free test01
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physics
Q. 1 A 2m wide truck is moving with a uniform speed v0 = 8 m/s along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is
1.
2.62 m/s
2.
4.6 m/s
3.
3.57 m/s
4.
1.414 m/s
1 marks
Q. 2 From an inclined plane two particles are projected with same speed at same
angle , one up and other down the plane as shown in figure. Which of the following statement is correct?
0
1.
the particles will collide the plane with same speed
2.
the times of flight of each particle are same
3.
both particles strike the plane perpendicularly
4.
the particles will collide in mid air if projected simultaneously and time of flight of each particle is more than the time of collision.
1 marks
Q. 3 Velocity-time graphs of a particle moving in a straight line is shown in the figure. Mass of the particle is 2 kg. Work done by all the forces acting on the particle in time interval t = 0 to t = 10 sec is
0
1.
300 J
2.
- 300 J
3.
zero
4.
- 400 J
1 marks
Q. 4 A particle is moving in x-y plane with y = x/2 and vx = 4 - 2t. The displacement versus time graph of the particle would be
1.
0
0
2.
3.
4.
1 marks
Q. 5 Two particles having position vectors and are
moving with velocities and If they collides after 2 sec, the value of ?a' is
1.
2
2.
4
0
3.
6
4.
8
1 marks
Q. 6 A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string AB, with the speed v. Friction between the bead and the string may be neglected. Let tP and tQ be the respective times taken by P and Q to reach the point B. Then
1.
tP < tQ
2.
tP = tQ
3.
tP > tQ
0
4.
1 marks
Q. 7 A particle of mass m = 5 units is moving with a uniform speed unit in x-y plane along the line y = x + 4 in given reference frame. If at t = 0 particle was at (0,4). Moment of inertia of mass about the x-axis at t = 1 sec will be
1.
340 units
2.
80 units
3.
60 units
4.
245 units
1 marks
Q. 8 In the gravitational field two masses are projected with the same horizontal
0
velocity from different points as shown in the figure. The time taken by the 2m mass to reach the ground after the m mass strikes the ground, is
1.
sec
2.
sec
3.
1 sec
4.
2 sec
1 marks
Q. 9 Block B moves downward with a constant velocity of 0.6 m/s. Then
0
1.
the velocity of block A is 0.9 m/sec
2.
the velocity of block C is 0.1 m/sec
3.
the velocity of portion D of the cable is 5.0 m/sec
4.
the relative velocity of portion D of the cable with respect to block B is 3.0m/sec
1 marks
Q. 10 A person traveling eastwards finds that the wind appears to blow directly from north. On doubling his speed it seems to come from north-east. If he trebles his speed in what direction it would appear to blow?
1.
in the direction making an angle sin-1 to east of south
2.
in the direction making an angle sin-1 to north of east
3.
in the direction making an angle tan-1 to north of east
0
0
4.
in the direction making an angle cos-1 to west of north
1 marks
Q. 11 A particle of mass m is executing oscillations about the origin on the x axis. Its potential energy is V (x) = k | x |3where k is a positive constant. If the amplitude of oscillation is a, then its time period T is
1.
Proportional to 1/
2.
Independent of a
3.
Proportional to
4.
Proportional to a3/2
1 marks
Q. 12 A particle is moved from (0, 0) to (a, a) under a force from two paths. Path 1 is OP and path 2 is OQP. Let W1 and W2 be the work done by this force in these two paths. Then
0
1.
W1 = W2
2.
W1 = 2W2
3.
W2 = 2W1
4.
W2 = 4W1
1 marks
Q. 13 A self-propelled vehicle of mass m, whose engine delivers constant power P, has an acceleration a = P/mv (assume that there is no friction). In order to increase its velocity from v1 to v2, the distance it has to travel will be.
1.
0
0
2.
3.
4.
1 marks
Q. 14 Force acting on a particle is . Work done by this force is zero, when a particle is moved on the line 3y + kx = 5. Here value of k is
1.
2
2.
4
3.
6
4.
8
1 marks
0
Q. 15 A particle moves in the x-y plane under the action of the force such that
the value of its linear momentum at time t is: px = 2 cos t and py = 2 sin t.
