question_answer1) The quantities RC and \[\left( \frac{L}{R} \right)\] ( where R, L and C stand for resistance, inductance and capacitance respectively ) have the dimensions of
A) force
B) linear momentum
C) linear velocity
D) time
View Answer play_arrowquestion_answer2) The correct vector relation between linear velocity \[\vec{v}\] and angular velocity \[\vec{\omega }\] in rigid body dynamics is ( where \[\vec{r}\] is the postion vector)
A) \[\vec{\omega }=\vec{v}\times \vec{r}\]
B) \[\vec{v}=\vec{r}/\vec{\omega }\]
C) \[\vec{v}=\vec{\omega }\times \vec{r}\]
D) \[\vec{r}=\vec{v}\times \vec{\omega }\]
View Answer play_arrowquestion_answer3) Which of the following cannot be speed-time graph?
A)
B)
C)
D)
View Answer play_arrowquestion_answer4) Magnitudes of four pairs of displacement vectors are given. Which pair of displacement vectors, under vector addition, fails to give a resultant vector of magnitude\[3\text{ }cm\]?
A) \[2\text{ }cm,7\text{ }cm\]
B) \[1\text{ }cm,4\text{ }cm\]
C) \[2\text{ }cm,3\text{ }cm~\]
D) \[2\text{ }cm,4\text{ }cm\]
View Answer play_arrowquestion_answer5) The maximum range of a projectile is\[100\text{ }m\]. The maximum height reached by it is
A) \[100\text{ }m\]
B) \[\text{25 }m\]
C) \[\text{200 }m\]
D) \[\text{75 }m\]
View Answer play_arrowquestion_answer6) The working principle of rocket propulsion is conservation of
A) angular momentum
B) mass
C) linear momentum
D) kinetic energy
View Answer play_arrowquestion_answer7) In inelastic collision
A) momentum, kinetic energy and total energy are conserved
B) momentum, kinetic energy and total energy are not conserved
C) momentum, and kinetic energy are conserved but total energy is not conserved
D) total energy and momentum are conserved but kinetic energy is not conserved
View Answer play_arrowquestion_answer8) A cricket ball of mass \[0.5\text{ }kg\]strikes a cricket bat normally with a velocity of \[20\text{ }m{{s}^{-1}}\] and rebounds with velocity of \[10\text{ }m{{s}^{-1}}\]. The impulse of the force exerted by the ball on the bat is
A) \[15\text{ }Ns\]
B) \[25\text{ }Ns\]
C) \[30\text{ }Ns\]
D) \[10\text{ }Ns\]
View Answer play_arrowquestion_answer9) Assuming earth to be an inertial frame, an example for inertial frame observer is
A) a driver in a train which is slowing down to stop
B) a person in a car moving with uniform velocity
C) a girl revolving in a merry-go-round
D) a passenger in an aircraft which is taking off
View Answer play_arrowquestion_answer10) If the force acting on a body is inversely proportional to its speed, then its kinetic energy is
A) linearly related to time
B) inversely proportional to time
C) inversely proportional to the square of time
D) a constant
View Answer play_arrowquestion_answer11) A body, possessing kinetic energy T, moving on a rough horizontal surface, is stopped in a distance y. The frictional force exerted on the. body is
A) \[Ty\]
B) \[\frac{\sqrt{T}}{y}\]
C) \[\frac{T}{y}\]
D) \[\frac{T}{\sqrt{y}}\]
View Answer play_arrowquestion_answer12) A particle is describing uniform circular motion. Its acceleration is
A) along the radius of the circular path pointing towards the centre
B) along the tangent to the circular path
C) along the radius of the circular path pointing away from the centre
D) zero
View Answer play_arrowquestion_answer13) \[{{I}_{1}}\] and \[{{I}_{2}}\] are the moments of inertia of two circular discs about their central axes perpendicular to their surfaces. Their angular frequencies of rotation are \[{{\omega }_{1}}\] and \[{{\omega }_{2}}\] respectively. If they are brought into contact face to face with their axes of rotation coinciding with each other, the angular frequency of the composite disc will be
A) \[\frac{{{I}_{1}}+{{I}_{2}}}{{{\omega }_{1}}+{{\omega }_{2}}}\]
B) \[\frac{{{I}_{2}}{{\omega }_{1}}-{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}-{{I}_{2}}}\]
