question_answer 1) Which of the following physical quantity unit is not a fundamental unit?
A)
Length
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B)
Mass
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C)
Magnetic field
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D)
Current
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question_answer 2) The dimensional formula of electric potential is
A)
\[M{{L}^{2}}{{T}^{-3}}{{A}^{-1}}\]
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B)
\[{{M}^{-1}}{{L}^{2}}{{T}^{-2}}A\]
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C)
\[{{M}^{-1}}{{L}^{2}}{{T}^{-2}}{{A}^{-1}}\]
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D)
\[M{{L}^{2}}{{L}^{2}}{{T}^{-2}}A\]
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question_answer 3) The motion of a particle in straight line is an example of
A)
constant velocity motion
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B)
uniformly accelerated motion
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C)
non-uniformly accelerated motion
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D)
zero velocity motion
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question_answer 4) The velocity vector of the motion described by the position vector of a particle, \[r=2t\,\,\hat{i}+{{t}^{2}}\hat{j}\]is given by
A)
\[V=2i+2t\,\hat{j}\]
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B)
\[V=2t\,\,\hat{i}+2t\,\hat{j}\]
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C)
\[V=t\,\,\hat{i}+{{t}^{2}}\,\hat{j}\]
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D)
\[V=2\,\,\hat{i}+{{t}^{2}}\,\hat{j}\]
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question_answer 5) The velocity-time graph of particle comes out to be a non-linear curve. The motion is
A)
uniform velocity motion
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B)
uniformly accelerated motion
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C)
non-uniform accelerated motion
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D)
nothing can be said about the motion
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question_answer 6) A projectile is thrown with initial velocity \[{{\upsilon }_{0}}\] and angle \[{{30}^{o}}\] with the horizontal. If it remains in the air for \[1\text{ }s,\] what was its initial velocity?
A)
\[19.6\text{ }m/s\]
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B)
\[9.8\text{ }m/s\]
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C)
\[4.9\text{ }m/s\]
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D)
\[1\text{ }m/s\]
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question_answer 7) Newton's second law of motion is
A)
\[F=dp/dt\]
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B)
\[F=mv\]
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C)
\[~F=m{{v}^{2}}\]
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D)
\[~F={{m}^{2}}v\]
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question_answer 8) The centripetal force is given by the expression
A)
\[\frac{M{{V}^{2}}}{R}\]
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B)
\[\frac{{{M}^{2}}V}{R}\]
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C)
\[\frac{Mv}{{{R}^{2}}}\]
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D)
\[\frac{Mv}{R}\]
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question_answer 9) Uniform circular motion is an example of
A)
constant speed motion
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B)
constant velocity motion
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C)
non-accelerated motion
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D)
zero accelerated motion
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question_answer 10) The scalar product of two vectors \[A=2\hat{i}+2\hat{j}-\hat{k}\] and \[B=-\hat{j}+\hat{k},\] is given by
A)
\[A.B=3\]
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B)
\[A.B=4\]
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C)
\[A.B=-4\]
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D)
\[A.B=-3\]
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question_answer 11) The linear momentum is conserved in
A)
elastic collisions
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B)
inelastic collisions
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C)
Both 1 and 2
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D)
Neither 1 nor 2
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question_answer 12) The power (P) of an engine lifting a mass of \[100\text{ }kg\]up to a height of \[10\text{ }m\]in \[1\text{ }min\]is
A)
\[P=163.3\,\,W\]
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B)
\[P=9800\text{ }W\]
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C)
\[P=10000\text{ }W\]
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D)
\[P=5000\,\,W\]
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question_answer 13) The conservation of angular momentum demands that
A)
the external force on the system must be zero
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B)
the external torque on the system must be zero
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C)
both the external force as well as the external torque must be zero
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D)
neither of them must be zero
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question_answer 14) The moment of inertia (J) and the angular momentum (L) are related by the expression
A)
\[I=L\omega \]
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B)
\[L=I\omega \]
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C)
\[L={{I}^{2}}\omega \]
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D)
\[\omega =LI\] where (0 is the angular velocity.
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question_answer 15) The moment of inertia (J) of a sphere of radius R and mass M is given by
A)
\[I=M{{R}^{2}}\]
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B)
\[I=(1/2)M{{R}^{2}}\]
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C)
\[I=(4/3)M{{R}^{2}}\]
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D)
\[I=(2/5)M{{R}^{2}}\]
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question_answer 16) The universal law of gravitation is the force law known also as the
A)
triangular law
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B)
square law
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C)
inverse square law
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D)
parallelogram law
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question_answer 17) The value of acceleration due to gravity at the surface of earth
A)
is maximum at the poles
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B)
is maximum at the equator
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C)
remains constant everywhere on the surface of the earth
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D)
is maximum at the international timeline
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question_answer 18) The escape velocity of a particle from the surface of the earth is given by
A)
\[{{(g/R)}^{1/2}}\]
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B)
\[{{(2\,gR)}^{1/2}}\]
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C)
\[{{(3\,\,gR)}^{1/2}}\]
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D)
\[{{(\,gR/2)}^{2}}\]
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question_answer 19) The Young's modulus of a rope of \[10\text{ }m\] length and having diameter of \[2\text{ }cm\]is \[200\times {{10}^{11}}\,dyne/c{{m}^{2}}\]. If the elongation produced in the rope is \[1\text{ }cm,\] the force applied on the rope is
A)
\[6.28\times {{10}^{5}}\,\,N\]
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B)
\[6.28\times {{10}^{4}}\,\,N\]
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C)
\[6.28\times {{10}^{4}}\text{ }dyne\]
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D)
\[6.28\times {{10}^{5}}\text{ }dyne\]
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question_answer 20) "The pressure exerted at any point in an enclosed fluid is transmitted equally in all directions". This is known as
A)
Archimedes 'principle
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B)
Law of floatation
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C)
Pascal?s law
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D)
Bernoulli principal
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question_answer 21)
There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to
A)
\[\sqrt{h}\]
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B)
\[h\]
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C)
\[{{h}^{3/2}}\]
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D)
\[{{h}^{2}}\]
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question_answer 22) The zeroth law of thermodynamics for three systems A, B and C in contact demands that
A)
A and B are in thermal equilibrium
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B)
B and C are in thermal equilibrium
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C)
A and C are in thermal equilibrium
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D)
A B and C are in thermal equilibrium
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question_answer 23) The efficiency of a Carnot engine kept at the temperatures of \[{{27}^{o}}C\] and \[{{127}^{o}}C\] is
A)
\[20%\]
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B)
\[25%\]
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C)
\[30%\]
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D)
\[40%\]
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question_answer 24) The average pressure of an ideal gas is
A)
\[p=(1/3)mnV_{av}^{2}\]
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B)
\[p=(1/3)mn{{V}_{av}}\]
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C)
\[p=(1/4)mnV_{av}^{2}\]
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D)
\[p=(1/3)mn{{V}_{av}}\] where symbols have their usual meanings.
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question_answer 25) According to equipartition law of energy each particle in a system of particles have thermal energy E equal to
A)
\[E={{k}_{B}}T\]
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B)
\[E=(1/2){{k}_{B}}T\]
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C)
\[E=3\,\,{{k}_{B}}T\]
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D)
\[E=(3/2)\,\,{{k}_{B}}T\]
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question_answer 26) The velocity of sound in a gas is \[1300\text{ }m/s\]at STP and specific heat at constant pressure is \[6.84\,cal\,{{K}^{-1}}\,mo{{l}^{-1}}\]. The rms velocity at STP is \[(R=1.98\,cal\,\,{{K}^{-1}}\,mo{{l}^{-1}})\]
A)
\[1300\text{ }m/s\]
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B)
\[2600\text{ }m/s\]
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C)
\[1898\text{ }m/s\]
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D)
\[650\text{ }m/s\]
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question_answer 27) The time period of a simple pendulum of length \[9.8\text{ }m\]is
A)
\[0.159\,\,s\]
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B)
\[3.14\,\,s\]
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C)
\[6.5\,\,s\]
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D)
\[6.28\text{ }s\]
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question_answer 28) The displacement, velocity and acceleration in a simple harmonic motion are related as the
A)
displacement, velocity and acceleration all act in the same direction
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B)
displacement and velocity act in the same direction but acceleration in the opposite direction
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C)
Velocity and acceleration are parallel and both are perpendicular to the displacement
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D)
displacement and acceleration are antiparallel and both perpendicular to the velocity
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question_answer 29) The beats are the examples of
A)
simple harmonic motion
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B)
interference of two or more waves having same amplitude but slightly different frequencies in the same direction
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C)
interference of two or more waves having different amplitude but same frequencies in the same direction
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D)
interference of two or more waves having same amplitude out slightly different frequencies in the perpendicular direction
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question_answer 30) The fundamental frequency of an open pipe of length \[1\text{ }m,\] if the speed of sound in air is \[340\text{ }m/s\]is
A)
\[340\text{ }Hz\]
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B)
\[170\text{ }Hz\]
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C)
\[680\text{ }Hz\]
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D)
\[85\text{ }Hz\]
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question_answer 31) A whistle with frequency \[1020\text{ }Hz\]is blown at a station. A man travelling in train moving towards the station at \[30\text{ }m/s\]hears the sound of the whistle. If the speed of sound is \[340\text{ }m/s,\] the apparent frequency heard by him is
A)
\[1020\text{ }Hz\]
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B)
\[1110\text{ }Hz\]
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C)
\[2040\text{ }Hz\]
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D)
\[610\text{ }Hz\]
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question_answer 32) An electric charge does not have which of hte following properties?