The angle between and at time t will be:
1.
900
2.
00
3.
1800
4.
300
1 marks
Q. 16 A particle is displaced form x = -6 m to x = +6m. A force F acting on the particle during its motion is shown in figure. Graph between work done by this force (W) and displacement (x) should be
0
0
1.
2.
3.
4.
1 marks
Q. 17 A ball of mass 50 gm and relative density 0.5 strikes the surface of water with a velocity of 20 m/s. It comes to rest at a depth of 2 m. Find the work done by resisting force of water.
1.
-6 J
2.
+7.5 J
3.
-9.0 J
4.
-10 J
1 marks
Q. 18
1.
2.
3.
0
0
4.
1 marks
Q. 19 An object of mass m slides down a hill of height h of arbitrary shape and after travelling a certain horizontal path stops because of friction. The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion. The work that a force must perform to return the object to its initial position along the same path is
1.
mgh
2.
2mgh
3.
4mgh
4.
-mgh
1 marks
Q. 20 A bob is suspended from a crane by a cable of length l = 5m. The crane and load are moving at a constant speed v0. The crane is stopped by a bumper and the bob on the cable swings out an angle of 600. The initial speed v0 is (g = 9.8 m/s2)
0
1.
10 m/s
2.
7 m/s
3.
4 m/s
4.
2 m/s
1 marks
Q. 21 A metallic wire of density d floats horizontal in water. The maximum radius of the wire so that it may not sink, will be (surface tension of water = T)
1.
0
0
2.
3.
4.
1 marks
Q. 22 A big drop of radius R is broken into 27 equal small drops under isothermal condition. Work done in the process is - (S Surface tension)
1.
2.
3.
4.
No work is done.
1 marks
0
Q. 23 The height of water in a vessel is h. The vessel wall of width b is at an angle
to the vertical. The net force exerted by the water on the wall is
1.
2.
3.
4.
zero
1 marks
Q. 24 An electric dipole is placed at center of sphere. Which of the following option are correct.(i) flux of electric field through sphere is zero.(ii) electric field is zero at every point of sphere. (iii) electric field is non-zero any where on sphere(iv) electric field is zero on a circle on sphere
0
0
1.
only (i)
2.
only (ii)
3.
only (i) and (iii)
4.
all are correct
1 marks
Q. 25 In the figure the potentiometer wire of length l = 100 cm and resistance 9 is joined to a cell of emf E1 = 10V and internal resistance r1 = 1 another cell of emf E2 = 5V and internal resistance r2 = 2 is connected as shown. The galvanometer G will show no deflection when the length AC is:
1. 50 cm
0
2.
55.55 cm
3.
52.67 cm
4.
54.33 cm
1 marks
Q. 26 The metal plate on the left in figure carries a charge +q. The metal plate on the right has a charge of -2q. What charge will flow through S when it is closed, if central plate is initially neutral
1.
zero
0
2.
-q
3.
+q
4.
+2q
1 marks
Q. 27 A dielectric slab of area A and thickness d is inserted between the plates of capacitor of area 2A and distance between plates d with a constant speed v as shown in figure. The capacitor is connected to a battery of emf E. The current in the circuit varies with time as
1.
2.
0
3.
4.
1 marks
Q. 28 One plate of a capacitor is connected to a spring as shown in figure. Area of both the plates is A. In steady state separation between the plates is 0.8d (spring was unstretched and the distance between the plates was d when the capacitor was uncharged). The force constant of the spring is approximately
1.
2.
0
3.
4.
1 marks
Q. 29 The potential field depends on x and y coordinates as V = (x2 - y2) corresponding electric field lines in x-y plane are as
1.
2.
0
3.
4.
1 marks
Q. 30 An electric dipole is placed inside a non-uniform electric field, increasing at the rate of per unit distance, along Z-axis. The dipole can undergo:
1.
rotational motion only.
2.
transnational motion along Z-axis only.
3.
a rotational motion as well as a translation motion along Z-axis.
4. None of these.
0
1 marks
Q. 31 Two moles of an ideal gas are undergone a cyclic process as shown in the figure. Net heat exchange is Q. Work done in process 2-3 is
1.
