
a) 2 b) 0 c) −1 d) 1 115. Number of non - zero integral solutions of the
equation 1 2x xi− = is
a) infinite b) one c) two d) none of these
116. For any complex number z, the minimum value of
1z z+ − is
a) 1 b) 0 c) 1/2 d) 3/2
117. The value of
8
8
sin cos8 8
sin cos8 8
i
i
π π
π π
+
−
is
a) −1 b) 0 c) 1 d) 2i
118. The locus represented by 1z z i− = + is
a) a circle of radius 1 b) an ellipse with foci at (1,0) and (0, −1) c) a straight line through the origin d) a circle on the line joining (1,0), (0,1) as diameter
119. 1 sin cos
1 sin cos
ni
i
θ θθ θ
+ + = + −
a) cos sin2 2
n nn i n
π πθ θ − + −
b) cos sin2 2
n nn i n
π πθ θ + + +
c) sin cos2 2
n nn i n
π πθ θ − + −
d) cos 2 sin 22 2
n nn i n
π πθ θ + + +
120. If ω is an imaginary cube root of unity , then (1+ω−ω2)7 is equal to a) 128 ω b) −128 ω c) 128 ω2 d) −128 ω2
KKEERRAALLAA MMOODDEELL EENNTTRRAANNCCEE EEXXAAMM RREEPPEEAATTEERRSS –– EENNGGIINNEEEERRIINNGG ((MMOODDUULLEE –– VVII))
PPHHYYSSIICCAALL WWOORRLLDD,, UUNNIITTSS AANNDD MMEEAASSUURREEMMEENNTTSS,, MMOOTTIIOONN IINN AA SSTTRRAAIIGGHHTT LLIINNEE,, MMOOTTIIOONN IINN AA
PPLLAANNEE,, LLAAWWSS OOFF MMOOTTIIOONN,, GGRRAAVVIITTAATTIIOONN,,PPEERRIIOODDIICC TTAABBLLEE,, HHYYDDRROOGGEENN,, SS && PP BBLLOOCCKK
EELLEEMMEENNTTSS,,RREEDDOOXX RREEAACCTTIIOONNSS,,SSTTRRAAIIGGHHTT LLIINNEESS,,CCIIRRCCLLEESS,,CCOONNIICCSS,,CCOOMMPPLLEEXX NNUUMMBBEERRSS
1. A satellite is revolving around the earth with a
kinetic energy E. The minimum addition of kinetic energy needed to make it escape from its orbit is a) 2E b) √E c) E/2 d) √E/2 e) E
2. If an object of mass m is taken from the surface of earth(radius R) to a height 2R, then the work done is
a) 2mgR b) mgR c) 2
3mgR
d) 3
2mgR e)
1
3mgR
3. A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off in two mutually perpendicular directions, one with a
velocity of -13̂i ms and the other with a velocity of
-14̂j ms . If the explosion occurs in 10-4 s, the average
force acting on the third piece in newton is
a) 4(3 4 ) 10i j −+ × ) b) 4(3 4 ) 10i j −− ×
c) 4(3 4 ) 10i j+ × d) 4(3 4 ) 10i j− + ×
e) 4(4 3 ) 10i j− × 4. A uniform metal chain is placed on a rough table
such that one end of it hangs down over the edge of the table. When one –third of its length hangs over the edge, the chain starts sliding. Then, the coefficient of static friction is a) 3/4 b) 1/4 c) 2/3 d) 1/3 e) 1/2
5. An object of mass 5 kg is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift . The reading on the spring balance when the lift is going up with an acceleration of 0.25 m s-2 is (take , g= 10ms-2 ) a) 51.25N b) 48.75 N c) 52.75 N d) 47.25N e) 55N
6. A ball is projected from the ground at a speed of 10 ms-1 making an angle of 300 with the horizontal. Another ball is simultaneously released from a point on the vertical line along the maximum height of the projectile. The initial height of the second ball is (take , g= 10ms-2) a) 6.25m b) 2.5 m c) 3.75 m d)5m e) 1.25m
7. A train of 150 m length is going towards North direction at a speed of 10 ms-1. A parrot flies at a speed of 5 ms-1 towards South direction parallel to the railway track. The time taken by the parrot to cross the train is equal to a) 12 s b) 8s c) 15s d) 10s e) 5s
8. A ball A is thrown up vertically with a speed u and at the same instant another ball B is released from a height h. At time t, then the speed of A relative to B is a) u b) 2u c) u-gt
d) 2( )u gt− e) gt
9. Which of the following sets of quantities have same dimensional formula? a) Frequency , angular frequency and angular momentum b) Surface tension, stress and spring constant c) Accleration , momentum and retardation d) thermal capacity, specific heat and entropy e) Work, energy and torque
10. It F denotes force and t time , then in equation F=at-1+bt2, the dimensions of a and b, respectively are a) [LT-4]and [LT-1] b) [LT-1]and [LT-4] c) [MLT -4]and [MLT-1] d) [MLT -1]and [MLT-4] e) [MLT-3]and [MLT-2]
11. Dimensional formula of Stefan`s constant is a) [MT-3K-4] b) [ML2T-2K-4] c) [ML2T-2] d) [ML -2L0] e) [MT-4L0]