A)
Total charge conservation
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B)
Quantization of charge
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C)
Two type of charge
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D)
Circular line of force
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question_answer 33) The net electric force on a charge of \[+3\mu C\] at the mid-point on the line joining two charges of magnitude \[+2\mu C\] and \[-2\mu C\] separated by the distance of \[6mm,\]is
A)
\[6000\,N\]
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B)
\[500\,N\]
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C)
\[60\,N\]
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D)
zero
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question_answer 34) A hollow sphere of radius \[0.1\text{ }m\] has a charge of \[5\times {{10}^{-8}}C.\]. The potential at a distance of \[5\text{ }cm\]from the centre of the sphere is \[=\left( \frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}\,\,N{{m}^{2}}\,\,{{C}^{-2}} \right)\]
A)
\[4000\,V\]
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B)
\[4500\,V\]
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C)
\[5000\,V\]
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D)
\[6000\,V\]
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question_answer 35) A parallel plate capacitor of capacitance 5 microfarad is charged to \[120\text{ }V\]and then connected to another uncharged capacitor. If the potential falls to \[40\text{ }V,\] and capacitance of the second capacitor is
A)
5 microfarad
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B)
10 microfarad
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C)
15 microfarad
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D)
20 microfarad
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question_answer 36) Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is
A)
\[1:1\]
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B)
\[1:2\]
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C)
\[1:3\]
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D)
\[1:4\]
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question_answer 37) An electron revolves in a circle at the rate of 1019 rounds per second. The equivalent current is \[(e=1.6\times {{10}^{-19}}C)\]
A)
\[1.0\,\,A\]
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B)
\[1.6\,\,A\]
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C)
\[2.0\text{ }A\]
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D)
\[2.6\text{ }A~\]
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question_answer 38) A silver wire of radius \[0.1\text{ }cm\]carries a current of\[2A\]. If the charge density in silver is \[5.86\times {{10}^{28}}{{m}^{-3}},\] the drift velocity is
A)
\[0.2\times {{10}^{-3}}m/s\]
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B)
\[0.4\times {{10}^{-4}}\text{ }m/s\]
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C)
\[0.68\times {{10}^{-4}}\text{ }m/s\]
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D)
\[7\times {{10}^{-4}}\text{ }m/s\]
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question_answer 39) A \[1\,m\] long wire of diameter of \[0.31\text{ }mm\] has a resistance of \[4.2\Omega \]. If it is replaced by another wire of same material of length \[1.5\text{ }m\]and diameter \[0.155\text{ }mm,\] the resistance of wire is
A)
\[25.2\text{ }\Omega \]
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B)
\[0.6\text{ }\Omega \]
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C)
\[26.7\text{ }\Omega \]
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D)
\[\text{0}\text{.8 }\Omega \]
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question_answer 40) 24 cells of emf \[1.5\text{ }V\]each having internal resistance of \[1\text{ }ohm\]are connected to an external resistance of\[1.5\text{ }ohms\]. To get maximum current
A)
all cells are connected in series combination
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B)
all cells are connected in parallel combination
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C)
4 cells in each row are connected in series and6 such rows are connected in parallel
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D)
6 cells in each row are connected in series and 4 such rows are connected in parallel
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question_answer 41) The temperature coefficient of the resistance of a wire is\[0.00125\text{ }per{{\text{ }}^{o}}C\]. At \[300\text{ K}\]its resistance is \[1\Omega \]. The resistance of wire will be \[2\,\,\Omega ,\] at
A)
\[1154\,\,K\]
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B)
\[1100\,\,K\]
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C)
\[1400\text{ }K\]
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D)
\[1127\,\,K\]
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question_answer 42) A long straight wire is carrying a current of\[12\text{ }A\]334. The magnetic field at a distance of \[8\text{ }cm\]is \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}\,\,N/{{A}^{2}})\]
A)
\[2\times {{10}^{-4}}Wb/{{m}^{2}}\]
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B)
\[3\times {{10}^{-5}}\text{ }Wb/{{m}^{2}}\]
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C)
\[4\times {{10}^{-4}}Wb/{{m}^{2}}\]
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D)
\[4\times {{10}^{-5}}\text{ }Wb/{{m}^{2}}\]
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question_answer 43) The magnetic field at a point on the axis of a long solenoid having 5 turns per cm length when a current of \[0.8\,A\]flows through it is
A)
\[5.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}\]
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B)
\[6.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}\]
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C)
\[7.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}\]
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D)
\[8.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}\]
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question_answer 44) Two straight wires each \[10\text{ }cm\]long are parallel to one another and separated by\[2\text{ }cm\]. When the current flowing in them is \[30\text{ }A\]and \[40\text{ }A\]respectively, the force experienced by either of the wires is
A)
\[1.2\times {{10}^{-3}}N\]
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B)
\[12\times {{10}^{-3}}N\]
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C)
\[11.2\times {{10}^{-3}}\text{ }N\]
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D)
\[10.2\times {{10}^{-3}}\text{ }N\]
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question_answer 45) The horizontal and vertical components of earth's magnetic field at a place are \[0.3\text{ }G\] and\[0.52\text{ }G\]. The earth's magnetic field and the angle of dip are
A)
\[0.3\text{ }G\]and \[\delta ={{30}^{o}}\]
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B)
\[0.4\text{ }G\]and \[\delta ={{40}^{o}}\]
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C)
\[0.5\text{ }G\]and \[\delta ={{50}^{o}}\]
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D)
\[0.6\text{ }G\]and \[\delta ={{60}^{o}}\]
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question_answer 46) A bar magnet of pole strength \[10\text{ }Am\]is cut into two equal parts breadthwise. The pole strength of each magnet is
A)
\[5\text{ }Am\]
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B)
\[~10\text{ }Am\]
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C)
\[15\text{ }Am\]
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D)
\[20\text{ }Am\]
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question_answer 47) A conductor of length \[5\text{ }cm\]is moved parallel to itself with a speed of \[2\text{ }m/s,\] perpendicular to a uniform magnetic field of\[{{10}^{-3}}\text{ }Wb/{{m}^{3}}\]. The induced e.m.f. generated is
A)
\[2\times {{10}^{-3}}V\]
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B)
\[1\times {{10}^{-3}}V\]
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C)
\[1\times {{10}^{-4}}V\]
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D)
\[2\times {{10}^{-4}}V\]
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question_answer 48) The induced emf in a coil of \[10\text{ }H\]inductance in which current varies from \[9\text{ }A\]to \[4\text{ }A\]in \[0.2\,\,s\] is
A)
\[200\,\,V\]
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B)
\[250\,\,V\]
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C)
\[300\,\,V\]
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D)
\[350\,\,V\]
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question_answer 49) The alternating current in a circuit is given by \[I=50\,\,\sin \,\,314t\]. The peak value and frequency of the current are
A)
\[{{I}_{0}}=25\,\,A\]and \[f=100\,\,Hz\]
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B)
\[{{I}_{0}}=50\,\,Hz\] and \[f=50\,Hz\]
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C)
\[{{I}_{0}}=50A\] and \[f=100\,\,Hz\]
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D)
\[{{\text{I}}_{0}}=25A\]and \[f=50\,\,Hz\]
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question_answer 50) A 5\[50\text{ }Hz\] AC signal is applied in a circuit of inductance of \[(1/\pi )H\] and resistance \[2100\,\Omega \]The impedance offered by the circuit is
A)
\[1500\text{ }\Omega \]
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B)
\[1700\,\,\Omega \]
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C)
\[2102\,\Omega \]
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D)
\[2500\,\,\Omega \]
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question_answer 51) If the alternating current \[I={{I}_{1}}\,\,\cos \,\,\,\omega t+{{I}_{2}}\,\,\sin \,\,\omega t\](of then the rms current is given by
A)
\[\frac{{{I}_{1}}+{{I}_{2}}}{\sqrt{2}}\]
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B)
\[\frac{|{{I}_{1}}+{{I}_{2}}|}{\sqrt{2}}\]
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C)
\[\sqrt{\left( \frac{I_{1}^{2}+I_{2}^{2}}{2} \right)}\]
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D)
\[\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{\sqrt{2}}}\]
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question_answer 52) The transverse nature of electromagnetic waves is proved by which of the following?
A)
Interference phenomena
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B)
Diffraction phenomena
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C)
Dispersion phenomena
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D)
Polarization phenomena
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question_answer 53) Which component of electromagnetic spectrum have maximum wavelength?