Q - 2RT0
2.
Q + 2RT0
3.
Q
4.
Zero
1 marks
Q. 32 A thermodynamic system undergoes cyclic process ABCDA as shown in figure. The work done by the system is
0
1.
P0V0
2.
2P0V0
3.
4.
zero
1 marks
Q. 33 A hollow sphere of radius R and mass m, and a solid sphere of mass 8m, radius R are kept in surrounding at same temperature. If both follow newtons law of cooling then (both have same emissivity, absorptivity & specific heat)
0
0
1.
Rate of cooling is same for both
2.
Rate of cooling is larger for solid sphere
3.
Rate of cooling is larger for hollow sphere
4.
All of above are wrong
1 marks
Q. 34 Unit mass of a liquid of volume V1 completely turns into a gas of volume V2 at constant atmospheric pressure P0 and temperature T. The latent heat of vaporization is L. Then the change in internal energy of the gas is
1.
L
2.
L + P(V2 - V1)
3.
L - P(V2 - V1)
4. zero
0
1 marks
Q. 35 Two ends of a uniform bar are maintained at constant temperature T1 and T2 (T1 > T2). Which of the following graph correctly represents temperature of a section vs its distance from hotter end
1.
2.
3.
4.
1 marks
Q. 36 When an ideal diatomic gas is heated at constant pressure, the fraction of
0
the heat energy supplied which increases the internal energy of gas is
1.
2/5
2.
3/5
3.
3/7
4.
5/7
1 marks
Q. 37 100 g of water at 100oC and 100 g of ice at 0oC are mixed then final temperature of mixture is
1.
2oC
2.
1oC
0
0
3.
0oC
4.
-1oC
1 marks
Q. 38 A spherical black body with a radius of 12 cm radiates 450 W power at 500K. If the radius were halved and the temperature doubled, the power radiated in watt would be:
1.
225
2.
450
3.
900
4. 1800
0
1 marks
Q. 39 Two wires of cross-sectional area a and 2a having densities 2 and respectively are subjected to same tension. Length of both wires is L and value of tension is F. If both wires are excited with the same turning fork with junction as node.Minimum possible frequency of tuning fork is
1.
2.
3.
4.
None of the above
1 marks
Q. 40 One end of a uniform rod of length 1 m is placed in boiling water while its other end is placed in melting ice. A point P on the rod is maintained at a constant temperature of 8000 C. The mass of steam produced per second is equal to the mass of ice melted per second. If specific latent heat of steam is 7 times the specific latent heat of ice, the distance of P from the steam chamber must be
0
1.
2.
3.
4.
1 marks
Q. 41 Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by x-rays then the observed pattern will reveal
1.
that the central maxima is narrower.
2.
more number of fringes.
3.
less number of fringes.
0
0
4.
no diffraction pattern.
1 marks
Q. 42 . Light falls from glass ( = 1.5) to air. Find the angle of incidence for which the angle of deviation is 90o.
1.
30o
2.
60o
3.
45o
4.
0oC
1 marks
Q. 43 In the adjacent figure, sin i/sin r:
0
1.
is equal to
2.
is equal to
3.
is equal to
4.
cannot be calculated.
1 marks
Q. 44 A thin prism is made of a material having refractive indices 1.61 and 1.65 for red and violet light. The dispersive power of the material is 0.07. It is found that a beam of yellow light passing through the prism suffers a minimum deviation of 4.0o in favourable conditions. Calculate the angle of the prism.
1.
4o
2.
7o
3. 3o
0
0
4.
5o
1 marks
Q. 45 A thin prism P, with angle 40 and made from glass of refractive index 1.54 combined with another thin prism P2 made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism P2 is:
1.
5.35o
2.
4o
3.
3o
4.
2.6o
1 marks
Q. 46 A photon of wavelength 300 nm is absorbed by a gas and then re-emits two photons. One re-emitted photon has wavelength 496 nm. Then the energy of other re-emitted photon is
0
1.
2.625 × 10-19 J
2.
1.625 × 10-20 J
3.
1.625 × 10-19 J
4.