12. The physical quantity angular momentum has the same dimensions as that of a) work b) force c) momentum d) torque e) planck`s constant
13. In a single pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time period is 3%. Then, the maximum percentage error in determination of the acceleration due to gravity g is a) 5% b) 6% c) 7% d) 8% e) 10%
14. The pitch and the number of circular scale divisions in a screw gauge with least count 0.02 mm are respectively a) 1mm and 100 b) 0.5 mm and 50 c) 1mm and 50 d) 0.5 mm and 100 e) 1mm and 200
15. A ball is dropped from the top of tower of height 100 m and at the same time another ball is projected vertically upward from ground with a velocity 25 ms-1 . Then , the distance from the top of the tower at which the two balls meet is a) 68.4 m b) 48.4 m c) 18.4 m d) 28.4 m e) 78.4m
2211--33--1199 VVeerrssiioonn CCooddee:: BB Time : 2 ½ Hours
16. A particle starting with certain initial velocity and uniform acceleration covers a distance of 12m in first 3 s and a distance of 30m in next 3s. The initial velocity of the particle is a) 3 ms-1 b) 2.5ms-1 c) 2 ms-1 d) 1.5 ms-1 e) 1 ms-1
17. A particle is moving with constant acceleration from A to B in a straight line AB. If u and v are the velocities at A and B , respectively then, its velocity at the mid-point C will be
a)
22 2
2
u v
u
+
b) 2
u v+
c) 2
v u− d)
2 2
2
u v+
e) None of these
18. A particle crossing the origin of coordinates at time t=0, moves in the xy-plane with a constant acceleration a in a y-direction. If, its equation of motion is y=bx2(where , is b is a constant) its velocity component in the x-direction is
a) 2b
a b)
2
a
b
c) a
b d)
b
a e) ab
19. A bullet fired into a fixed wooden block loses half of its velocity after penetrating 40cm. It comes to rest after penetrating a further distance of
a ) 22
cm3
b) 40
cm3
c) 20
cm3
c) 22
cm5
d) 26
cm5
20. A boat travels 50 km due to east, then 120 km due north and finally it comes back to the starting point through the shortest distance. The total time of journey is 3h. What is the average speed (in kmh-1) over the entire trip? a) Zero b) 100 c) 17 d) 33.33 e) 86.7
21. A cyclist starts from the centre O of a circular park of radius 1km , reaches the edge P of the park, then cycle along the circumference and returns to the point O as shown in figure. If the round trip takes 10 min, the net displacement and average speed of the cyclist (in metre and kilometer per hour) are
a) 0, 1 b) 4
, 02
π +
c) 4
21.4, 2
π + d) 0, 21.4 e) 0, 24.14
22. The coordinates of a particle moving in XY-plane at any instant of time t are x= 4t2, y=3t2. The speed of the particle at that instant is
a) 10t b) 5t c) 3t d) 2t e) 13t 23. The resultant of two vectors P and Q is R. If the
magnitude of Q is doubled, then the new resultant becomes perpendicular to P. Then, the magnitude of R is a) P+Q b) Q c) P
d) 2
P Q+ e) P-Q
24. A bridge is in the form of a semi-circle of radius 40m. The greatest speed with which a motor cycle can cross the bridge without leaving the ground at the highest point is (take , g=10ms-2 and frictional force is negligibly small ) a) 40ms-1 b) 20ms-1 c) 30ms-1 d) 15 ms-1 e) 25 ms-1
25. The time period f the second`s hand of a watch is a) 1 h b) 1s c) 12h d) 1 min e) 0.1h
26. Two projectiles A and B thrown with speeds in the ratio 1:√2 acquired the same heights. If A is thrown at an angle of 450 with the horizontal , the angle of projection of B will be a) 00 b) 600 c) 300 d) 450 e) 150
27. An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the positions 10s apart is 300, then the speed of the aircraft is a) 19.63 ms-1 b) 1963 ms-1 c) 108ms-1 d) 196.3ms-1 e) 10.8 ms-1
28. A block of mass m is resting on a smooth horizontal surface. One end of the uniform rope of mass m/3 is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is
a) 8
6F b)
1
7F
c) 1
8F d)
1
5F
e) 7
8F
29. A particle of mass 2kg is initially at rest. A force acts
on it whose magnitude changes with the time. The force –time graph is shown below.