A)
Radio waves
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B)
Visible spectrum
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C)
Gamma rays
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D)
X-rays
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question_answer 54) An object is 8 cm high. It is desired to form a real image \[4\text{ }cm\]high at \[60\text{ }cm\]from the mirror. The type of mirror needed with the focal length is
A)
convex mirror with focal length \[f=40\text{ }cm\]
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B)
convex mirror with focal length \[f=20\text{ }cm\]
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C)
concave mirror with focal length \[f=-40\text{ }cm\]
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D)
concave mirror with focal length \[f=-20\text{ }cm\]
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question_answer 55) When an object is placed \[40\text{ }cm\]from a diverging lens, its virtual image is formed \[20\text{ }cm\]from the lens. The focal length and power of lens are
A)
\[F=-20cm,\,P=-5\,D\]
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B)
\[F=-40cm,\,P=-5\,D\]
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C)
\[F=-40cm,\,P=-2.5\,D\]
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D)
\[F=-20\,cm,\,P=-2.5\,D\]
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question_answer 56) A magnifying glass of focal length \[5\text{ }cm\]is used to view an object by a person whose smallest distance of distinct vision is\[25\text{ }cm\]. If he holds the glass close to eye, the magnification is
A)
\[5\]
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B)
\[6\]
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C)
\[2.5\]
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D)
\[3\]
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question_answer 57) A person has a minimum distance of distinct vision as\[50\text{ }cm\]. The power of lenses required to read a book at a distance of \[25\text{ }cm\]is
A)
\[3\,\,D\]
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B)
\[1\,\,D\]
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C)
\[2\,\,D\]
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D)
\[4\,\,D\]
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question_answer 58) If two slits in Young's experiment are \[0.4\text{ }mm\]apart and fringe width on a screen \[200\text{ }cm\]away is \[2\text{ }mm\]the wavelength of light illuminating the slits is
A)
\[500\text{ }nm\]
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B)
\[600\text{ }nm\]
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C)
\[400\text{ }nm\]
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D)
\[300\text{ }nm\]
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question_answer 59) Electric field strength due to a diple at a point on the axial line of dipole is
A)
from positive charge to negative charge
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B)
from negative charge to positive charge
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C)
along the equatorial line
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D)
at an angle to axial line
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question_answer 60) The distance of moon form the earth is \[3.8\times {{10}^{5}}\text{ }km\]. Supposing that the eye is most sensitive to the light of wavelength \[550\text{ }nm,\] the separation of two points on the moon that can be resolved by a \[500\text{ }cm\]telescope is
A)
\[50\,\,m\]
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B)
\[55\,\,m\]
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C)
\[51\text{ }m\]
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D)
\[60\,\,m\]
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question_answer 61) Unpolarized light falls on two polarizing sheets placed one on top of other. If the intensity of transmitted light is one fourth of the incident light, the angle between them is
A)
\[{{35}^{o}}\]
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B)
\[{{40}^{o}}\]
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C)
\[{{45}^{o}}\]
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D)
\[{{50}^{o}}\]
done
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E)
Not available
done
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question_answer 62) The Brewster's law is given by the expression
A)
\[\mu =\frac{\sin \,i}{\sin \,r}\]
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B)
\[\mu =\tan \,{{\theta }^{o}}\]
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C)
\[\mu =\cos \theta \]
done
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D)
\[\mu =sin\theta \]
done
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question_answer 63) Einstein's photoelectric equation is
A)
\[{{E}_{\max }}=hv-\phi \]
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B)
\[E=m{{c}^{2}}\]
done
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C)
\[{{E}^{2}}={{p}^{2}}{{c}^{2}}+m_{0}^{2}{{c}^{4}}\]
done
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D)
\[E=\left( \frac{1}{2} \right)m{{v}^{2}}\]
done
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question_answer 64) The Davission-Germer experiment is the direct evidence of
A)
particle nature of electrons
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B)
wave nature of electrons
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C)
wave nature of light
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D)
particle nature of light
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question_answer 65) The Rutherford scattering experiment porves that an atom consists of
A)
a sphere of positive charge in which electrons are embedded like seeds of water-melon
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B)
a sphere of negative charge in which protons are embedded like seeds of water-melon
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C)
a sphere of electron cloud in which the positive charge in placed at the centre of the sphere
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D)
a sphere of neutral charge
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question_answer 66) According to Bohr model of hydrogen atom, only those orbits are permissible which satisfy the condition
A)
\[mv=nh\]
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B)
\[\frac{m{{v}^{2}}}{r}=n\left( \frac{h}{2\pi } \right)\]
done
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C)
\[mvr=n\left( \frac{h}{2\pi } \right)\]
done
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D)
\[mv{{r}^{2}}=n\left( \frac{h}{2\pi } \right)\]
done
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question_answer 67) The radioactive decay of thorium \[(A=232,\,\,Z=90)\] releases six alpha and four beta particles. The atomic number and mass number of the final product is
A)
\[Z=80,\,\,A=207\]
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B)
\[Z=82,\,\,A=208\]
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C)
\[Z=92,\,\,A=209\]
done
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D)
\[Z=90,\,\,A=207\]
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question_answer 68) Polonium has a half-life of \[140\] days. If we take \[20\,\,g\]of polonium initially then the amount of it that remains after 280 days is
A)
\[2.5\,\,g\]
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B)
\[5\,\,g\]
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C)
\[10\text{ }g\]
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D)
\[15\text{ }g\]
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question_answer 69) Based on the band theory of conductors, insulators and semi-conductors, the forbidden gap is smallest in
A)
conductors
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B)
insulators
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C)
semi-conductors
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D)
All of these
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question_answer 70) Based on the I-V characteristics of the diode, we can classify diode as
A)
bi-directional device
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B)
ohmic device
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C)
non-ohmic device
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D)
passive element
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question_answer 71) The Boolean expression for the XOR gate is
A)
\[Y=A+B\]
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B)
\[Y=A.B\]
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C)
\[Y=AB=BA\]
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D)
\[Y=A\oplus B\]
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question_answer 72) Which of the following logic gates are also known as the Universal gates?
A)
AND, OR. NOT gate
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B)
XOR, XNOR gate
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C)
NAND, NOR gate
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D)
All logic gates
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question_answer 73) The length of antenna (L) required to propagate a signal of wavelength \[\lambda \] is given as
A)
\[L=\frac{\lambda }{2}\]
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B)
\[L=2\lambda \]
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C)
\[L=\frac{\lambda }{3}\]
done
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D)
\[L=\frac{\lambda }{4}\]
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question_answer 74) The modulation is the process in which the
A)
modulating signal is sent by antenna in the air
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B)
carrier signal is sent by the antenna in the air
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C)
modulated signal formed by the mixing of modulating signal with the carrier signal is sent by the antenna
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D)
modulated signal formed by the mixing of modulating signal with the carrier signal is received by a receiver antenna
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question_answer 75) The demodulator or detector circuit consists of a
A)
resistor
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B)
transistor
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C)
diode
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D)
capacitor
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question_answer 76) Which of the following would contain the same number of atoms as 20 g of calcium? [At. masses:\[Ca=40,Mg=24,C=12\]]
A)
24 g of magnesium
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B)
12 got carbon
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C)
24 got carbon
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D)
12 g of magnesium
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question_answer 77) 100 mL of \[\text{N}{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]is mixed with 100 mL of \[\text{1 M NaOH}\]solution. The resulting solution will be
A)
highly acidic
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B)
neutral
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C)
highly basic
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D)
slightly acidic
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question_answer 78) The bond order of\[\text{N}_{\text{2}}^{\text{+}}\]on the basis of molecular orbital theory is [Atomic number of\[\text{N}\,\text{=}\,\text{7}\]]
A)
3
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B)
2.5
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C)
2
done
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D)
1.5
done
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question_answer 79) What is the total number of electrons that can have the values \[n=2,l=1,s=1/2\]in the electronic configuration\[1{{s}^{2}}2{{s}^{2}}2{{p}^{3}}\]
A)
1
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B)
3
done
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C)
5
done
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D)
7
done
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question_answer 80) Calculate the wavelength associated with an electron moving with a velocity of \[{{10}^{6}}\,m/s\](mass of electron \[=9.1\times {{10}^{-31}}\,kg,\]\[h=6.6\times {{10}^{-34}}\,kg\,{{m}^{2}}\,{{s}^{-1}}\])
A)
\[6.2\times {{10}^{-8}}\,m\]
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B)
\[7.25\times {{10}^{-8}}\,m\]
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C)
\[6.25\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
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D)
None of the above
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question_answer 81) Which of the following pairs is not correctly matched?
A)
Hund's rule In orbitals of equivalent energy electron spins remain unpaired if possible
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B)
Pauli's exclusion No two electrons can principle have all the four quantum numbers identical
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C)
Zeeman effect The effect of magnetic field on the atomatic spectra
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D)
Uncertainty It is impossible to principle determine the position of an electron
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question_answer 82) The orbital diagram in which Aufbau principle is violated is
A)
done
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B)
done
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C)
done
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D)
done
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question_answer 83) The \[{{[\text{OH}]}^{-}}\]in a solution is \[1\,\text{mol}\,{{\text{L}}^{-1}}.\] The pH of the solution is
A)
1
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B)
0
done
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C)
14
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D)
\[{{10}^{-14}}\]
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question_answer 84) The solubility of \[\text{Fe(OH}{{\text{)}}_{\text{3}}}\]is \[x\,\text{mol}\,{{\text{L}}^{-1}}.\]Its\[{{K}_{sp}}\] would be
A)
\[9{{x}^{3}}\]
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B)
\[3{{x}^{3}}\]
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C)
\[27{{x}^{4}}\]
done
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D)
\[9{{x}^{4}}\]
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question_answer 85) In which of the following reactions, increase in pressure will favour the forward reaction?
A)
\[PC{{l}_{5}}(g)\rightleftharpoons PC{{l}_{3}}(g)+C{{l}_{2}}(g)\]
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B)
\[2NO(g)+{{O}_{2}}(g)\rightleftharpoons 2N{{O}_{2}}(g)\]
done
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C)
\[C(s)+{{H}_{2}}O(g)\rightleftharpoons CO(g)+{{H}_{2}}(g)\]
done
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D)
\[2HI(g)\rightleftharpoons {{H}_{2}}(g)+{{I}_{2}}(g)\]
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question_answer 86) Which of the following is a Lewis acid?
A)
\[BF_{4}^{-}\]
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B)
\[O{{H}^{-}}\]
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C)
\[AlC{{l}_{3}}\]
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D)
\[RN{{H}_{2}}\]
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question_answer 87) According to collision theory of chemical reactions rates of the reaction increase with increase in the temperature of a reaction because of
A)
increase in the velocity of the reacting molecules
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B)
increase in the number of collisions
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C)
increase in the number of molecules having the activation energy (threshold energy)
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D)
None of the above
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question_answer 88) Consider the reaction, \[2{{N}_{2}}O{{}_{5}}(g)\xrightarrow{{}}4N{{O}_{2}}(g)+{{O}_{2}}(g)\] The rate law for this reaction is rate\[=k[{{N}_{2}}{{O}_{5}}].\] Which of the following statements is true regarding the above reaction?
A)
Its order is 1 and molecularity is 1
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B)
Its order is 1 and molecularity is 2
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C)
Its order is 2 and molecularity is 2
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D)
Its order is 2 and molecularity is 1
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question_answer 89) A catalyst is a substance which
A)
increases the rate of forward reaction in reversible reaction
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B)
increases the rate of both forward and backward reaction in a reversible reaction
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C)
does not influence a reversible reaction
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D)
increases the rate of backward reaction in a reversible reaction.
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question_answer 90) Which of the following solutions will have the highest boiling point?
A)
1 M glucose solution
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B)
1 M sodium nitrate solution
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C)
1 M barium chloride solution
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D)
1 M aluminium chloride solution
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question_answer 91) Which of the following is a colligative property?