C) \[\frac{{{I}_{2}}{{\omega }_{1}}+{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\]
D) \[\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\]
View Answer play_arrowquestion_answer14) A child stands at one end of a boat moving with a speed v in still water. If the child starts running towards the other end of the boat with a speed u, the centre of mass of the system (boat and child) will move with a speed
A) \[v-u\]
B) \[v\]
C) \[u\]
D) \[v+u\]
View Answer play_arrowquestion_answer15) In planetary motion, the quantity that remains unchanged is
A) radius of the orbit
B) speed along the orbit
C) total angular momentum
D) angular speed
View Answer play_arrowquestion_answer16) Work done in taking a mass from one point to another in a gravitational field depends on
A) the end points, only
B) the path followed
C) the velocity of the mass
D) both the length of the path and the and points
View Answer play_arrowquestion_answer17) A body is projected up from the surface of the earth with a velocity equal to \[\frac{3}{4}th\] of its escape velocity. If R be the radius of earth, the height it reaches is
A) \[\frac{3R}{10}\]
B) \[\frac{9R}{7}\]
C) \[\frac{8R}{5}\]
D) \[\frac{9R}{5}\]
View Answer play_arrowquestion_answer18) A satellite moving round the earth in circular orbit of radius r and speed v suddenly loses some of its energy. Then,
A) r will increase and v will decrease
B) both r and v will decrease
C) both r and v will increase
D) r will decrease and v will increase
View Answer play_arrowquestion_answer19) The stress required to double the length of wire of Young's modulus Y is
A) \[\frac{Y}{2}\]
B) \[2Y\]
C) \[Y\]
D) \[4\,y\]
View Answer play_arrowquestion_answer20) Water flows through a pipe of varying cross-section. Then the ratio of the speeds of water at two points 1 and 2, where the radii of the pipe are \[{{r}_{1}}\] and \[{{r}_{2}}\] is
A) \[\frac{r_{2}^{2}}{r_{1}^{2}}\]
B) \[\frac{{{r}_{2}}}{{{r}_{1}}}\]
C) \[\frac{r_{1}^{2}}{r_{2}^{2}}\]
D) \[\frac{{{r}_{1}}}{{{r}_{2}}}\]
View Answer play_arrowquestion_answer21) A piece of ice, with a stone embedded inside it, is floating in water contained in a vessel. When the ice melts completely, the level of water in vessel
A) remains unchanged
B) rises
C) falls
D) falls in the beginning and rises to the same level later
View Answer play_arrowquestion_answer22) The excess pressure inside a cylindrical drop of liquid or a cylindrical bubble of radius R in a liquid of surface tension T is
A) \[\frac{T}{4R}\]
B) \[\frac{T}{R}\]
C) \[\frac{2T}{R}\]
D) \[\frac{4T}{R}\]
View Answer play_arrowquestion_answer23) Two small spheres of radii r and \[4r\] fall through a viscous liquid with the same 'terminal velocity. The ratio between the viscous forces acting on them is
A) \[1:2\]
B) \[4:1\]
C) \[1:16\]
D) \[1:4\]
View Answer play_arrowquestion_answer24) A certain quantity of heat energy is given to a diatomic ideal gas which expands at constant pressure. The fraction of the heat energy that is converted into work is
A) \[2/3\]
B) \[2/7\]
C) \[1/5\]
D) \[1/7\]
View Answer play_arrowquestion_answer25) When the temperature of a gas is increased
A) its molecular kinetic energy increases
B) molecular potential energy decreases and molecular kinetic energy also decreases, total energy remaining constant
C) molecular potential energy increases and molecular kinetic energy decreases; total energy remaining constant
D) its molecular potential energy increases
View Answer play_arrowquestion_answer26) Two monoatomic ideal gases A and B occupying the same volume V, are at the same temperature T and pressure p. If they are mixed, the resultant mixture has volume V and temperature T. The pressure of the mixture is
A) \[P\]
B) \[\frac{P}{2}\]
C) \[4\,P\]
D) \[2\,P\]
View Answer play_arrowquestion_answer27) The requirement for heat conduction to take place in a solid is
A) density gradient