The velocity of the particle after 10s is a) 20 ms-1 b) 10 ms-1
c) 75ms-1 d) 26 ms-1 e) 50 ms-1
30. Two masses m1 =1 kg and m2=2 kg are connected by a tight inextensible string and suspended by means of a weightless pulley as shown in figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in 2s is (take , g=10m/s2)
a) 20
m9
b) 40
m9
c) 2
m3
d) 1
m3
e) 4m
31. A block at rest slides down a smooth inclined plane which makes an angle 600 with the vertical and it reaches the ground in t1 second. Another block is dropped vertically from the same point and reaches the ground in t2 second. Then the ratio of t1:t2 is 1:2 b) 2:1 c) 1:3 d) 1:√2 e) 3:1
32. A block of mass m is placed on a surface with a vertical cross –section given by y=x3/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is
a) 1
m6
b) 2
m3
c) 1
m3
d) 1
m2
33. A monkey climbs up and another monkey climbs down a rope hanging from a tree with same uniform acceleration separately. If the respective masses of monkeys are in the ratio 2:3, the common acceleration must be a) g/5 b) 6g c) g/2 d) g e) g/3
34. Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle . Their orbital velocity is
a) GM
L b)
3
2
GM
L
c) 3GM
L d)
2
3
GM
L e)
3
GM
L
35. The ratio of radii of the earth to another planet is 2
3and the ratio of their mean densities is
4
5. If an
astronaut can jump to a maximum height of 1.5 m on the earth, with the same effort, the maximum height he can jump on the planet is a) 1m b) 0.8 m c) 0.5 m d) 1.25 m e) 2 m
36. At what depth below the surface of the earth, the value of g is the same as that height of 5 km? a) 1.25km b) 2.5 km c) 5 km d) 7.5 km e) 10km
37. If a body of mass has to be taken from the surface to the earth to a height h=R , then the amount of energy required is (R=radius of the earth)
a) mgR b) 3
mgR
c) 2
mgR d)
12
mgR e)
9
mgR
38. A body is projected with a velocity of 2×11.2 km/s from the surface of earth. The velocity of the body when it escapes the gravitational pull of the earth is
a) 3×11.2 km/s b) 11.2 km/s
c) 3×11.2 km/s d) 0.5 × 11.2 km/s e) 2 ×11.2 km/s
39. Infinite number of masses each 1 kg are placed along the X-axis at x =±1m, ±2m, ±4m, ±8m, ±16m….The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin (x=0) is a) G/2 b) G c) 2G d) 4G e) 8G
40. A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R. The ratio of their respective periods is a) 4:1 b) 1:8 c) 8:1 d) 1:4 e) 1:2
41. Calculate the volume strength of H2O2 sample containing 3g H2O2 in 100 ml. a) 3 volume b) 30 volume c) 10 volume d) 100 volume e) 15 volume
42. Energy of an electron in the ground state of the hydrogen atom is - 2.18 ×10-18J. What the ionization enthalpy of atomic hydrogen in terms of J mol-1. a) 2.18×10-18J mol-1 b) 1.31 ×106 J mol-1 c) 1.31 ×10-6 J mol-1 d) 2.18×106 J mol-1
e) 2.18×10-6 J mol-1 43. In diborane
a) 4 – bridged hydrogens and two terminal hydrogens are present b) 2 – bridged hydrogens and four terminal hydrogens are present c) 3 – bridged and three terminal hydrogens are present d) None of these
44. In an acidic medium reaction, H2O2 acts oxidising agent and reducing agent, the number of electrons involved in the reduction and oxidation half separately are a) 1,1 b) 1,2 c) 2,2 d) 2,1 e) 3,2
45. The stability of +1 oxidation state increases in the sequence a) Tl < In < Ga< Al b) In< Tl < Ga < Al c) Ga < Ln < Al < Tl d) Al < Ga <In < Tl e) Al < In < Ga < Tl
46. In which of the following cases, the central atoms have different oxidation states a) Br3O8 b) C3O2 c) Fe3O4 d) All of these
47. Which of the following property H2O has higher value than D2O a) Enthalpy of formation b) Temperature of maximum density c) Dielectric constant d) Viscocity e) None of these
48. True about KMnO4 a) Always acts as oxidising agent irrespective of the medium of reaction b) Always acts as reducing agent irrespective of the medium of reaction c) Can act both as oxidising or reducing agent with respect to medium d) Can act as oxidising agent only in acidic medium. e) Can act as oxidising agent only in basic medium.