2.125 × 10-19 J
1 marks
Q. 47 A truck moving on horizontal road towards east with velocity 20 ms-1 collides elastically with a light ball moving with velocity 25 ms-1 along west. The velocity of the ball just after collision.
1.
65 ms-1 towards east
2.
25 ms-1 towards west
3.
65 ms-1 towards west
4.
20 ms-1 towards east
0
0
1 marks
Q. 48 The kinetic energy K of a photo-electron varies with the frequency f of the incident radiation as
1.
2.
3.
4.
1 marks
Q. 49 The decay constant for an a-decay of Th232 is 1.58 × 10-10 sec-1. The number of -decays that occur from 1 g sample in 365 day is
1.
5.496 × 1018
2.
1.298 × 1020
0
0
3.
5.496 × 1019
4.
1.298 × 1019
1 marks
Q. 50 A spherometer has a least count of 0.05 mm and its head scale is divided into 200 equal divisions. The distance between consecutive threads on the spherometer screw is
1.
0.005 mm
2.
1.0 mm
3.
1.0 cm
4.
0.0025 mm
1 marks
Q. 51 The ratio of rms velocity and average velocity at a given temperature of a gas is:
0
0
1.
2.
3.
4.
1 marks
Q. 52 When water act as Lewis base the hybridisation of O
1.
changed
2.
does not change
3.
may change
4.
oxygen gets unhybridised
1 marks
Q. 53 Calculate the volume of 3M Barium permanganate needed to neutralize 2cc, 1.5 M Ferrous thiosulphate. The products are
0
0
1.
10 cc
2.
5 cc
3.
7.5 cc
4.
None of these
1 marks
Q. 54 Oxidation number of Pt in [Pt(NH3)Cl3] - is
1.
+ 1
2.
+ 2
3.
+ 3
4.
+ 4
1 marks
Q. 55 In a reaction involving one single reactant, the fraction of the reactant
consumed may be defined as where C0 and C are the concentrations of the reactant at the start and after time, t. For a first order reaction.
0
1.
2.
3.
4.
1 marks
Q. 56 The value of kp for the reaction at 27oC is 1 atm. At equilibrium in a closed container partial pressure of BrCl gas is 0.1 atm and at this temperature the vapour pressure of Br2( ) is also 0.1 atm. Then what will be minimum moles of Br2( ) to be added to 1 mole of Cl2, initially to get above equilibrium situation :
1.
2.
3.
4.
2 moles
1 marks
0
0
Q. 57 pH of a mixture containing 0.10 M X - (base) and 0.20 M HX with pKb(X -) = 4 is
1.
4 + log 2
2.
4 - log 2
3.
10 + log 2
4.
10 - log 2
1 marks
Q. 58 Which one of the following reactions leads to formation of optically inactive mixture ?
1.
2.
3.
4.
both (A) & (C)
0
0
1 marks
Q. 59 A sample of hard water contains 192 ppm of ions and 305 ppm of
ions with Ca2+ with as the only cations. The concentration in ppm of Ca2+ ions (Atomic mass = 40) in the hard water is:
1.
100
2.
180
3.
140
4.
80
1 marks
Q. 60 An electron initially with zero velocity is accelerated by an electrical field of 15 volt. The de-Broglie wavelength associated with electron is
1.
5.30
2.
2.54
3.
3.33
4.
3.80
0
0
1 marks
Q. 61 In the molecule , the states of hybridization of C -1, C-2, C-3 and C-4 (as marked) are, respectively.
1.
sp2, sp, sp and sp3
2.
sp3, sp, sp and sp
3.
sp2, sp, sp2 and sp3
4.
sp2, sp2, sp and sp3
1 marks
Q. 62 Among the species: (a) BF3, (b) N(CH 3)2, (c) N(SiH3)2 and (d) SO2, the planar molecules are
1.
a and d
2.
a and b
3.
a, c and d
4.
a, b and d
0
0
1 marks
Q. 63 The EC of the atom of atom of an element is [Ne]3s23p4. Hence the position of the element in the periodic table will be
1.
Group IIIA and 6th Pd
2.
Group VI A and 3rd Pd
3.
Group IVA and 4th Pd
4.