B) uniform density
C) temperature gradient
D) uniform temperature
View Answer play_arrowquestion_answer28) A Carnot's engine working between \[{{27}^{o}}C\] and \[{{127}^{o}}C\] has a work output of\[200\text{ }J/cycle\]. The energy supplied to the engine from the source in each cycle is
A) \[400\text{ }J\]
B) \[800\text{ }J\]
C) \[600\text{ }J\]
D) \[500\text{ }J\]
View Answer play_arrowquestion_answer29) A particle is executing linear simple harmonic motion. The fraction of the total energy that is potential, when its displacement is \[\frac{1}{4}\] of the amplitude is
A) \[1/16\]
B) \[1/8\]
C) \[1/2\]
D) \[1/4\]
View Answer play_arrowquestion_answer30) The equation \[y=A\,\,\sin \,k(vt-x)\] represents \[\left( k=\frac{2\pi }{\lambda } \right)\]
A) a plane progressive wave travelling along negative X-direction
B) a plane progressive wave travelling along positive X-direction
C) a stationary wave
D) a plane progressive wave travelling along positive Y-direction
View Answer play_arrowquestion_answer31) The third overtone of an open organ pipe is in resonance with the second overtone of a closed organ pipe. If the length of the open pipe is \[8\text{ }cm,\] then the length of closed pipe is
A) \[10\text{ }cm\]
B) \[8\text{ }cm\]
C) \[12\,\,cm\]
D) \[5\,\,cm\]
View Answer play_arrowquestion_answer32) When a wave undergoes refraction
A) its frequency changes
B) its amplitude changes
C) its velocity changes
D) both amplitude and frequency change
View Answer play_arrowquestion_answer33) A sound wave with frequency \[256\text{ }Hz\]falls normally on a perfectly reflecting wall. The shortest distance from the wall at which the air particles will have maximum amplitude of vibrations is nearly ( velocity of sound in air is \[336\,m{{s}^{-1}}\])
A) \[32.8\,\,cm\]
B) \[50\,\,cm\]
C) \[65.8\,\,cm\]
D) \[25\,\,cm\]
View Answer play_arrowquestion_answer34) When air medium in which two charges kept apart at a distance r is replaced by a dielectric medium of dielectric constant K, the force between the charges
A) remains unchanged
B) decreases K times
C) increases K times
D) increases \[{{K}^{2}}\]times
View Answer play_arrowquestion_answer35) The magnitude of electric field E required to balance an oil drop of mass m, carrying charge q is (g = acceleration due to gravity)
A) \[\frac{q}{m}\]
B) \[\frac{mg}{{{q}^{2}}}\]
C) \[mgq\]
D) \[\frac{mg}{q}\]
View Answer play_arrowquestion_answer36) Three charges \[-q,\] \[+Q\] and \[-q\] are placed in a straight line as shown. If the total potential energy of the system is zero, then the ratio \[\frac{q}{Q}\]is
A) \[2\]
B) \[5.5\]
C) \[4\]
D) \[1.5\]
View Answer play_arrowquestion_answer37) Electric flux emanating through a surface element \[\overrightarrow{ds}=5\hat{i}\] placed in an electric field \[\vec{E}=4\hat{i}+4\hat{j}+4\hat{k}\] is
A) \[10\text{ }units\]
B) \[20\text{ }units\]
C) \[~4\text{ }units\]
D) \[16\text{ }units\]
View Answer play_arrowquestion_answer38) A parallel plate capacitor is charged to a potential of V volt. The battery is then disconnected and the distance between the plates of the capacitor is increased using an insulating handle. The potential difference between the plates of the capacitor will
A) increase
B) decrease
C) not change
D) become zero
View Answer play_arrowquestion_answer39) Energy stored per unit volume of a parallel plate capacitor having plate area A and plate separation d when charged to a potential of V volts is (air space in between the plates)
A) \[\frac{1}{2}{{C}^{2}}{{V}^{2}}\]
B) \[\frac{{{q}^{2}}}{4\,C}\]
C) \[\frac{1}{2}{{E}_{0}}\left( \frac{V}{d} \right)\]
D) \[\frac{1}{2}{{E}_{0}}\left( \frac{{{V}^{2}}}{{{d}^{2}}} \right)\]
View Answer play_arrowquestion_answer40) The mutual electrostatic potential energy between two protons which are at a distance of \[9\times 10{{-}^{15}}\text{ }m,\] in \[_{92}{{U}^{235}}\] nucleus is
A) \[1.56\times {{10}^{-14}}J\]