49. Which of the following reaction do not involve redox change a) CH2 = CH2(g) + H2(g) →H3C –CH3(g) b) 3Fe2O3 +CO→2Fe3O4 +CO2 c) Na2[Zn(CN)4] +Cu2+ →Na[Cu(CN)4]+Zn2+ d) Dissolving chlorine in lime water
50. Anhydrous AlCl3 cannot be obtained from which of the following reactions? a) Heating AlCl3, 6H2O b) By passing dry HCl over hot aluminium power c) By passing dry Cl2 over hot aluminium power d) By passing dry Cl2 over a hot mixture of alumina and coke.
51. Cl2O7(g) + H2O2(aq) →ClO 2(aq)− +O2(g) +H+
Find coefficients of oxidising and reducing agent in balanced equation . a) 4,2 b) 2,4 c) 2,1 d) 1,4 e)1,2
52. Glass reacts with HF to produce a) SiF4 b) H2SiF6 c) H2SiO3 d) Na3AlF6 e) H2SiF8
53. Na2B4O7. 10 H2O is correctly represented as a) 2 NaBO2. Na2B2O2.10 H2O
b) Na2[B4O5(OH)4].8 H2O
c) Na2[B4(H2O)4O7].6H2O
d) Na2[B4(H2O)7O4].5H2O
e) All of the above
54. The equivalent weight of K2Cr2O7 in acidic medium is M/6, calculate the weight of CO2 that formed by the reaction 6 equivalent of K2Cr2O7 with oxalic acid. (Where M is the molecular weight of K2Cr2O7) a) 6 g b) 44g c) 7.33g d) 264 g e) 50g
55. BeCO3 is always kept in an atmosphere of CO2. The reason is that… a) It is unstable and may react with other air components b) It is unstable at room temperature and decomposes c) It is stable to heat
d) The given statement is false e) H evaporates
56. Alkali metals can liberate H2 gas from which of the following a) H2O b) Alcohol c) Ethyne d) All of the above
57. Gypsum is added to cement to slows down setting of a) Tricalcium aluminate b) Tricalcium silicate c) Dicalcium silicate d) Dicalcium aluminate e) All of them
58. MgCl2.8H2O on heating undergoes a) Hydrolysis b) Dehydration c) Dehydration takes place when heated in presence of HCl d) a and c e) None of these
59. H2 gas is not released when a) Sn reacts with acid b) Sn reacts with alkali c) Ba reacts with water d) Ca reacts with alkali
60. Electrolysis of aqueous solution of sodium salt of formic acid liberates H2 gas a) At cathode b) At anode c) At cathode and anode d) No H2 gas formed
61. Water soluble compound is a) BeF2 b) BeO c) Be(OH)2 d) BaSO4 e) None of these
62. On addition of excess of sodium hydroxide solution to stannous chloride solution, we obtain a) Sn (OH)2 b) SnO2. H2O c) Na2SnO2 d)NaSnO2 e)None of these
63. A compound with low coordination number of cation and anion show Frenkel defect because the compound have a) cation and anion of the same size b) cation and anion of same coordination number c) A highly polarizing cation and an easily polarisable anion d) A highly polarizing anion and easily polarisable cation. e) None of these
64. The correct order of standard reduction potentials a) Li < Na < K < Ca < Mg b) Li < K < Ca< Na < Mg c) Li < Mg < K < Ca < Na d) Mg < Na < K < Ca < Li e) Mg < Li < Ca < K < Na
65. Alkali metals reacts with ethyne and forms ethynide except a) Rb b) K c) Li d) Na
66. The coordination number of alkaline earth metals in their complexes with liq. NH3 a) 4 b) 5 c) 6 d) They do not form complexes e) 3
67. To a piece of charcoal, sulphuric acid is added. Then: a)there is no reaction b) water gas is formed c) SO2 and CO2 are evolved d) CO and SO2 are evolved e) SO2 and CO are evolved