Can't be said
1 marks
Q. 64 4.48 litre of methane at STP corresponds to
1.
1.2 × 1022 molecules of methane
2.
0.5 mole of methane
3.
3.2 gm of methane
4.
0.1 mole of methane
1 marks
0
0
Q. 65 Insulin contains 3.4% sulphur. What will be the minimum molecular weight of insulin? (atomic weight of sulphur = 32)
1.
94.117
2.
1884
3.
941.76
4.
976
1 marks
Q. 66 The reacion CH2 = CH - CH3 + HBr CH3CHBrCH3 is
1.
nucleophilic additon
2.
electrophilic substitution
3.
electrophilic addition
4.
free radical addition
1 marks
0
0
Q. 67 Which bond angle, would result in the maximum dipole moment for the triatomic molecular XY2 show below:
1.
= 90o
2.
= 120o
3.
= 150o
4.
= 180o
1 marks
Q. 68
1.
2.
(CH3)3CCOOH
3.
0
0
4.
1 marks
Q. 69 Each of the following compound gives a meta-nitro compound on nitration except
1.
2.
3.
4.
1 marks
Q. 70
Identify (C)
1.
0
0
2.
3.
4.
none of these
1 marks
Q. 71 If N and S both are present in an organic compound during Lassaigne's test, both will change into
1.
Na2S and NaCN
2.
NaSCN
3.
Na2SO3 and NaCN
4.
Na2S and NaCNO
1 marks
Q. 72 The decreasing order of polarity of the bond in NH3, PH3, AsH3 and SbH3 is in the order
0
0
1.
NH3 > PH3 > AsH3> SbH3
2.
SbH3 > AsH3 > PH3 > NH3
3.
NH3 > AsH3 > PH3 > SbH3
4.
NH3 > SbH3 > AsH3 > PH3
1 marks
Q. 73 Molarity of HCl ( ) if its density is 1.17 gm/cc is
1.
36.5
2.
32
3.
18.25
4.
63.5
1 marks
Q. 74 What is the normality of 0.30 M H3PO4 (tribasic acid ) in the following reaction ?.
0
0
1.
0.30 N
2.
0.60 N
3.
0.90 N
4.
0.15 N
1 marks
Q. 75 The ore magnesite is
1.
MgCO3.CaCO3
2.
MgCl2.KCl.6H2O
3.
MgSO4.7H2O
4.
MgCO3.
1 marks
Q. 76 2g sample of a mixture of Na2CO3 (anhydrous) and NaHCO3 containing 42% NaHCO3 was heated to constant heat. The mass of the residue (solid) left will be(MW = Na2CO3 = 106 and NaHCO3 = 84
0
0
1.
1.16g
2.
0.84g
3.
2g
4.
1.69g
1 marks
Q. 77 Which of the following graphs is NOT a correct representation of the Boyle's law?
1.
2.
3.
0
4.
1 marks
Q. 78 The decomposition of nitrogen pentoxide can be represented as
N2O5(g) 2NO2(g) + O2(g) .The rate of the reaction can be expressed as
1.
2.
3.
4.
1 marks
Q. 79
For the reaction, N2 + 3H2 2NH3, is equal to
1.
RT
2.
0
0
3.
(RT)2
4.
.
1 marks
Q. 80 The solubility of Fe(OH)3 is x mol L-1. Its Ksp would be
1.
9x3
2.
3x4
3.
27x4
4.
9x4
1 marks
Q. 81 Among KO2, Al , BaO2 and N , unpaired electron is present in
1.
N and BaO2
2.
KO2 and Al
3. KO2 only
0
0
4.
BaO2 only
1 marks
Q. 82 Carbinol is the trial name for
1.
(CH3)3COH
2.
C2H5OH
3.
CH3OH
4.
CH3CH2CHOHCH3
1 marks
Q. 83 Which of the following is most stable carbanion?
1.
I
2.
II
0
0
3.
III
4.
IV
1 marks
Q. 84 Petrol for aviation purposes must contain
1.
straight chain hydrocarbon
2.
aromatic hydrocarbons
3.
olefinic hydrocarbons
4.
highly branched chain paraffins
1 marks
Q. 85 Position of double bond in alkenes can be identified by
1.