A)
Lowering of vapour pressure
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B)
Osmotic pressure
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C)
Boiling point
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D)
Change in entropy
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question_answer 92) van't Hoff factor for \[\text{Ca(N}{{\text{O}}_{\text{3}}}{{\text{)}}_{\text{2}}}\]is
A)
1
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B)
2
done
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C)
3
done
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D)
4
done
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question_answer 93) What will be the freezing point of 1% solution of glucose in water, given that molal depression constant for water is \[1.84\,\text{K}\,\text{mo}{{\text{l}}^{-}}\]
A)
272.898 K
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B)
\[~0.102{{\,}^{o}}C\]
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C)
273 K
done
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D)
\[108{{\,}^{o}}C\]
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question_answer 94) If\[\Delta H\]and\[\Delta S\]are positive for a reaction, the reaction will be spontaneous only when
A)
\[T\Delta S=\Delta H\]
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B)
\[T\Delta S>\Delta H\]
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C)
\[T\Delta S<\Delta H\]
done
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D)
\[T\Delta S\]is negative
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question_answer 95) Calculate the enthalpy change for the reaction, \[{{C}_{2}}{{H}_{4}}(g)+{{H}_{2}}(g)\xrightarrow{{}}{{C}_{2}}{{H}_{6}}(g)\] using the data given below \[{{C}_{2}}{{H}_{4}}(g)+3{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g)+2{{H}_{2}}O(l)\] \[\Delta H=-1415\,kJ\] \[{{C}_{2}}{{H}_{6}}(g)+\frac{7}{2}{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g)+3{{H}_{2}}O\] \[\Delta H=-1566\,kJ\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l);\Delta H=-286\,kJ\]
A)
\[-437\,kJ\]
done
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B)
\[135\,kJ\]
done
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C)
\[-135\,kJ\]
done
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D)
None of these
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question_answer 96) In thermodynamics, a quantity whose value simply depends upon the initial and final state of the system is called
A)
a thermodynamic quantity
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B)
a state function
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C)
an adiabatic quantity
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D)
a path function
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question_answer 97) All naturally occurring processes proceed spontaneously in a direction which leads to
A)
increase in enthalpy of system
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B)
decrease in entropy of system
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C)
decrease in free energy of system
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D)
increase in free energy of system
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question_answer 98) When an electrolytic solution conducts electricity, the current is carried by
A)
the electrons
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B)
cations and anions
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C)
neutral molecules
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D)
the atoms of the electrolyte
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question_answer 99) An electrochemical cell has two half cell reactions as, \[{{A}^{2+}}+2{{e}^{-}}\xrightarrow{{}}A;\] \[E_{{{A}^{2+}}/A}^{o}=0.34\,V\] \[X\xrightarrow{{}}{{X}^{2+}}+2{{e}^{-}};\] \[E_{{{x}^{2}}/x}^{0}=-2.37\,V\] The cell voltage will be
A)
\[2.71\,V\]
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B)
\[2.03\,V\]
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C)
\[-2.71\,V\]
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D)
\[-2.03\,V\]
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question_answer 100) In the electrolysis of dilute £[2804 using platinum electrode
A)
\[{{\text{H}}_{\text{2}}}\]is liberated at cathode
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B)
\[{{\text{O}}_{\text{2}}}\]is produced at cathode
done
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C)
\[\text{C}{{\text{l}}_{\text{2}}}\] is obtained at cathode
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D)
\[\text{N}{{\text{H}}_{\text{3}}}\] is produced at anode
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question_answer 101) When a solution of sodium hydroxide is added to acetic acid solution, the conductivity of the resulting solution will
A)
increase
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B)
remain unchanged
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C)
decrease
done
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D)
become zero
done
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question_answer 102) The behaviour of a real gas approaches ideal behaviour at
A)
low temperature, low pressure
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B)
high temperature, high pressure
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C)
low temperature, high pressure
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D)
high temperature, low pressure
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question_answer 103) Which of the following is not the postulate of the kinetic theory of gases?
A)
Gas molecules are in a permanent state of random motion
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B)
Pressure of gas is due to molecular impacts on the walls
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C)
The molecules are perfectly elastic
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D)
The molecular collisions are elastic
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question_answer 104) When a cation leaves its normal position in the crystal and moves to some interstitial space, the defect in the crystal is known as
A)
Schottky defect
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B)
F-centre
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C)
Frenkel defect
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D)
non-stoichiometric defect
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question_answer 105) Fog is a colloidal system of
A)
gas in liquid
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B)
liquid in gas
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C)
gas in gas
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D)
gas in solid
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question_answer 106) The purification of a colloidal solution could be done by
A)
sedimentation
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B)
ultrafiltration
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C)
filtration
done
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D)
precipitation
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question_answer 107) Bakelite is a product of the reaction between
A)
formaldehyde and NaOH .
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B)
aniline and urea
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C)
phenol and methanol
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D)
phenol and chloroform
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question_answer 108) How does electron affinity change when we move from left to right in a period in the Periodic Table?
A)
It increases
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B)
It decreases
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C)
It remains unchanged
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D)
It first increases and then decreases
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question_answer 109) Which of the following statements is not correct?
A)
lonisation energy increases on going down a group in the Periodic Table
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B)
Among alkaline earth metals, reducing character increases down the group
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C)
Fluorine is the most electronegative element
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D)
Metallic character increases on going down a group in the Periodic Table
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question_answer 110) Which of the following species has a trigonal planar shape?
A)
\[_{.}^{.}CH_{3}^{-}\]
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B)
\[CH_{3}^{+}\]
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C)
\[BF_{4}^{-}\]
done
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D)
\[Si{{H}_{4}}\]
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question_answer 111) Which of the following will have maximum dipole moment?
A)
\[N{{F}_{3}}\]
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B)
\[N{{H}_{3}}\]
done
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C)
\[C{{H}_{4}}\]
done
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D)
\[PC{{l}_{3}}\]
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question_answer 112) Which of the following forces is the strongest?
A)
Hydrogen bonding
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B)
Dipole-dipole forces
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C)
van der Waals' forces
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D)
Coordinate bonding
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question_answer 113) Which of the following statements is correct?
A)
\[s{{p}^{3}}-\] hybrid orbitals have equal s and p character
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B)
The bond angle decreases with the decrease of s character of a hybridized orbital
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C)
Resonance decreases the stability of a molecule
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D)
Resonance is due to delocalization of sigma electrons
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question_answer 114) Which of the following is the correct order of increasing oxidising character of oxoacids of chlorine?
A)
\[HCl{{O}_{3}}<HCl{{O}_{4}}<HCl{{O}_{2}}<HClO\]
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B)
\[~HCl{{O}_{4}}<HCl{{O}_{3}}<HCl{{O}_{2}}<HClO\]
done
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C)
\[~HClO<HCl{{O}_{4}}<HCl{{O}_{3}}<HCl{{O}_{2}}\]
done
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D)
\[HClO<HCl{{O}_{2}}<HCl{{O}_{3}}<HCl{{O}_{4}}\]
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question_answer 115) Which of the following oxides of group 16 has the highest boiling point?
A)
\[{{H}_{2}}O\]
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B)
\[{{H}_{2}}S\]
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C)
\[{{H}_{2}}Se\]
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D)
\[{{H}_{2}}Te\]
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question_answer 116) The +1 oxidation state of thallium is more stable than its +3 oxidation state because of
A)
its atomic size
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B)
its ionization potential
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C)
inert pair effect
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D)
diagonal relationship
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question_answer 117) Which of the following statements is false regarding alkali metals?
A)
Alkali metals are soft and can be cut with the help of knife
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B)
Alkali metals do not occur in free state in nature
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C)
Alkali metals are highly electropositive elements
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D)
Alkali metal hydrides are covalent in character
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question_answer 118) Among the following outermost configurations of transition metals, which shows the highest oxidation state?
A)
\[~3{{d}^{3}}4{{s}^{2}}\]
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B)
\[~3{{d}^{5}}\text{ }4{{s}^{1}}\]
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C)
\[3{{d}^{5}}\text{ }4{{s}^{2}}\]
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D)
\[3{{d}^{2}}\text{ }4{{s}^{2}}\]
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question_answer 119) The tendency of transition metals to form stable complexes is due to their
A)
low ionization energies
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B)
variable oxidation states
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C)
strong electropositive nature
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D)
high charge/size ratio and vacant d orbitals
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question_answer 120) The transition metal ions are generally paramagnetic in nature because
A)
they have coloured salts
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B)
they have one or more unpaired cf-electrons
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C)
they have one or more paired s-electrons
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D)
they are reducing agents
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question_answer 121) The most common oxidation state of lanthanides is
A)
\[+\,4\]
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B)
\[+\text{ }3\]
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C)
\[+\,6\]
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D)
\[+\,2\]
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question_answer 122) Specify the coordination number of cobalt in \[[Co(CN)({{H}_{2}}O){{(en)}^{2}}]{{~}^{2+}}\]
A)
6
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B)
4
done
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C)
0
done
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D)
3
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question_answer 123) Which of the following complexes is square planar and diamagnetic?
A)
\[{{[NiC{{l}_{4}}]}^{2-}}\]
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B)
\[{{[NI{{(CN)}_{4}}]}^{2-}}\]
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C)
\[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
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D)
\[{{[CuC{{l}_{4}}]}^{2-}}\]
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question_answer 124) Which type of isomerism is exhibited by\[[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]?\]
A)
Coordination isomerism
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B)
Linkage isomerism
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C)
Optical isomerism
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D)
Geometrical isomerism
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question_answer 125) Ethylene diamine tetraacetate ion is a
A)
unidentate ligand
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B)
bidentate ligand
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C)
pentadentate ligand
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D)
hexadentate ligand
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question_answer 126) Which of the following is an ore of zinc?
A)
Galena
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B)
Pyrolusite
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C)
Sphaterite
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D)
Magnetite
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question_answer 127) The impurities associated with the ore after mining are collectively called
A)
flux
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B)
slag
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C)
minerals
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D)
gangue
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question_answer 128) During extraction of iron, the iron obtained at the bottom of blast furnace is known as
A)
steel
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B)
wrought iron
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C)
cast iron
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D)
None of these
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question_answer 129) Select the molecule which has only one \[\pi -\]bond
A)
\[CH\equiv CH\]
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B)
\[C{{H}_{2}}=CH-CHO\]
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C)
\[C{{H}_{3}}-CH=C{{H}_{2}}\]
done
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D)
\[C{{H}_{3}}-CH=CH-COOH\]
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question_answer 130) Which of the following groups is ortho and para directing?