68. When Sn is treated with conc. HNO3 a) It is converted into stannous nitrate b) It is converted into stannic nitrate c) It is converted into metastannic acid d) It becomes passive e) None of these
69. In castnerkellner cell for the manufacture of NaOH, a) Aq. NaCl is used as electrolyte and NaOH formed in the middle compartment of the cell b) Cl2 gas formed at anode of outer compartment and H2 gas formed at the cathode of middle compartment c) Compartment separation is used to prevent the disproportion of Cl2 with NaOH d) Hg act as anode in outer compartment and as cathode in middle compartment e) Hg act as cathode in outer compartment and as anode in middle compartment
70. The compound that do not react with caustic soda a) NaHCO3 b) Na2CO3 c) Be(OH)2 d) Both a and b e) All of these
71. Which of the following methods of removal hardness involves precipitation a) By using EDTA b) By using slaked lime c) By using polyphosphates d) All of the above
72. Correct statement a) On mass by mass consideration, hydrogen is better fuel than LPG and CH4 b) LPG is more efficient fuel than H2 and CH4 per mole or per litre consideration c) Energy released by 1g H2 is lesser than 1 mol H2 or 1L H2 d) All are correct
73. The maximum oxidation state of an element is given by a) 8 b) Valance electrons c) 8 – valance electrons d) 6
74. Steam reforming is the preparation of H2 gas from a) Carbon and steam b) Water gas c) CH4 and Steam d) Iron and steam e) None of these
75. Incorrect statement among the following a) Urea retards decomposition of H2O2 b) Metals like Ag, PT accelerate decomposition of H2O2 c) Dust cant induce explosive decomposition on H2O2 d) H2O2 do not react with glass bottle.
76. The formula of the stable binary compounds that would be formed by the combination of element 71 (X) and fluorine is a) XF b) XF2 c) XF3 d) XF4 d) XF5
77. The electron gain enthalpy and electron affinity can be related at any temperature as
a) eg AH E∆ = − b) eg AH E∆ = −
c) eg A
5RT
2H E∆ = − + d)
eg A
5RT
2H E∆ = − −
78. Select correct statement a) IE1 of Ne(inert gas) is larger than IE2 b) IE2 of Ca(2nd group ) is lesser than IE1 c) The first ionization enthalpies for two isotopes of the same element should be same d) All are correct
79. Which does not exist a) [SnCl6]
2- b) [GeCl6]2-
c) [SiCl6]2- d) [CCl6]
2- 80. Which of the following noble gas are found in
minerals of radioactive origin? a) He & Ne b) Ne & Ar c) Ar &Kr d) Kr & Xe e) He & Kr
81. The tangent to the circle x2+ y2 = 169 at (5, 12) and ( 12 , −5) are a) parallel b) perpendicular c) coincide d) none of these
82. The normal at the point (3,4) on a circle cuts the circle at the point ( −1, −2). Then the equation of the circle is a) x2+ y2 −2x – 2y – 11 = 0 b) x2+ y2 −2x – 2y + 14 = 0 c) x2+ y2 −2x – 2y – 13 = 0 d) x2+ y2 −2x + 2y +12 = 0
83. In non – zero numbers a, b, c are in H.P., then
the straight line 1
0x y
a b c+ + = always passes
through a fixed point, that point is
a) (1, - 2) b) 11,
2 −
c) ( - 1, 2) d) (-1, -2) 84. In a rhombus ABCD, the diagonals AC and BD