B) \[5.5\times {{10}^{-14}}J\]
C) \[2.56\times {{10}^{-14}}J\]
D) \[4.56\times {{10}^{-14}}J\]
View Answer play_arrowquestion_answer41) The SI units of electron mobility are
A) \[{{m}^{2}}{{s}^{-1}}{{V}^{-1}}\]
B) \[ms\,\,{{V}^{-1}}\]
C) \[m{{s}^{-1}}\,\,V\]
D) \[{{m}^{2}}{{s}^{-2}}\,\,{{V}^{-2}}\]
View Answer play_arrowquestion_answer42) A copper wire and a silicon wire are heated from room temperature to \[{{60}^{o}}C\]. Then
A) resistance of both the wires decreases
B) resistance of both the wires increases
C) resistance of copper wire decreases and that of silicon wire increases
D) resistance of copper wire increases and that of silicon wire decreases
View Answer play_arrowquestion_answer43) The tungsten filaments of two electric bulbs are of the same length. If one of them gives \[25\text{ }W\]power and the other \[60\text{ }W\]power, then
A) both the filaments are of same thickness
B) \[25\text{ }W\]bulb has thicker filament
C) \[60\text{ }W\] bulb has thicker filament
D) both the filaments have same cross-section area
View Answer play_arrowquestion_answer44) Heater coil A takes \[{{t}_{1}}\] second to boil certain quantity of water. Heater coil B takes 13 second to boil same quantity of water. If A and B are connected in series, the time taken to boil the same quantity of water by the combination is
A) \[-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{2}\]
B) \[\frac{1}{\sqrt{2}},-\frac{1}{2},\frac{1}{2}\]
C) \[-\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]
D) \[\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]
View Answer play_arrowquestion_answer45) When the cold and hot junctions of a thermocouple are interchanged, the thermo emf
A) changes sign
B) remains the same
C) becomes zero
D) is doubled
View Answer play_arrowquestion_answer46) A charge q coulomb makes n revolutions in one second in a circular orbit of radius r. The magnetic field at the centre of the orbit in \[N{{A}^{-1}}{{m}^{-1}}\]is
A) \[\frac{2\pi rn}{q}\times {{10}^{-7}}\]
B) \[\left( \frac{2\pi q}{r} \right)\times {{10}^{-7}}\]
C) \[\frac{1}{2}({{t}_{1}}+{{t}_{2}})\]
D) s\[\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]
View Answer play_arrowquestion_answer47) In a moving coil galvanometer, to make the field radial
A) coil is wound on wooden frame
B) magnetic poles are cylindrically cut
C) a horse-shoe magnet is used
D) the number of windings in the coil is decreased
View Answer play_arrowquestion_answer48) An electron travelling with velocity v, enters a region of space in which electric and magnetic fields exist. Then the electron goes uneffected for all values of fields
A) if both electric and magnetic fields are normal to v
B) if the magnetic field alone in normal to v
C) if both electric and magnetic fields are parallel to v
D) if the electric field alone is normal to v
View Answer play_arrowquestion_answer49) Magnetic field at the centre of a coil in the form of a square of side \[2\text{ }cm\]carrying a current of \[1.414\text{ }A\]is
A) \[8\times {{10}^{-5}}T\]
B) \[8\times {{10}^{-5}}T\]
C) \[1.5\times {{10}^{-5}}T\]
D) \[6\times {{10}^{-5}}T\]
View Answer play_arrowquestion_answer50) The resistance of an ideal voltmeter is
A) zero
B) low
C) high
D) infinity
View Answer play_arrowquestion_answer51) The relation connecting magnetic susceptibility \[{{\chi }_{m}}\]and relative permeability \[{{\mu }_{r}}\] is
A) \[{{\chi }_{m}}={{\mu }_{r}}+1\]
B) \[{{\chi }_{m}}={{\mu }_{r}}-1\]
C) \[{{\chi }_{m}}=\frac{1}{{{\mu }_{r}}}\]
D) \[{{\chi }_{m}}=3(1+{{\mu }_{r}})\]
View Answer play_arrowquestion_answer52) Whenever there is a relative motion between a coil and a magnet, the magnitude of induced emf set up in the coil does not depend upon the
A) relative speed between the coil and magnet
B) magnetic moment of the coil
C) resistance of the coil
D) number of turns in the coil