A)
\[-COCl\]
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B)
\[-CHO\]
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C)
\[-OH\]
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D)
\[-COC{{H}_{3}}\]
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question_answer 131) Amongst the given cations, the most stable carbonium ion is
A)
\[{{\,}^{+}}C{{H}_{3}}\]
done
clear
B)
\[{{(C{{H}_{3}})}_{3}}{{C}^{+}}\]
done
clear
C)
\[C{{H}_{3}}C{{H}_{2}}\]
done
clear
D)
\[{{(C{{H}_{3}})}_{2}}\overset{+}{\mathop{C}}\,H\]
done
clear
View Answer play_arrow
question_answer 132) The hybridization of carbon atoms in C?C single bond of\[HC=C-CH=C{{H}_{2}}\] is
A)
\[s{{p}^{3}}-s{{p}^{2}}\]
done
clear
B)
\[s{{p}^{2}}-s{{p}^{3}}\]
done
clear
C)
\[sp-s{{p}^{2}}\]
done
clear
D)
\[s{{p}^{3}}-s{{p}^{3}}\]
done
clear
View Answer play_arrow
question_answer 133) The number of optical isomers of the compound\[C{{H}_{3}}CHBrCHBrCOOH\]is
A)
0
done
clear
B)
1
done
clear
C)
3
done
clear
D)
4
done
clear
View Answer play_arrow
question_answer 134) Electrolysis of an aqueous solution of sodium ethanoate gives
A)
methane
done
clear
B)
ethane
done
clear
C)
butane
done
clear
D)
methyl ethanoate
done
clear
View Answer play_arrow
question_answer 135) Which of the following compounds will exhibit cis-trans (geometrical) isomerism?
A)
2-butene
done
clear
B)
2-butyne
done
clear
C)
2-butanol
done
clear
D)
1-butanol
done
clear
View Answer play_arrow
question_answer 136) The reaction given below is an example of which of the following? \[2C{{H}_{3}}Br+2Na\xrightarrow{\text{dry}\,\text{ether}}{{C}_{2}}{{H}_{6}}+2NaBr\]
A)
Reimer-Tiemann reaction
done
clear
B)
Wurtz reaction
done
clear
C)
Hoffman bromamide reaction
done
clear
D)
Aldol condensation
done
clear
View Answer play_arrow
question_answer 137) Chlorobenzene can be prepared by reacting aniline with
A)
hydrochloric acid in the presence of nitrous acid
done
clear
B)
cuprous chloride in the presence of aluminium chloride
done
clear
C)
chlorine in the presence of aluminium chloride
done
clear
D)
nitrous acid followed by heating with cuprous chloride
done
clear
View Answer play_arrow
question_answer 138) Phenol on treatment with cone. \[\text{HN}{{\text{O}}_{\text{3}}}\]gives
A)
o-nitrophenol
done
clear
B)
p-nitrophenol
done
clear
C)
o-and p-nitrophenol
done
clear
D)
2, 4, 6-trinitrophenol
done
clear
View Answer play_arrow
question_answer 139) Which of the following compounds will be formed when methoxy benzene is reacted with HBr?
A)
Phenol and bromomethane
done
clear
B)
Methanol and bromobenzene
done
clear
C)
Phenol and methanol
done
clear
D)
Bromobenzene and bromomethane
done
clear
View Answer play_arrow
question_answer 140) When ethanol and\[{{\text{I}}_{\text{2}}}\]are heated in the presence of\[\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\text{,}\]the yellow crystals obtained are of
A)
\[{{C}_{2}}{{H}_{5}}l\]
done
clear
B)
\[C{{H}_{3}}l\]
done
clear
C)
\[CH{{l}_{3}}\]
done
clear
D)
\[C{{H}_{2}}{{l}_{2}}\]
done
clear
View Answer play_arrow
question_answer 141) Identify B in the following series of reaction \[C{{H}_{3}}CHO\xrightarrow{C{{H}_{3}}MgX}A\xrightarrow{HOH}B\]
A)
2-propanol
done
clear
B)
1-propanol
done
clear
C)
ethanol
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 142) Which of the following compounds has maximum acidic character?
A)
Dichloroacetic acid
done
clear
B)
Acetic acid
done
clear
C)
Trichloroacetic ucid
done
clear
D)
Triflouoroacetic acid
done
clear
View Answer play_arrow
question_answer 143) Among the following, the least reactive aldehyde is
A)
\[HCHO\]
done
clear
B)
\[{{C}_{6}}{{H}_{5}}CHO\]
done
clear
C)
\[C{{H}_{3}}CHO\]
done
clear
D)
\[{{C}_{2}}{{H}_{5}}CHO\]
done
clear
View Answer play_arrow
question_answer 144) Propanal on reaction with lithium aluminium hydride gives
A)
1-propanol
done
clear
B)
2-propanol
done
clear
C)
ethanol
done
clear
D)
butanol
done
clear
View Answer play_arrow
question_answer 145) Idenitfy Z in the following sequence \[C{{H}_{3}}C{{H}_{2}}I\xrightarrow{KCN}X\xrightarrow{{{H}_{3}}{{O}^{+}}/{{H}_{2}}O}Y\] \[\xrightarrow[\Delta ]{{{H}_{3}}{{O}^{+}}/{{H}_{2}}O}Z\]
A)
\[C{{H}_{3}}COCl\]
done
clear
B)
\[C{{H}_{3}}CON{{H}_{2}}\]
done
clear
C)
\[C{{H}_{3}}COOH\]
done
clear
D)
\[C{{H}_{3}}C{{H}_{2}}COOH\]
done
clear
View Answer play_arrow
question_answer 146) Treatment of aniline with bromine water produces
A)
2,4,6-tribromoaniline
done
clear
B)
a mixture of ortho and para bromoaniline
done
clear
C)
bromobenzene
done
clear
D)
N-bromoaniline
done
clear
View Answer play_arrow
question_answer 147) \[{{C}_{6}}{{H}_{5}}COCl\xrightarrow{N{{H}_{3}}}X\xrightarrow{{{P}_{2}}{{O}_{5}}}Y\xrightarrow[{{H}_{2}}]{Ni}Z\] The end product in the above sequence of reactions is
A)
benzole acid
done
clear
B)
aniline
done
clear
C)
benzyl amine
done
clear
D)
benzonitrile
done
clear
View Answer play_arrow
question_answer 148) Which of the following is least reactive to nitration?
A)
Benzene
done
clear
B)
Nitrobenzene
done
clear
C)
Chlorobenzene
done
clear
D)
Aniline
done
clear
View Answer play_arrow
question_answer 149) Nucleic acids are polymers of
A)
nucleotides
done
clear
B)
nucleosides
done
clear
C)
nuclei of heavy metals
done
clear
D)
proteins
done
clear
View Answer play_arrow
question_answer 150) Which of the following enzymes helps in digestion of proteins?
A)
Invertase
done
clear
B)
Trypsin
done
clear
C)
Tryosinase
done
clear
D)
Urease
done
clear
View Answer play_arrow
question_answer 151) The value of\[\cos \left( \frac{3\pi }{2}+x \right)\,\cos \,(2\pi +x)\left\{ \cot \left( \frac{3\pi }{2}-x \right)+\cot \,(2\pi +x) \right\}\]is
A)
\[0\]
done
clear
B)
\[1\]
done
clear
C)
\[cos\text{ }x\]
done
clear
D)
\[sin\text{ }x\]
done
clear
View Answer play_arrow
question_answer 152) If \[\sin B=3\sin (2A+B),\] then \[2\tan A+\tan (A+B)\] is equal to
A)
\[0\]
done
clear
B)
\[-2\]
done
clear
C)
\[1\]
done
clear
D)
\[1\]
done
clear
View Answer play_arrow
question_answer 153) If \[\theta =\frac{\pi }{{{2}^{n}}+1},\] then the value of \[{{2}^{n}}\cos \theta \,\cos \,2\theta \,\cos \,{{2}^{2}}\theta .....\cos {{2}^{n-1}}\theta \] is
A)
\[\sin \theta \]
done
clear
B)
\[\frac{\pi }{2}\]
done
clear
C)
\[0\]
done
clear
D)
\[1\]
done
clear
View Answer play_arrow
question_answer 154) Using the principal values, the value of \[{{\sin }^{-1}}\left\{ \sin \frac{5\pi }{6} \right\}+{{\tan }^{-1}}\left\{ \tan \frac{\pi }{6} \right\}\]is equal to
A)
\[\frac{\pi }{6}\]
done
clear
B)
\[\frac{2\pi }{3}\]
done
clear
C)
\[\frac{\pi }{3}\]
done
clear
D)
\[\frac{5\pi }{6}\]
done
clear
View Answer play_arrow
question_answer 155) Find the value of \[{{\cos }^{-1}}\left( \frac{4}{5} \right)+{{\tan }^{-1}}\left( \frac{3}{5} \right)\].