intersect at the point (3,4) . If the point A is (1,2), the diagonal BD has the equation a) x – y – 1 = 0 b) x + y – 1 = 0 c) x – y + 1 = 0 d) x+ y – 7 = 0
85. The locus of mid – point of the portion intercepted between the axes by the line x cos α + y sin α = p. where p is a constant is
a) x2+ y2 = 4p2 b) 2 2 2
1 1 4
x y p+ =
c) x2+ y2 = 2
4
p d)
2 2 2
1 1 2
x y p+ =
86. The area of the triangle with vertices at the points (a , b+ c), (b, c+ a), (c, a + b) is a) 0 b) a+ b+ c c) ab+ bc +ca d) none of them
87. The distance between the lines 3x+ 4y = 9 and 6x+ 8y = 15 is a) 3/2 b) 3/10 c) 6 d) none of these
88. If the equation ax2 + by2 + 2hxy + 2gx +2fy + c = 0 represents a circle , the condition will be a) a = b and c = 0 b) f = g and h = 0 c) a = b and h = 0 d) f = g and c = 0
89. The equation of the circle orthogonal to both the circles x2+ y2 + 3x - 5y + 6 = 0 and 4x2 + 4y2 - 28x + 29 = 0 and whose centre lies on 3x+ 4y + 1 = 0 is
a) 2 2 29
2 4
yx y+ + = −
b) 2 2 3 50
2 4
xx y+ + + =
c) 2 2 7 35 0
2 2
y xx y+ + + + =
d) none of these
90. 100
1 3
2
− + −
+100
1 3
2
− − −
is equal to
a) 2 b) 0 c) −1 d) 1
91. The complex number 1 2
1
i
i
+−
lies in
a) first quadrant b) second quadrant c) third quadrant d) fourth quadrant
92. If e and e ′ be the eccentricities of a hyperbola
and its conjugate, then 2 2
1 1
'e e+ is equal to
a)0 b) 1 c) 2 d) none of these 93. If ω is an imaginary cube root of unity , then
(1+ω−ω2)7 is equal to a) 128 ω b) −128 ω c) 128 ω2 d) −128 ω2
94. The tangents from the origin to the parabola y2+ 4 = 4x are inclined at a) π/6 b) π/4 c) π/3 d) π/2
95. If the straight line y = 4x + c is a tangent to
the ellipse 2 2
18 4
x y+ = , then c will be equal to
a) ±4 b) ±6
c) ±8 d) 132± 96. Equation of the hyperbola with eccentricity
3/2 and foci at ( ±2,0) is
a) 2 2 4
4 5 9
x y− = b) 2 2 4
9 9 9
x y− =
c) 2 2
14 9
x y− = d) none of these
97. The locus represented by 1z z i− = + is
a) a circle of radius 1 b) an ellipse with foci at (1,0) and (0, −1) c) a straight line through the origin d) a circle on the line joining (1,0), (0,1) as diameter
98. For any complex number z, the minimum value of
1z z+ − is
a) 1 b) 0 c) 1/2 d) 3/2
99. If a circle passes through the point A (a,b) and cuts the circle x2+ y2 = 4 orthogonally , then locus of its centre is a) 2ax + 2by + (a2 + b2 + 4) = 0 b) 2ax + 2by - (a2 + b2 + 4) = 0 c) 2ax−2by + (a2 + b2 + 4) = 0 d) 2ax − 2by + (a2 + b2 + 4) = 0
100. The equation of the line passing through (1,2) and perpendicular to x+ y + 1 = 0 is a) y –x + 1 = 0 b) y –x − 1 = 0 c) y –x + 2 = 0 d) y –x − 2 = 0
101. The line segment joining the points (1,2) and (−2,1) is divided b y the line 3x+4y = 7 in the ratio a) 3: 4 b) 4: 3 c) 9:4 d) 4:9
102. The distance of the line 5x+ y + 3 = 0 from the point (1,2) measured parallel to the line 5x – 12y +1 = 0 is a) 5 b) 1 c) 10 d) 2
103. The number of lines that can be drawn
through the point (4, 13) at a distance of 3 units from the point ( −2, 0) is a) 0 b) 1 c) 2 d) infinite
104. The ratio in which the line 3x + 4y + 2 = 0 divides the distance between 3x+4y+ 5 = 0 and 3x+ 4y− 5 = 0 is a) 7:3 b) 3: 7 c) 2: 3 d) none of these
105. The angle between two tangents from the origin to the circle ( x – 7) 2 + ( y+ 1) 2 = 25 is a) π/3 b) π/6 c) π/2 d) 0