Bromine water
2.
Ammoniacal silver nitrate solution
3.
Ozonolysis
0
0
4.
None of these
1 marks
Q. 86 The amount of heat liberated when 1 mole H2SO4 and 1 mole Ba(OH)2 reacts with each other (assuming both are strong acid and base respectively)
1.
- 13.7 k.cal
2.
- 27.4 k.cal
3.
- 10 k.cal
4.
- 41.1 k.cal
1 marks
Q. 87 In a cubic unit cell, seven of the eight corners are occupied by atoms A and centers of faces are occupied by atoms B. The general formula of the compound is
1.
A7B6
2.
A7B12
3.
A7B24
0
0
4.
A24B7
1 marks
Q. 88 The vapour pressure of a solution of 5 g of non electrolyte in 100 g of water at a particular temperature is 2985 Nm-2. The vapour pressure of pure water at that temperature is 3000 Nm-2. The molecular weight of the solute is
1.
180
2.
90
3.
270
4.
200
1 marks
Q. 89 Carbyl amine reaction will be given by:
1.
CH3CH2NH2
2.
(CH3)2CHNH2
3.
(CH3)3CNH2
0
0
4.
All of them
1 marks
Q. 90 Amongst TiFl6-2, CoFl6-3, Cu2Cl2 and NiCl4-2, the colourless species are
1.
CoF6
-3 and NiCl4-2
2.
TiF6
-2 and CoF6-3
3.
Cu2Cl2 and NiCl4-2
4.
TiF6
-2 and Cu2Cl2
1 marks
Q. 91 Standard electrode potentials of Fe2+ + 2e- Fe and Fe3+ + 3e- Fe are 0.440 V and - 0.036 V respectively. The standard electrode potential (E0) for Fe+3 + e- Fe+2 is
1.
- 0.476 V
2.
- 0.404 V
3.
+ .404 V
0
0
4.
+ 0.772 V
1 marks
Q. 92 Gold atoms form f.c.c. structure and impurities occupy tetrahedral and octahedral voids. Closest distance between impurity atom and gold atom in tetrahedral void is
1.
a
2.
a
3.
a
4.
a/2
1 marks
Q. 93 CO2 gas along with solid [X] is obtained when lithium salt [Y] is heated. [Y] is again obtained when CO2 gas is passed into of aqueous solution of [X] hence [Y] and [X] are:
1.
Li2CO3, Li2O
2.
Li2CO3, LiHCO3
3.
Li HCO3, Li2CO3
0
0
4.
Li2CO3, LiOH
1 marks
Q. 94 Mercury is transported in the container made of
1.
Ag
2.
Pb
3.
Al
4.
Fe
1 marks
Q. 95 Elevation of boiling point studies of Ca(NO3)2 give molar mass as 65.6. The degree of dissociation of Ca(NO3)2 is
1.
100 %
2.
75 %
3.
50%
4. 25 %
0
0
1 marks
Q. 96 Composition of super phosphate of lime is
1.
2.
3.
4.
1 marks
Q. 97 The vapour pressure of a solution of 5 g of non electrolyte in 100 g of water at a particular temperature is 2985 Nm-2. The vapour pressure of pure water at that temperature is 3000 Nm-2. The molecular weight of the solute is
1.
180
2.
90
3.
270
0
0
4.
200
1 marks
Q. 98 The following reaction represents the oxidation of glucose
Consider the following data in this regard:
Based on the above data, the standard free energy ( G0) for oxidation of glucose is
1.
+ 67.0 kcal
2.
- 67.0 kcal
3.
- 688.0 kcal
4.
+ 688.0 kcal
1 marks
Q. 99 For the reaction2A + 2B + C A2B + BCthe rate expression is rate a [A]2 [B] rate constant is 3 × 10 -2 L2mol2 sec-1. Relation between the initial concentration of the reactants are
moles/litre. The rate of the reaction after 25%C is converted into products is
0
0
1.
11.25 × 10-8 L2 mol -2 sec-1
2.
3.2 × 10 -2 L2 mol -2 sec-1
3.
0
4.