A)
\[{{\tan }^{-1}}\left( \frac{7}{10} \right)\]
done
clear
B)
\[{{\tan }^{-1}}\left( \frac{27}{11} \right)\]
done
clear
C)
\[{{\sin }^{-1}}\left( \frac{7}{5} \right)\]
done
clear
D)
\[{{\tan }^{-1}}\left( \frac{1}{5} \right)\]
done
clear
View Answer play_arrow
question_answer 156) If \[X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right]\] and \[X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right]\], then X is equal to
A)
\[\left[ \begin{matrix} 5 & 0 \\ 0 & 4 \\ \end{matrix} \right]\]
done
clear
B)
\[\left[ \begin{matrix} 7 & 0 \\ 1 & 5 \\ \end{matrix} \right]\]
done
clear
C)
\[\left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right]\]
done
clear
D)
\[\left[ \begin{matrix} 7 & 1 \\ 0 & 4 \\ \end{matrix} \right]\]
done
clear
View Answer play_arrow
question_answer 157) If \[\left| \begin{matrix} x+7 & 5 \\ x+-3 & 3 \\ \end{matrix} \right|=26,\] then x is equal to
A)
\[1\]
done
clear
B)
\[3\]
done
clear
C)
\[5\]
done
clear
D)
\[7\]
done
clear
View Answer play_arrow
question_answer 158) The value of \[\left| \begin{matrix} {{a}^{2}} & 2ab & {{b}^{2}} \\ {{b}^{2}} & {{a}^{2}} & 2ab \\ 2ab & {{b}^{2}} & {{a}^{2}} \\ \end{matrix} \right|\] is
A)
\[{{({{a}^{2}}+{{b}^{2}})}^{3}}\]
done
clear
B)
\[{{({{a}^{3}}+{{b}^{3}})}^{2}}\]
done
clear
C)
\[{{({{a}^{4}}+{{b}^{4}})}^{2}}\]
done
clear
D)
\[{{({{a}^{2}}+{{b}^{2}})}^{4}}\]
done
clear
View Answer play_arrow
question_answer 159) If \[A=\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right],\] then \[(A-A')\] is equal to (where, A 'is transpose of matrix A)
A)
null matrix
done
clear
B)
identity matrix
done
clear
C)
symmetric
done
clear
D)
skew-symmetric
done
clear
View Answer play_arrow
question_answer 160) If \[{{A}^{-1}}=\left[ \begin{matrix} 5 & -2 \\ -7 & 3 \\ \end{matrix} \right]\] and \[{{B}^{-1}}=\frac{1}{2}\left[ \begin{matrix} 9 & -7 \\ -8 & 6 \\ \end{matrix} \right],\] then \[{{(AB)}^{-1}}\] is equal to
A)
\[\left[ \begin{matrix} 47 & -39/2 \\ -41 & 17 \\ \end{matrix} \right]\]
done
clear
B)
\[\left[ \begin{matrix} 94 & -82 \\ -39 & 34 \\ \end{matrix} \right]\]
done
clear
C)
\[\left[ \begin{matrix} -47 & 46 \\ 39/2 & -17 \\ \end{matrix} \right]\]
done
clear
D)
\[\left[ \begin{matrix} -47 & 39/2 \\ 46 & -17 \\ \end{matrix} \right]\]
done
clear
View Answer play_arrow
question_answer 161) The value of \[\underset{x\to 1}{\mathop{\lim }}\,\frac{x-1}{{{\log }_{e}}x}\] is
A)
\[1\]
done
clear
B)
\[0\]
done
clear
C)
Not defined
done
clear
D)
\[-1\]
done
clear
View Answer play_arrow
question_answer 162) \[\underset{x\to 0}{\mathop{\lim }}\,\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}}\]is equal to
A)
\[e\]
done
clear
B)
\[{{e}^{2}}\]
done
clear
C)
\[1/e\]
done
clear
D)
\[1/{{e}^{2}}\]
done
clear
View Answer play_arrow
question_answer 163) The value of \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\left\{ \frac{1+2+3+....+n}{n+2}-\frac{n}{2} \right\}\] is
A)
\[\frac{1}{2}\]
done
clear
B)
\[1\]
done
clear
C)
\[-1\]
done
clear
D)
\[-\frac{1}{2}\]
done
clear
View Answer play_arrow
question_answer 164) If \[y=1+\frac{x}{1!}+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{3}}}{3!}.....,\]then \[\frac{dy}{dx}\] is equal to
A)
\[{{e}^{x}}\]
done
clear
B)
\[\sin \,x\]
done
clear
C)
\[y\]
done
clear
D)
\[x\]
done
clear
View Answer play_arrow
question_answer 165) The value of \[\frac{d}{dx}({{x}^{n}}\,{{\log }_{a}}\,x{{e}^{x}})\] is
A)
\[{{e}^{x}}\,{{\log }_{a}}\,x+\frac{{{x}^{n-1}}}{{{\log }_{e}}\,a}\]
done
clear
B)
\[{{e}^{x}}{{x}^{n-1}}\,\left\{ x{{\log }_{a}}\,x+\frac{1}{{{\log }_{e}}\,a}+n\,{{\log }_{a}}x \right\}\]
done
clear
C)
\[n{{x}^{n-1}}\,{{\log }_{a}}\,x{{e}^{x}}\]
done
clear
D)
\[{{x}^{n}}\,{{\log }_{a}}x.{{e}^{x}}\]
done
clear
View Answer play_arrow
question_answer 166) The interval in which the function \[f(x)=\sin x-\cos x,\,\,\,\,0\le x\le 2\pi \] is strictly decreasing, is
A)
\[0<x<\frac{3\pi }{4}\]
done
clear
B)
\[\frac{7\pi }{4}<x<2\pi \]
done
clear
C)
\[\frac{3\pi }{4}<x<\frac{7\pi }{4}\]
done
clear
D)
\[0<x<\frac{7\pi }{4}\]
done
clear
View Answer play_arrow
question_answer 167) The slope of normal to the curve \[y={{x}^{3}}+2x+6\] which is parallel to line \[x+14y+4=0\] is
A)
\[-\frac{1}{3}\]
done
clear
B)
\[-\frac{1}{14}\]
done
clear
C)
\[-4\]
done
clear
D)
\[-\frac{1}{2}\]
done
clear
View Answer play_arrow
question_answer 168) The approximate value of \[{{(0.009)}^{1/3}}\] is
A)
\[0.2\]
done
clear
B)
\[0.2083\]
done
clear
C)
\[0.0032\]
done
clear
D)
\[0.0083\]
done
clear
View Answer play_arrow
question_answer 169) If \[\left\{ \begin{matrix} \frac{(1-\cos \,4x)}{{{x}^{2}}}, & if & x<0 \\ a, & if & x=0, \\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & if & x>0 \\ \end{matrix} \right.\]then \[f(x)\] is continuous at \[x=0,\] for a
A)
\[4\]
done
clear
B)
\[\sqrt{32}\]
done
clear
C)
\[8\]
done
clear
D)
\[16\]
done
clear
View Answer play_arrow
question_answer 170) The value of \[\int_{0}^{\pi /2}{\frac{dx}{1+\tan x}}\] is
A)
\[\frac{\pi }{2}\]
done
clear
B)
\[0\]
done
clear
C)
\[\frac{\pi }{4}\]
done
clear
D)
\[\frac{\pi }{8}\]
done
clear
View Answer play_arrow
question_answer 171) Evaluate \[\int{\frac{3x-2}{(x+3){{(x+1)}^{2}}}}\,dx.\]
A)
\[\frac{11}{4}\log \,[|x+1|\,|x+3|]+\frac{5}{2(x+1)}+C\]
done
clear
B)
\[\frac{11}{4}\log \,\left| \frac{x+3}{x+1} \right|+\frac{1}{x+1}+C\]
done
clear
C)
\[\frac{11}{4}\log \,|x+2|+\frac{5}{2}(x+3)+\frac{1}{x+1}+C\]
done
clear
D)
\[\frac{11}{4}\log \,\left| \frac{x+1}{x+3} \right|+\frac{5}{2(x+1)}+C\]
done
clear
View Answer play_arrow
question_answer 172) The general solution of the linear differential equation \[\frac{dy}{dx}+\sec \,x.\,y=\tan x\] \[\left( 0\le x\le \frac{\pi }{2} \right)\]is
A)
\[y=-x\,{{(\sec x+\tan x)}^{-1}}+\frac{C}{\sec x+\tan x}+1\]
done
clear
B)
\[y=x+\frac{C}{\sec x+\tan x}+\frac{1}{\tan x}\]
done
clear
C)
\[y=\frac{x+1}{\sec x+\tan x}+C\]
done
clear
D)
\[y=x+\sec x-\tan \,x+C\]
done
clear
View Answer play_arrow
question_answer 173) On solving the differential equation \[{{x}^{2}}y\,dx-({{x}^{3}}+{{y}^{2}})dy=0,\]the value of \[\log \,y\] is
A)
\[\frac{{{x}^{3}}}{3{{y}^{3}}}+C\]
done
clear
B)
\[\frac{{{x}^{2}}}{{{y}^{2}}}+C\]
done
clear
C)
\[\frac{{{x}^{2}}}{3{{y}^{3}}}+C\]
done
clear
D)
\[\frac{{{x}^{3}}}{{{x}^{3}}+{{y}^{3}}}+C\]
done
clear
View Answer play_arrow
question_answer 174) The value of \[\int{\frac{2+\sin x}{1+\cos x}}\,{{e}^{x/2}}dx\] is
A)
\[2.{{e}^{x/2}}\,\tan \frac{x}{2}+C\]
done
clear
B)
\[{{e}^{x/2}}\,\tan \,x+C\]
done
clear
C)
\[\frac{1}{2}{{e}^{x/2}}\,\sin x+C\]
done
clear
D)
\[\frac{1}{2}\,\,{{e}^{x/2}}\,\sin \frac{x}{2}+C\]
done
clear
View Answer play_arrow
question_answer 175) On evaluation, the value of \[\int_{0}^{4}{f(x)\,\,dx,}\]where \[f(x)=\left\{ \begin{matrix} |x-2|+2, & x\le 2 \\ {{x}^{2}}-2, & x>2 \\ \end{matrix} \right.\] is
A)
\[\frac{56}{3}\]
done
clear
B)
\[\frac{60}{3}\]
done
clear
C)
\[\frac{66}{3}\]
done
clear
D)
\[\frac{62}{3}\]
done
clear
View Answer play_arrow
question_answer 176) The particular solution of the differential equation \[\frac{dy}{dx}+y\,\cot \,x=2x+{{x}^{2}}\,\cot \,x,\]such that \[y(\pi /2)=0\] is
A)
\[y=\frac{{{\pi }^{2}}}{4\,\cos \,x},(x\ne 0)\]
done
clear
B)
\[y={{x}^{2}}-\frac{\pi }{2}\tan x\]
done
clear
C)
\[y=\frac{2x}{\sin x}+\frac{1}{{{x}^{2}}},(x\ne 0)\]
done
clear
D)
\[y={{x}^{2}}-\frac{{{\pi }^{2}}}{4\sin x}(\sin x\ne 0)\]
done
clear
View Answer play_arrow
question_answer 177) The differential equation corresponding to the equation\[{{y}^{2}}=a(b-{{x}^{2}})\] where a, b are constants is
A)
\[{{y}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}=a\left( b-\frac{dy}{dx}+x \right)\]
done
clear
B)
\[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}+x{{\left( \frac{dy}{dx} \right)}^{2}}-y\frac{dy}{dx}=0\]
done
clear
C)
\[y{{\left( \frac{dy}{dx} \right)}^{2}}-x\frac{dy}{dx}+1=0\]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 178) The area bounded by the circle \[{{x}^{2}}+{{y}^{2}}=16\] and the line \[y=x\]in the first quadrant is
A)
\[4\pi \,\,\,sq\,units\]
done
clear
B)
\[8\pi \,\,\,sq\,units\]
done
clear
C)
\[2\pi \,\,\,sq\,units\]
done
clear
D)
\[\pi \,\,\,sq\,units\]
done
clear
View Answer play_arrow
question_answer 179) The focal distance of the point \[(x,y)\] from the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\,\,\,\,a>b\] is
A)
\[a\pm \sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}y\]
done
clear
B)
\[b\pm \sqrt{1-\frac{{{a}^{2}}}{{{b}^{2}}}}y\]
done
clear
C)
\[a\pm \sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}\,x\]
done
clear
D)
\[b\pm \sqrt{1-\frac{{{a}^{2}}}{{{b}^{2}}}}\,x\]
done
clear
View Answer play_arrow
question_answer 180) The lines \[3x+y-14=0\] \[\lambda x-2y=0\] \[3x-8y+4=0\] are concurrent. Then, the value of \[\lambda \] is
A)
\[1\]
done
clear
B)
\[2\]
done
clear
C)
\[3\]
done
clear
D)
\[4\]
done
clear
View Answer play_arrow
question_answer 181) The equation of a straight line which cuts off intercept on X-axis which is twice that on y-axis and is at a unit distance from . origin is given by
A)
\[x+y=0\]
done
clear
B)
\[x+2y\pm \sqrt{2}=0\]
done
clear
C)
\[x+2y\pm \sqrt{5}=0\]
done
clear
D)
\[x+\sqrt{5}y\pm 2=0\]
done
clear
View Answer play_arrow
question_answer 182) The equation of a straight line upon which the length of the perpendicular from the origin is 5 and slope of this perpendicular is \[3/4\] is
A)
\[2x+5y\pm 16=0\]
done
clear
B)
\[4x+3y\pm 25=0\]
done
clear
C)
\[4x+3y\pm 5=0\]
done
clear
D)
\[2x+5y\pm 4=0\]
done
clear
View Answer play_arrow
question_answer 183) The radius of the circle \[{{(x\,\cos \theta +y\sin \theta -a)}^{2}}+(x\,\sin \theta -y\cos \theta )={{k}^{2}}\] is
A)
\[{{a}^{2}}+{{b}^{2}}-{{k}^{2}}\]
done
clear
B)
\[a\,sin\,\theta -b\,\cos \,\theta \]
done
clear
C)
\[{{a}^{2}}+{{b}^{2}}\]
done
clear
D)
\[k\]
done
clear
View Answer play_arrow
question_answer 184) The locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to its distance from a fixed straight line in the same plane represents
A)
a circle
done
clear
B)
a parabola
done
clear
C)
a hyperbola
done
clear
D)
an ellipse
done
clear
View Answer play_arrow
question_answer 185) The eccentricity of the ellipse \[25{{x}^{2}}+9{{y}^{2}}-150x-90y+225=0\]is
A)
\[\frac{4}{5}\]
done
clear
B)
\[\frac{3}{5}\]
done
clear
C)
\[\frac{4}{15}\]
done
clear
D)
\[\frac{9}{5}\]
done
clear
View Answer play_arrow