106. If the line y = x+ 3 meets the circle x2+ y2 = a2 at A and B , then the equation of the circle on AB as diameter is a) x2 + y2 + 3x – 3y – a2+ 9 = 0 b) x2 + y2 − 3x + 3y – a2+ 9 = 0 c) x2 + y2 + 3x + 3y – a2+ 9 = 0 d) none of these
107. The equation of the circumcircle of the triangle formed by the lines
3 6, 3 6y x y x+ = − = and y = 0 is a) x2+ y2 – 4y = 0 b) x2+ y2 + 4x = 0 c) x2+ y2 – 4y = 12 d) x2+ y2 + 4x = 12
108. The equation of the common tangent to the circle x2+ y2 – 4x – 6y – 12 = 0 and x2+ y2 + 6x + 18 y + 26 = 0 at their point of contract is a) 12x + 5y + 19 = 0 b) 5x+ 12y + 19= 0 c) 5x – 12y + 19 = 0 d) 12x – 5y + 19 = 0
109. The intercept on the line y = x by the circle x2+ y2 – 2x = 0 is AB. The equation of circle on AB as a diameter is a) x2+ y2 – x – y = 0 b) x2+ y2 – x + y = 0 c) x2+ y2 + x + y = 0 d) x2+ y2 − x − y = 0
110. Any point on the parabola whose focus is (0,1) and the directrix is x + 2 = 0 is given by a) ( t2 + 1 , 2t – 1) b) (t2 + 1, 2t +1) c) (t2, 2t) d) (t2−1, 2t +1)
111. The length of the common chord of the parabola 2y2 = 3( x+ 1) and the circle x2+ y2 + 2x = 0 is
a) 3 b) 2 3
c) 3 / 2 d) none of these 112. P is a point. Two tangents are drawn from it to
the parabola y2 = 4x such that the slope of one tangent is three times the slope of the other. The locus of P is a) an ellipse b) a circle c) parabola d) a straight line
113. The eccentricity of ellipse 9x2 + 5y2 – 30 y =0 is
a) 1/3 b) 2/3 c) 3
4 d) none of these
114. The minimum area of triangle formed by the
tangent to the ellipse 2 2
2 21
x y
a b+ = coordinates
axes is
a) ab sq. units b) 2 2
.2
a bsq units
+
c) ( )2
.2
a bsq units
+ d) 2 2
.3
a ab bsq units
+ +
115. The angle between line joining the origin to the points of intersection of the line
3 2x y+ = and the curve y2 - x2 =4 is
a) 1 2tan
3−
b) 6
π
c) 1 3tan
2−
d) 2
π
116. 1 sin cos
1 sin cos
ni
i
θ θθ θ
+ + = + −
a) cos sin2 2
n nn i n
π πθ θ − + −
b) cos sin2 2
n nn i n
π πθ θ + + +
c) sin cos2 2
n nn i n
π πθ θ − + −
d) cos 2 sin 22 2
n nn i n
π πθ θ + + +
117. The square root of 5+ 12 i is a) 3+ 2i b) 3− 2i c) ± (3+ 2i) d) none of these
118. If 2
1
5
7
z
zis a purely imaginary number, then
1 2
1 2
2 3
2 3
z z
z z
+−
is equal toe
a) 5/7 b) 7/5 c) 25/49 d) none of these
119. Number of non - zero integral solutions of the
equation 1 2x xi− = is
a) infinite b) one c) two d) none of these
120. The value of
8
8
sin cos8 8
sin cos8 8
i
i
π π
π π
+
−
is
a) −1 b) 0 c) 1 d) 2i
KKEERRAALLAA MMOODDEELL EENNTTRRAANNCCEE EEXXAAMM RREEPPEEAATTEERRSS –– EENNGGIINNEEEERRIINNGG ((MMOODDUULLEE –– VVII))
PPHHYYSSIICCAALL WWOORRLLDD,, UUNNIITTSS AANNDD MMEEAASSUURREEMMEENNTTSS,, MMOOTTIIOONN IINN AA SSTTRRAAIIGGHHTT LLIINNEE,,
MMOOTTIIOONN IINN AA PPLLAANNEE,, LLAAWWSS OOFF MMOOTTIIOONN,, GGRRAAVVIITTAATTIIOONN,,PPEERRIIOODDIICC TTAABBLLEE,, HHYYDDRROOGGEENN,,
SS && PP BBLLOOCCKK EELLEEMMEENNTTSS,,RREEDDOOXX RREEAACCTTIIOONNSS,,SSTTRRAAIIGGHHTT
LLIINNEESS,,CCIIRRCCLLEESS,,CCOONNIICCSS,,CCOOMMPPLLEEXX NNUUMMBBEERRSS
AANNSSWWEERR KKEEYY VVEERRSSIIOONN CCOODDEE –– AA
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
D A E E D C E E D B A B B D A