None of these
1 marks
Q. 100
Which of the following arrangements violates Hund's Rule?
1.
2.
3.
4.
1 marks
Mathematics
0
Q. 101
If |z| - z = 1 + 2i then z =
1.
2.
3.
3 - 4i
4.
3 + 4i
2 marks
Q. 102
If z1 and z2 are two non zero complex numbers such that |z1 + z2| = |z1| + |z2|, then arg z1 - arg z2 is equal to
1.
2.
0
3.
4.
2 marks
0
0
Q. 103
Let = , and . Then depends on
1.
only x
2.
only y
3.
neither x nor y
4.
both x and y
2 marks
Q. 104 .The vectors are collinear if equals
1.
3
2.
4
3.
5
4.
6
2 marks
0
0
Q. 105
.If A is a 3 × 3 matrix and det.(3A) = k {det. (A)}. Then k is equal to
1.
9
2.
6
3.
1
4.
27
2 marks
Q. 106
equals to
1.
0
2.
1
3.
4.
none of these.
2 marks
0
0
Q. 107
. is equal to
1.
2.
3.
4.
2 marks
Q. 108
From a set of 17 cards numbered 1, 2, 3 ............. 17 one is drawn at random. The probability then the number is divisible by 3 or 7 is
1.
2.
3.
4.
2 marks
0
0
Q. 109
If x is real, then the value of lies between
1.
1 and 3
2.
1 and 7
3.
1/7 and 7
4.
1/14 and 1
2 marks
Q. 110
The trace of the matrix : A = is
1.
36
2.
12
3.
20
4.
4
0
0
2 marks
Q. 111
If ax2 + bx + c = , then c = ?
1.
150
2.
-150
3.
150
4.
none of these
2 marks
Q. 112
Given Cr = nCr, then the value of is
1.
n(n - 1)
2.
n(n + 1)
3.
n2 - 1
0
0
4.
n2 + 1
2 marks
Q. 113
The value of cos2 48o - sin2 12o is
1.
2.
3.
4.
none of these
2 marks
Q. 114 .The value of is equal to
1.
2.
3.
0
0
4.
2 marks
Q. 115 If 2cos = a + 1/a, then cos3 is equal to
1.
[a3 + 1 /a3]
2.
3a + 1/3a
3.
2[a3 + 1/a3]
4.
none of these
2 marks
Q. 116
If two sides of a triangle are and the included angle is 600, then the third side is
1.
2.
3.
0
0
4.
2
2 marks
Q. 117 If f(x + 1) + f(x - 1) = f(x) for all x R, then the period of f(x) is
1.
3
2.
6
3.
12
4.
9
2 marks
Q. 118
The domain of definition of the function f(x) = is
1.
, n I
2.
, n I
3.
, n I
0
0
4.
none of these
2 marks
Q. 119
1.
2.
1
3.
0
4.
2 marks
Q. 120
is equal to
1.
1
2.
0
0
3.
4.
2 marks
Q. 121
Number of critical points of f (x) = are
1.
1
2.
2
3.
3
4.
none of these
2 marks
Q. 122
If the function f (x) = cos |x| - 2ax + b increases for all x R, then
1.
a b
2.
a = b/2
0
0
3.
a -1/2
4.
a -3/2
2 marks
Q. 123 is
1.
2.
3.
4.
none of these
2 marks
Q. 124
If f (a + b - x) = f (x), then is equal to
1.
2.
0
0
3.
0
4.
none of these
2 marks
Q. 125 The solution of the differential equation is
1.
y =
2.
log (y +1) =
3.
c(y + 1) =
4.
none of these
2 marks
Q. 126
The foot of perpendicular from the point (2, 4) upon x + y = 1 is
1.
2.
0
0
3.
4.
2 marks
Q. 127
Let P(-1, 0), Q(0, 0) and R(3, 3 ) be three points, then the equation of the bisector of the angle PQR is
1.
2.
x + = 0
3.
+ y = 0
4.
x +
2 marks
Q. 128
The radius of the circle touching the straight line x - 2y - 1 = 0 and 3x - 6y + 7 = 0 is
1.
2.
0
0
3.
4.