View Answer play_arrowquestion_answer53) A uniformly wound coil of self-inductance \[1.2\times {{10}^{-4}}H\]and resistance \[3\Omega \]. is broken up into two identical coils. These coils are then connected parallel across a \[6V\]battery of negligible resistance. The time constant for the current in the circuit is (neglect mutual inductance)
A) \[0.4\times {{10}^{-4}}s\]
B) \[0.2\times {{10}^{-4}}\text{ }s\]
C) \[0.5\times {{10}^{-4}}\text{ }s\]
D) \[0.1\times {{10}^{-4}}\text{ }s\]
View Answer play_arrowquestion_answer54) In AC circuit Ohm's law is applicable for
A) instantaneous values of current and voltage only
B) rms values of current and voltage only
C) peak values of current and voltage only
D) all values of current and voltage
View Answer play_arrowquestion_answer55) The average power dissipated in a pure capacitance AC circuit is
A) \[CV\]
B) zero
C) \[\frac{1}{C{{V}^{2}}}\]
D) \[\frac{1}{4}C{{V}^{2}}\]
View Answer play_arrowquestion_answer56) The instantaneous values of current and voltage in an AC circuit are given by \[I=6\,\,\sin \,\left( 100\,\pi t+\frac{\pi }{4} \right),\] \[V=5\,\,\sin \,\left( 100\,\pi t-\frac{\pi }{4} \right),\] then
A) current leads the voltage by \[{{45}^{o}}\]
B) voltage leads the current by \[{{90}^{o}}\]
C) current leads the voltage by \[{{90}^{o}}\]
D) voltage leads the current by \[{{45}^{o}}\]
View Answer play_arrowquestion_answer57) The velocity of an electromagnetic wave in vacuum can be changed by changing
A) frequency
B) amplitude
C) wavelength
D) None of these
View Answer play_arrowquestion_answer58) The relationship between phase difference \[\Delta \phi \] and the path difference \[\Delta x\] between two interfering waves is given by (\[\lambda \]= wavelength)
A) \[\Delta x=\left( \frac{\lambda }{2\pi } \right)\Delta \phi \]
B) \[\Delta x=\left( \frac{2\pi }{\lambda } \right)\Delta \phi \]
C) \[\Delta \phi =\left( \frac{\pi }{\lambda } \right)\Delta x\]
D) \[\Delta \phi =(2\pi )\,\,\Delta x\]
View Answer play_arrowquestion_answer59) In Young's double slit experiment, the fringe width with light of wavelength \[6000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]is\[3\text{ }mm\]. The fringe width, when the wavelength of light is changed to \[4000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]is
A) \[3\text{ }mm\]
B) \[1\text{ }mm\]
C) \[\text{2 }mm\]
D) \[\text{4 }mm\]
View Answer play_arrowquestion_answer60) If the width of the slit in single slit diffraction experiment is doubled, then the central maximum of diffraction pattern becomes
A) broader and brighter
B) sharper and brighter
C) sharper and fainter
D) broader and fainter
View Answer play_arrowquestion_answer61) Transverse nature of light was confirmed by the phenomenon of
A) refraction of light
B) diffraction of light
C) dispersion of light
D) polarization of light
View Answer play_arrowquestion_answer62) If a transparent parallel plate of uniform thickness t and refractive index \[\mu ,\] is interposed perpendicularly in the path of a light beam, the optical path is
A) increased by \[(\mu -1)\,t\]
B) decreased by \[\mu \,t\]
C) decreased by \[(\mu -1)\,t\]
D) increased by \[\mu \,t\]
View Answer play_arrowquestion_answer63) If the photoelectric work function for a metallic surface is \[4.125\text{ }eV,\]the cut-off wavelength for photoelectric phenomenon for the surface is
A) \[4500\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[1700\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[2800\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[3000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
View Answer play_arrowquestion_answer64) The masses of two particles having same kinetic energies are in the ratio\[1:2\]. Then their de-Broglie wavelengths are in the ratio
A) \[2:1\]
B) \[1:2\]
C) \[\sqrt{2}:1\]
D) \[\sqrt{3}:1\]
View Answer play_arrowquestion_answer65) Balmer series of hydrogen atom lies in
A) microwave region .