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
B D B D C B D A E E A E B A D
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
D A B E C A C C B A B D C D C
46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
A C C B D A B D C B C D C B A
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
D C C D D D C D B D B C A B D
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
C A C C B A B D B D B A D B A
91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
C D A A C B B A B A D D A C B
106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
B D A B C B C D C D A C C A D
AANNSSWWEERR KKEEYY VVEERRSSIIOONN CCOODDEE –– BB
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
A C D E A B D A E D A E D C E
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
E D B B B D A B B D C D E E A
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
B A D A B E C A C B C B B C D
46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
D C A C A D B B D B D A D D C
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
A C C B C C C C D B B D B C D
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
C D C D A B A A D B A B C A C
91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
B B D D A C C A B B D D A B D
106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
A C B A D A C B A C A C D D C
2211..0033..1199
AANNSSWWEERRSS AANNDD SSOOLLUUTTIIOONNSS
First No: Version code: A Second No: Version code: B 1. 10
2. 11
3. 12
4. 9
5. .13
6. 14
7. 15
8. 16
9. .17
10. 18
15. 22
16. 23
17. 7
18. 24
19. 25
20. 26
21. 6
22. 27
23. 5
24. 28
25. 29
26. 30
27. 4
28. .31
29. .32
30. 3
31. 33
33. 35
34. 36
35. 37
36. 38
38. 39
39. 40
40. 1
47. 67
48. 68
56. 41
3g H2O2 in 100 ml = 3% H2O2
Volume strength = percentage strength
0.3035
= 3
0.3035= 10 volume
57. 72 Energy released on combustion in kJ state)
Dihydrogen (in gaseous state)
Dihydrogen (in liquid)
LPG
CH4
gas
per mole 286 285 2220 880
Per gram 143 142 50 53
Per litre 12 9968 2590 35
61. 54
Cr2O27
− +3C2O24
− +14H+ →2Cr3++6CO2 +7H2O
6 equivalent dichromate = 1 mol dichromate, which produces 6 mole CO2 Therefore Mass of CO2 formed=6 ×44 = 264g]
66. 51
Cl2O7(g)+4H2O2(aq)→2ClO2(aq)− +4O2(aq)+2H+
+3H2O] 67. 76
The element with the atomic number 71 is Lutetium (Lu). It has valency 3. Hence, the formula of the compound is LuF3]
68. 45
69. 52
71. 42
it is given that the energy of an electron in the ground state of the hydrogen atom is – 2.18 ×10-18J. Therefore, the energy required to remove that electron from the ground state of hydrogen atom is 2.18×10-18J. Hence, ionization enthalpy of atomic hydrogen in terms of J mol-1 = 2.18 ×10-18 ×6.02 ×1023 J mol-1 = 1.31×106 J mol-1)
73. 50
75. 79
76. 62
78. 44
H2O2 +2H+ +2e→2H2O(reduction half) H2O2 →O2 +2H+ +2e(oxidation half)
81. 86
82. 100
83. 101
84. 87
85. 102
86. 85
87. 103
88. 84
89. 104
91. 88
92. 105
93. 89
94. 106
95. 107
96. 81
97. 108
98. 82
99. 99
100. 109
101. 110
102. 94
103. 111
104. 112
105. 113
2 2
(1 sin 2 ) (1 sin 2 ) 29 16
x yt t+ = + + − =
106. 95
107. 114
108. 96
(1 sin 2 ) (1 sin 2 ) 2t t+ = + + − =
109. 92
110. 115
111. 91
112. 117
113. 118
114. 90
115. 119
116. 98
117. 120
118. 97
119. 116
120. 93