question_answer 186) The mean deviation from the median is
A)
equal to that measured from another value
done
clear
B)
maximum, if all observations are positive
done
clear
C)
greater than that measured from any other value
done
clear
D)
less than measured from any other value
done
clear
View Answer play_arrow
question_answer 187)
The variance of the data \[x:1\] \[a\] \[{{a}^{2}}\] ?.. \[{{a}^{n}}\] \[f{{:}^{n}}{{C}_{0}}\] \[^{n}{{C}_{1}}\] \[^{n}{{C}_{2}}\] ?.. \[^{n}{{C}_{n}}\]
A)
\[{{\left( \frac{1+{{a}^{2}}}{2} \right)}^{n}}-{{\left( \frac{1+a}{2} \right)}^{2n}}\]
done
clear
B)
\[{{\left( \frac{1+{{a}^{2}}}{2} \right)}^{2n}}-{{\left( \frac{1+a}{2} \right)}^{n}}\]
done
clear
C)
\[{{\left( \frac{1+a}{2} \right)}^{2n}}-{{\left( \frac{1+{{a}^{2n}}}{2} \right)}^{n}}\]
done
clear
D)
\[{{\left( \frac{1+a}{2} \right)}^{n}}-{{\left( \frac{1+{{a}^{2n}}}{2} \right)}^{n}}\]
done
clear
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question_answer 188)
An analysis of the weekly wages paid to workers in two firms A and B, belonging to the same industry gives the following results Firm A Firm B Number of wage earners \[586\] \[648\] Average of weekly wages Rs. \[52.5\] Rs. \[47.5\] Variance of the distribution of wages \[100\] \[121\]
Then, which firm pays out larger amount and which shows greater variability, respectively?
A)
\[A,\,B\]
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B)
\[B,\,A\]
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C)
\[B,\,B\]
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D)
\[A,\,A\]
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question_answer 189) If the standard deviation of a variable X is \[\sigma ,\] then the standard deviation of variable \[\frac{aX+b}{c}\]is
A)
\[a\sigma \]
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B)
\[\frac{a}{c}\sigma \]
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C)
\[\left| \frac{a}{c} \right|\sigma \]
done
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D)
\[\frac{a\sigma +b}{c}\]
done
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question_answer 190) A bag contains 50 tickets numbered 1, 2, 3, ...,50 of which five are drawn at random and arranged in ascending order of magnitude \[({{x}_{1}}<{{x}_{2}}<{{x}_{3}}<{{x}_{4}}<{{x}_{5}}),\] then the probability that \[{{x}_{3}}=30\] is
A)
\[\frac{^{29}{{C}_{2}}{{\times }^{20}}{{C}_{2}}}{^{50}{{C}_{5}}}\]
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B)
\[\frac{^{30}{{C}_{1}}{{\times }^{29}}{{C}_{1}}}{^{50}{{C}_{5}}}\]
done
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C)
\[\frac{^{5}{{C}_{1}}{{\times }^{50}}{{C}_{2}}}{^{50}{{C}_{5}}}\]
done
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D)
\[\frac{^{50}{{C}_{2}}{{\times }^{29}}{{C}_{1}}}{^{50}{{C}_{5}}}\]
done
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question_answer 191) If S is the sample space and \[P(A)=\frac{1}{3}\,P(B)\]and \[S=A\cup B,\] where A and B are two mutually exclusive events, then \[P(A)\] is equal to
A)
\[\frac{1}{4}\]
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B)
\[\frac{1}{2}\]
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C)
\[\frac{3}{4}\]
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D)
\[\frac{3}{8}\]
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question_answer 192) Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is
A)
\[\frac{^{7}{{P}_{5}}}{{{7}^{5}}}\]
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B)
\[\frac{{{7}^{5}}}{^{7}{{P}_{5}}}\]
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C)
\[\frac{6}{^{6}{{P}_{5}}}\]
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D)
\[\frac{^{5}{{P}_{5}}}{{{5}^{5}}}\]
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question_answer 193) In a three dimensional space the equation \[{{x}^{2}}-5x+6=0\]represents
A)
points
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B)
planes
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C)
curves
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D)
None of these
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question_answer 194) If \[(3,\,4,-1)\] and \[(-1,\,2,3)\] be end points of the diameter of a sphere, then the radius of the sphere is
A)
\[2\]
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B)
\[3\]
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C)
\[6\]
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D)
\[7\]
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question_answer 195) If the position vector a of a point \[(12,\,\,n)\] is such that \[|a|=13,\] then the value of \[\pi \] is
A)
\[\pm \,\,3\]
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B)
\[\pm \,\,4\]
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C)
\[\pm \,\,5\]
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D)
\[\pm \,\,6\]
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question_answer 196) The following lines are \[r=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k}),\] and \[r=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-2\hat{k})\]
A)
collinear
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B)
skew-lines
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C)
coplanar lines
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D)
parallel lines
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question_answer 197) The position vector of a point R which divides the line joining \[P(6,\,3,-2)\]and \[Q(3,1,-4)\]Q(3,1, - 4) in the ratio \[2:1\] externally is
A)
\[\hat{i}+3\hat{j}-2\hat{k}\]
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B)
\[3\hat{i}-\hat{k}\]
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C)
\[-\hat{j}-6\hat{k}\]
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D)
\[2\hat{i}-\hat{j}\]
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question_answer 198) If \[a=\hat{i}+2\hat{j}-3\hat{k}\] and \[b=2\hat{i}+4\hat{j}+9\hat{k},\] then the unit vector parallel to \[a+b\] is
A)
\[\frac{1}{6}\,5\hat{i}-\hat{k}\]
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B)
\[\frac{1}{\sqrt{35}}(5\hat{i}+3\hat{j}-\hat{k})\]
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C)
\[\frac{1}{5}(3\hat{j}-5\hat{k})\]
done
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D)
\[3\hat{i}+6\hat{j}-6\hat{k}\]
done
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E)
None of these
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question_answer 199) The angle between the lines \[\frac{x-5}{-3}=\frac{y+3}{-4}=\frac{z-7}{0},\,\frac{x}{1}=\frac{y-1}{-2}=\frac{z-6}{2}\]is
A)
\[\frac{\pi }{3}\]
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B)
\[{{\tan }^{-1}}\left( \frac{1}{5} \right)\]
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C)
\[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]
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D)
\[\frac{\pi }{2}\]
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question_answer 200) If \[|a|=2,\,\,|b|=5\] and \[|a\times b|=8,\] then \[a\,.\,b\] is equal to
A)
\[3\]
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B)
\[4\]
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C)
\[5\]
done
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D)
\[6\]
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question_answer 201) Suppose \[{{A}_{1}},{{A}_{2}}.....,{{A}_{30}}\]are thirty sets each with five elements and \[{{B}_{1}},{{B}_{2}}.....,{{B}_{n}}\] are 'n' sets each with three elements. Let \[\underset{i=1}{\mathop{\overset{30}{\mathop{\cup }}\,}}\,\,\,{{A}_{i}}=\underset{j=1}{\mathop{\overset{n}{\mathop{\cup }}\,}}\,\,\,\,{{B}_{j}}=S.\] Assume that each element of S belongs to exactly 10 of \[{{A}_{i}}s\] and exactly 9 of \[{{B}_{j}}s,\]then the value of x is
A)
\[90\]
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B)
\[15\]
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C)
\[9\]
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D)
45
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question_answer 202) A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then the value of x is
A)
\[39\le x\le 63\]
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B)
\[63\]
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C)
\[39\]
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D)
\[139\ge x\]
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question_answer 203) The cartesian product \[A\times A\] has 9 elements among which are found \[(-1,0)\] and \[(0,1),\] then set A is equal to
A)
\[\{1,\,\,0\}\]
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B)
\[\{1,\,\,-1,\,\,\,0\}\]
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C)
\[\{\,0,\,\,-1\}\]
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D)
\[\{1,\,\,-1\}\]
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question_answer 204) If \[S=\{(a,\,b):b=|a-1|,a\in Z\] and \[|a|<3\},\] where Z denotes the set of integers. Then, the range set of S is
A)
\[\{1,\,2,\,3\}\]
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B)
\[\{-1,\,2,\,3,\,1\}\]
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C)
\[\{0,\,1,\,2,\,3,\,4\}\]
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D)
\[\{-\,1,-\,2,-\,3,-\,4\}\]
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question_answer 205) Pisa relation from \[\{11,\,12,\,13\}\]to \[\{8,\,10,\,12\}\] defined by \[y=x-3\]. Then, \[{{R}^{-1}}\] is
A)
\[\{(8,\,11),\,(10,13)\}\]
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B)
\[\{(11,\,8),\,(13,10)\}\]
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C)
\[\{(10,\,13),\,(8,11),\,(12,\,10)\}\]
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D)
None of the above
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question_answer 206) The quotient of the identity function by the reciprocal function is given by
A)
\[{{x}^{2}}\,\forall \,\,x\,\in \,R\] (set of real numbers)
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B)
\[\frac{1}{{{x}^{2}}}\,\,\forall \,\,x\in R-\{0\}\]
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C)
\[{{x}^{2}}\,\,\forall \,\,x\in R-\{0\}\]
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D)
None of the above
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question_answer 207) Which of the following is not a function?