2 marks
Q. 129
Equation of tangent of the parabola y2 = 4ax parallel to y = 2x + 3 is
1.
y = 2x + a
2.
2y = 4x - a
3.
2y = 4x + a
4.
none of these
2 marks
Q. 130
The latus rectum of an ellipse is equal to half of its minor axis. Then its eccentricity is
1.
2.
0
0
3.
1/2
4.
2 marks
Q. 131
The parametric co-ordinates of any point on the director circle of
ellipse is
1.
((a2 + b2 )cos , (a2 + b2 ) sin )
2.
(a2 cos , b2 sin )
3.
((a2 - b2)cos , (a2 - b2) sin )
4.
2 marks
Q. 132
.The number of real tangents that can be drawn to the ellipse 3x2 + 5y2 = 32 passing through (3, 5) is
1.
0
2.
1
0
0
3.
2
4.
none of these
2 marks
Q. 133
If the normal at on the curve xy = c2 meets the curve again in t', then
1.
t' =
2.
t' =
3.
t' =
4.
t2 =
2 marks
Q. 134
The line y = x + 2 touches the hyperbola 5x2 - 9y2 = 45 at the point
1.
(0, 2)
2.
(3, 1)
0
0
3.
4.
2 marks
Q. 135
The area bounded by the curves y = xex , y = xe-x and the line x = 1 is
1.
2.
3.
4.
2 marks
Q. 136
.From a bag containing 5 white, 7 red and 4 black balls a man draws 3 balls at random. Then the probability of them being all white
1.
2.
0
0
3.
4.
2 marks
Q. 137
The equation of plane passing through P(2, 6, 3) and perpendicular to OP(O, being origin), is
1.
x + 4y + 3z = 49
2.
2x + 6y + z = 9
3.
2x + 6y + 3z = 49
4.
2x + 3y + 7z = 49
2 marks
Q. 138
If the plane 6x+4y+3z-12=0 cuts the axes at ABC, then the area of ABC is
1.
2.
0
0
3.
4.
2 marks
Q. 139
If angles made by a line with positive axes, then
is
1.
1
2.
2
3.
3
4.
4
2 marks
Q. 140
.If a is the angle between two forces 3N and 6N and 7N is their resultant, then is
1.
sin-1
2.
sin-1
0
0
3.
sin-1
4.
sin-1
2 marks
Q. 141
The numerical difference of the roots of x2 - 7x - 9 = 0 is
1.
5
2.
3.
4.
2 marks
Q. 142
Range of 2, 3, 4, 5, 9, 8, 7, 6, 5, 7, 4, 3 is
1.
7
2.
8
0
0
3.
9
4.
2
2 marks
Q. 143
The mean of the following distribution is 2.6 x; 1 2 3 4 5f 4 5 k 1 2 then k is
1.
4
2.
8
3.
12
4.
16
2 marks
Q. 144 .If 1 + then x is equal to
1.
2.
0
0
3.
4.
none
2 marks
Q. 145
If equation sin-1 x + sin-1y = and x2 + y2 = k2 hold simultaneously, then k equals
1.
2
2.
4
3.
6
4.
no such k exists
2 marks
Q. 146
Let , be the roots of the equation x2 - kx + k = 0, k R. If 2 + 2 is the minimum, then the roots of the equation are
1.
0
0
2.
3.
4.
2 marks
Q. 147
In a ABC, the angles A and B are two values of satisfying sin + cos = , | | < 2, then angle C is
1.
60o
2.
90o
3.
120o
4.
none of these
2 marks
Q. 148 (sin-1x)2 - (cos-1x)2 = , then x is
1.
1/2
0
0
2.
3.
-1/2
4.
none of these
2 marks
Q. 149
The locus of the middle points of chords of the parabola y2 = 4x, which pass through its focus is
1.
y2 = x - 1
2.
y2 = 2x - 2
3.
x2 = y - 1
4.
x2 = y + 1
2 marks
Q. 150
Tangents are drawn to the circle x2 + y2 = 10 at the points where it is met by the circle x2 + y2 + 4x - 3y + 2 = 0. The point of intersection of these tangents is
1.
0
0
2.
3.
4.
2 marks
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