B) visible region
C) ultraviolet region
D) infrared region
View Answer play_arrowquestion_answer66) The shortest wavelength of X-rays coming from an X-ray tube depends on the
A) voltage applied to the tube
B) current in the tube
C) atomic number of target element
D) nature of gas in the tube
View Answer play_arrowquestion_answer67) The nuclear force
A) is purely an electrostatic force
B) obeys inverse square law of distance
C) is equal in strength to gravitational force
D) is short range force
View Answer play_arrowquestion_answer68) A radioactive isotope A with a half-life of \[1.25\times {{10}^{10}}\text{ }yr\]decays into B which is stable. A sample of rock from a planet is found to contain both A and B present in the ratio\[1:15\]. The age of the rock is (in years)
A) \[9.6\times {{10}^{10}}\]
B) \[4.2\times {{10}^{10}}\]
C) \[5\times {{10}^{10}}\]
D) \[1.95\times {{10}^{10}}\]
View Answer play_arrowquestion_answer69) Enriched uranium is used in nuclear reactors because, it contains greater proportion of
A) \[{{U}^{238}}\]
B) \[{{U}^{235}}\]
C) \[{{U}^{239~}}\]
D) \[{{U}^{233}}\]
View Answer play_arrowquestion_answer70) The weakest bond in solids is
A) van der Waals'
B) metallic
C) covalent
D) ionic
View Answer play_arrowquestion_answer71) In a semiconducting material \[1/5th\]of the total current is carried by the holes and the remaining is carried by the electrons. The drift speed of electrons is twice that of holes at this temperature, the ratio between the -number densities of electrons and holes is
A) \[21/6\]
B) \[5\]
C) \[3/8\]
D) \[2\]
View Answer play_arrowquestion_answer72) In a transistor, the base is
A) a conductor with high conductivity
B) an insulator
C) an extrinsic semiconductor
D) an intrinsic semiconductor
View Answer play_arrowquestion_answer73) The following figure represents
A) OR gate
B) NOT gate
C) NOR gate
D) AND gate
View Answer play_arrowquestion_answer74) In amplitude modulation, the bandwidth is
A) twice the audio signal frequency
B) thrice the audio signal frequency
C) thrice the carrier wave frequency
D) twice the carrier wave frequency
View Answer play_arrowquestion_answer75) In a typical optical fibres, the difference between the refractive indices of core material and cladding material is of the order of
A) \[{{10}^{-5}}\]
B) \[{{10}^{-6}}\]
C) \[{{10}^{-1}}\]
D) \[{{10}^{-3}}\]
View Answer play_arrowquestion_answer76) The equivalent mass of potassium permanganate in alkaline medium is its
A) \[\frac{\text{molar}\,\text{mass}}{\text{5}}\]
B) \[\frac{\text{molar}\,\text{mass}}{3}\]
C) \[\frac{\text{molar}\,\text{mass}}{\text{2}}\]
D) molar mass itself
View Answer play_arrowquestion_answer77) The number of molecules in 18 mg of water in terms of Avogadro number N is
A) \[{{10}^{-3}}N\]
B) \[{{10}^{-2}}N\]
C) \[{{10}^{-1}}N\]
D) \[10N\]
View Answer play_arrowquestion_answer78) If the de-Broglie wavelength of a particle of mass m is 100 times its velocity then its value in terms of its mass\[(m)\] and Plants constant \[(h)\] is
A) \[\frac{1}{10}\sqrt{m/h}\]
B) \[10\sqrt{h/m}\]
C) \[\frac{1}{10}\sqrt{h/m}\]
D) \[10\sqrt{m/h}\]
View Answer play_arrowquestion_answer79) How much volume of oxygen at STP, in litre is required to burn 4g of methane gas completely?
A) 11.2
B) 5.6
C) 2.8
D) 8
View Answer play_arrowquestion_answer80) The set of quantum numbers \[n=4,l=0\]and \[s=+\frac{1}{2}\] correspond to the most loosely bound, ground state electron of which one of the following atoms?
A) \[Na\]
B) \[Cl\]
C) \[Cr\]
D) \[Rb\]
View Answer play_arrowquestion_answer81) The\[\beta \]decay of a radioactive element results in the formation of its
A) isotope
B) isobar
C) isodiapher
D) nuclear isomer
View Answer play_arrowquestion_answer82) In the radioactive, decay, \[_{y}{{X}^{z}}\xrightarrow{(-8\alpha \,\text{and}\,\text{6}\beta )}{{\,}_{82}}P{{b}^{206}},x,y\]and \[z\]are
A) U, 92 and 235
B) Th, 90 and 232
C) Pu, 94 and 238
D) U, 92 and 238
View Answer play_arrowquestion_answer83) In which one of the following equilibria, the increase of pressure over the equilibrium will favour the reaction?
A) Pecomposition equilibrium of HI
B) Formation equilibrium of\[\text{S}{{\text{O}}_{\text{3}}}\]
C) Decomposition equilibrium of\[\text{N}{{\text{H}}_{3}}\]
D) Formation equilibrium of \[PC{{l}_{5}}\]
View Answer play_arrowquestion_answer84) Which one of the following is the correct quadratic form of the Ostwald's dilution law equation?