A)
\[\{(x,y):\,x,\,y\,\in R,{{x}^{2}}=y\}\]
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B)
\[\{(x,y):\,x,\,y\,\in R,{{y}^{2}}=x\}\]
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C)
\[\{(x,y):\,x,\,y\,\in R,x={{y}^{3}}\}\]
done
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D)
\[\{(x,y):\,x,\,y\,\in R,y={{x}^{3}}\}\]
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question_answer 208) If \[(1+i)\,(2i+1)\,(1+3i)....(1+ni)=x+iy,\] then \[2.5.10....(1+{{n}^{2}})\] is equal to
A)
\[1\]
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B)
\[i\]
done
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C)
\[{{x}^{2}}+{{y}^{2}}\]
done
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D)
\[1+{{n}^{2}}\]
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question_answer 209) The value of \[|{{z}_{1}}|=|{{z}_{2}}|=...=|{{z}_{n}}|=1,\] then \[|{{z}_{1}}+{{z}_{2}}+{{z}_{3}}+....+{{z}_{n}}|\] is (where, \[{{z}_{1}}\] is complex number with \[i=1\] to n)
A)
\[\left| \frac{1}{{{z}_{1}}+{{z}_{2}}+{{z}_{3}}+....+{{z}_{n}}} \right|\]
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B)
\[\left| \frac{1}{{{z}_{1}}}+\frac{1}{{{z}_{2}}}+\frac{1}{{{z}_{3}}}+...+\frac{1}{{{z}_{n}}} \right|\]
done
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C)
\[\left| \frac{1}{{{z}_{1}}{{z}_{2}}}+\frac{1}{{{z}_{3}}{{z}_{4}}}+....+\frac{1}{{{z}_{n-1}}{{z}_{n}}} \right|\]
done
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D)
\[1\]
done
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question_answer 210) The non-zero solutions of the equation \[{{z}^{2}}+|z|=0,\] where z is a complex number, are
A)
\[\pm \,\,1\]
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B)
\[\pm \,\,i\]
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C)
\[1\pm \,\,i\]
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D)
\[\pm \,\,1\pm i\]
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question_answer 211) Which of the following shaded regions represents the solution set of in equation \[|x-y|\ge 1\]
A)
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B)
done
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C)
done
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D)
done
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question_answer 212) The values of x for which \[-11\le 4x-3\le 13\]is
A)
\[-4\le x\le 5\]
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B)
\[-2\le x\le 4\]
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C)
\[-8\le x\le 16\]
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D)
\[-11\le x\le 10\]
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question_answer 213) The solution set of the following linear in equations \[x-2y\ge 0;\,\,\,2x-y\le -2;\,\,x\ge 0,y\ge 0\]is given by
A)
\[[1,\,\,2]\]
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B)
Null set
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C)
\[x\ge 1\]
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D)
Set of real numbers
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question_answer 214) For the given LPP (Linear Programming Problem) max \[z=5x+3y\] \[2x+y\le 12\] \[3x+2y\le 20\] \[x\ge 0,\,y\ge 0\] the optimal solution set is
A)
\[(0,\,\,0)\]
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B)
\[(6,\,\,0)\]
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C)
\[(4,\,\,4)\]
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D)
\[(0,\,\,10)\]
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question_answer 215)
A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin content of 1 kg food is given below Food Vitamin A Vitamin B Vitamin C x 1 2 3 y 2 2 1
\[1\text{ }kg\]of food X costs \[Rs.\text{ }16\]and \[1\text{ }kg\] of food Y costs \[Rs.\text{ }20\]. Find the least cost of the mixture which will produce the required diet.
A)
\[Rs.\,100\]
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B)
\[Rs.\,98\]
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C)
\[Rs.\,116\]
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D)
\[Rs.\,112\]
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question_answer 216) Which of the following is a purely imaginary term of the sequence \[8-6i,\] \[7-4i,\,6-2i,...\]?
A)
9th term
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B)
2nd term
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C)
4th term
done
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D)
8 term
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question_answer 217) If \[{{S}_{n}}\] denotes the sum of first n terms of AP \[<{{a}_{n}}>,\]such that \[\frac{{{S}_{m}}}{{{S}_{n}}}=\frac{{{m}^{2}}}{{{n}^{2}}},\] then \[\frac{{{a}_{m}}}{{{a}_{n}}}\] is equal to
A)
\[\frac{2m+1}{2n+1}\]
done
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B)
\[\frac{2m-1}{2n-1}\]
done
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C)
\[\frac{m-1}{n-1}\]
done
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D)
\[\frac{m+1}{n+1}\]
done
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question_answer 218) The sum of all possible products of the first n natural numbers taken two by two is
A)
\[\frac{n(n+1)}{2}\]
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B)
\[\frac{n(n+1)(n+2)}{6}\]
done
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C)
\[\frac{n({{n}^{2}}-1)(3n+2)}{12}\]
done
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D)
\[2{{n}^{3}}+3{{n}^{2}}-1\]
done
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question_answer 219) How many four digit numbers are there with distinct digits?
A)
\[5040\]
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B)
\[4536\]
done
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C)
\[30240\]
done
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D)
\[5274\]
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question_answer 220) If \[^{n}{{C}_{r}}{{+}^{n}}{{C}_{r+1}}{{=}^{n+1}}{{C}_{x}},\]then x is equal to
A)
\[r\]
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B)
\[r-1\]
done
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C)
\[n\]
done
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D)
\[r+1\]
done
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question_answer 221) The coefficient of the term independent of x in the expansion \[\left( \frac{x+1}{{{x}^{2/3}}-{{x}^{1/3}}+1}-\frac{x-1}{x-{{x}^{1/2}}} \right)\]is
A)
\[8064\]
done
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B)
\[210\]
done
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C)
\[-546\]
done
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D)
\[5040\]
done
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question_answer 222) There are 12 points in a plane. The number of straight lines joining any two of them, when 3 of them are collinear, is
A)
\[60\]
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B)
\[63\]
done
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C)
\[64\]
done
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D)
\[65\]
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question_answer 223) Which of the following is the correct principle of Mathematical induction?
A)
Let \[P(n)\] be a statement such that n be any integer and \[P(1)\] is true. Also. \[P(m)\] is true for m, any natural number, then \[P(n)\] is true for all integers n
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B)
Let \[P(n)\] be a statement involving natural number n such that \[P(1)\] is true and\[P(m)\] is true whenever \[P(n)\] is true for every \[n\ge m,\]then \[P(n)\] is true for all \[n\in N\] (set of natural numbers)
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C)
Let\[P(n)\] be a statement where \[n\in N\]such that\[P(1)\] is true and \[P(n),\,P(n+1)\]also holds, then \[P(n)\] is true \[\forall n\in N\]
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D)
Let \[P(n)\] be a statement involving the natural number n, such trial P(1) is true and s\[P(m+1)\] is true for all \[n\le m\]Then, \[P(n)\] is true for all \[n\in N\]
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question_answer 224) If \[x>0\]and \[{{\cot }^{-1}}\,(x+2)=\frac{\pi }{12},\] then the value of x is
A)
\[2\sqrt{3}\]
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B)
\[\sqrt{3}\]
done
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C)
\[\frac{1}{\sqrt{3}}\]
done
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D)
\[\sqrt{3}-1\]
done
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question_answer 225) If \[\cot \,\theta (1+\sin \theta )=4m\] and \[\cot \theta (1-\sin \theta )=4n,\] then \[{{({{m}^{2}}-{{n}^{2}})}^{2}}\]is equal to
A)
\[mn\]
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B)
\[\tan \theta \]
done
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C)
\[1\]
done
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D)
\[\frac{m+n}{4}\]
done
clear
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