A) \[{{\alpha }^{2}}C+\alpha K-K=0\]
B) \[{{\alpha }^{2}}C-\alpha K-K=0\]
C) \[{{\alpha }^{2}}C-\alpha K+K=0\]
D) \[{{\alpha }^{2}}C+\alpha K+K=0\]
View Answer play_arrowquestion_answer85) Which one of the following aqueous solutions of salts has the lowest, pH value?
A) \[C{{H}_{3}}COONa\]
B) \[NaCl\]
C) \[N{{H}_{4}}OOCC{{H}_{3}}\]
D) \[N{{H}_{4}}Cl\]
View Answer play_arrowquestion_answer86) The solubility product of a sparingly soluble metal hydroxide \[\text{M(OH}{{\text{)}}_{\text{2}}}\]at 298 K is\[\text{5}\times \text{1}{{\text{0}}^{-16}}\,mo{{l}^{3}}\,d{{m}^{-9}}.\]The pH value of its aqueous and saturated solution is
A) 5
B) 9
C) 11.5
D) 8.5
View Answer play_arrowquestion_answer87) In the synthesis of ammonia from nitrogen and hydrogen gases, if \[6\times {{10}^{-2}}\] moles of hydrogen disappears in 10 min, the number of moles of ammonia formed in 3 min is
A) \[1.8\times {{10}^{-2}}\]
B) \[1.2\times {{10}^{-2}}\]
C) \[4.0\times {{10}^{-2}}\]
D) \[3.6\times {{10}^{-2}}\]
View Answer play_arrowquestion_answer88) In a reversible reaction, the enthalpy change and the, activation energy in the forward direction are respectively \[-x\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\] and \[y\,kJ\,mo{{l}^{-1}},\]Therefore, the energy of activation in the backward direction in \[kJmo{{l}^{-1}},\]is
A) \[(y-x)\]
B) \[(x+y)\]
C) \[(x-y)\]
D) \[-(x+y)\]
View Answer play_arrowquestion_answer89) The rate constant for a first order reaction is \[6.909\,{{\min }^{-1}},\]Therefore, the time required, in minute, for the participation of 75% of the initial reactant is
A) \[2/3\text{ }log2\]
B) \[~2/3\text{ }log\text{ }4\]
C) \[~3/2\text{ }log\,2\]
D) \[~3/2\text{ }log\text{ }4\]
View Answer play_arrowquestion_answer90) A solution with negative deviation among the following is
A) ethanol-acetone
B) chlorobenzene-bromobenzene
C) chloroform-acetone
D) benzene-toluene
View Answer play_arrowquestion_answer91) At 300 K, two pure liquids A and B have vapour pressures respectively 150 mm Hg and 100 mm Hg, In an equimolar liquid mixture of A and\[B,\] the mole fraction of B in the vapour mixture at this temperature is
A) 0.6
B) 0.5
C) 0.8
D) 0,4
View Answer play_arrowquestion_answer92) The molar mass of the solute sodium hydroxide obtained from the measurement of the osmotic pressure of its aqueous solution at \[\text{27}{{\,}^{\text{o}}}\text{C}\]is\[25\,\text{g}\,\text{mo}{{\text{l}}^{-1}}.\]Therefore, its ionization percentage in this solution is
A) 75
B) 60
C) 80
D) 70
View Answer play_arrowquestion_answer93) 25 g of a solute of molar mass \[250\,g\,mo{{l}^{-1}}\] is dissolved in 10 mL of water to obtain a solution whose density is \[1.25\,g{{(mL)}^{-1}}.\] The molarity and molality of the solution are respectively
A) 0.75 M and 1 m
B) 0.8 M and 1 m
C) 1 M and 0.8 m
D) 1 M and 0.75 m
E) None of These
View Answer play_arrowquestion_answer94) The standard enthalpies of formation of A \[A(N{{H}_{3}}),B(C{{O}_{2}}),C(HI)\]are respectively \[-\,46,19,-\text{ }393.4,+\,24,94\] and\[-296.9\,\text{kJmo}{{\text{l}}^{-1}},\]The increasing order of their stability is
A) B < D < A < C
B) C < A < D < B
C) D < B < C < A
D) A < C < D < B
View Answer play_arrowquestion_answer95) When 400 mL of 0.2 N solution of a weak acid is neutralised by a dilute aqueous solution of sodium hydroxide under standard conditions, \[4.4\,kJ\]amount of heat is liberated. Therefore, the standard enthalpy bf neutralisation of this weak acid, in \[kJ\,\text{equi}{{\text{v}}^{-1}},\]is
A) \[-11\]
B) \[-44\]
C) \[-\text{ }55\]
D) \[~-22\]
View Answer play_arrowquestion_answer96) The incorrect statement among the following is
A) The entropy of the universe remains constant
B) Heat can be completely converted into work only under specified conditions
C) The absolute entropy of a perfect crystalline solid at absolute zero temperature is zero
D) The total energy of an isolated system remains constant
View Answer play_arrowquestion_answer97) Which one of the following is always not negative?
A) Enthalpy of combustion
B) Enthalpy of formation
C) Enthalpy of neutralisation
D) Lattice enthalpy
View Answer play_arrowquestion_answer98) The oxidation numbers of the sulphur atoms in peroxomonosulphuric acid\[({{H}_{2}}S{{O}_{5}})\]and peroxodisulphuric acid \[({{H}_{2}}{{S}_{2}}{{O}_{8}})\] are respectively
A) +8 and +7
B) +3 and +3
C) +6 and +6
D) +4 and +6
View Answer play_arrowquestion_answer99) In the electrolysis of aqueous solution of \[\text{CuS}{{\text{O}}_{\text{4}}}\] using copper electrodes, the process taking place at the anode is
A) \[SO_{4}^{2-}\xrightarrow{{}}S{{O}_{4}}+2{{e}^{-}}\]
B) \[Cu\xrightarrow{{}}C{{u}^{+}}+{{e}^{-}}\]
C) \[2O{{H}^{-}}\xrightarrow{{}}{{H}_{2}}O+\frac{1}{2}{{O}_{2}}+2{{e}^{-}}\]
D) \[Cu\xrightarrow{{}}C{{u}^{2+}}+2{{e}^{-}}\]
View Answer play_arrowquestion_answer100) The correct expression in SI system relating the equivalent conductance\[({{\Lambda }_{c}}),\]specific conductance \[(\kappa )\]and equivalent concentration [C] is (where C is the number of gram-equivalents of the electrolyte in one litre of the solution)
A) \[{{\Lambda }_{c}}=\frac{\kappa }{C}\]
B) \[{{\Lambda }_{c}}=\kappa \times \frac{1000}{c}\]
C) \[{{\Lambda }_{c}}=\kappa \times \frac{{{10}^{-3}}}{c}\]
D) \[{{\Lambda }_{c}}=\kappa \times \frac{{{10}^{6}}}{c}\]
View Answer play_arrowquestion_answer101) The standard reduction electrode potentials of the three electrodes P, Q and R are respectively \[-1.76\text{ }V,0.34\text{ }V\]and 0.8 V, then
A) metal Q will displace the cation of P from its aqueous solution and deposit the metal P
B) both metals Q-and R will displace the cation of P from its aqueous solution and deposit the metal P
C) metal R will displace the cation of P from its aqueous solution and deposit the metal P
D) metal P will displace the cation of R from its aqueous solution and deposit the metal R
View Answer play_arrowquestion_answer102) If the ratio of the rates of diffusion of two gase A and B is 4 :1, the ratio of their densities in the same order is
A) 16: 1
B) 1:4
C) 4 : 1
D) 1 : 16
View Answer play_arrowquestion_answer103) The van der Waals' constants for four gases P Q, R and S are 4J7, 3.59, 6.71 and 3.8 atm\[{{L}^{2}}.mo{{l}^{-2}}.\] Therefore, the ascending order of their liquification is
A) R < P < S < Q
B) Q < S < R < P
C) Q < S < P < R
D) R < P < Q < S
View Answer play_arrowquestion_answer104) The unit cell of a binary alloy composed of ,A and B metals, has a ccp structure with A atoms occupying the corners and B atoms occupying centres of each face of the cube. If during the crystallisation of this alloy, in the unit cell two A atoms are missed, the overall composition per unit cell is
A) \[A{{B}_{6}}\]
B) \[A{{B}_{4}}\]
C) \[A{{B}_{8}}\]
D) \[{{A}_{5}}{{B}_{24}}\]
View Answer play_arrowquestion_answer105) When an excess and a very dilute aqueous solution of\[\text{KI}\]is added to a very dilute aqueous solution of silver nitrate, the colloidal particles of silver iodide are associated with the Helmholtz double layer
A) \[AgI:A{{g}^{+}}:NO_{3}^{-}\]
B) \[AgI:{{K}^{+}}:NO_{3}^{-}\]
C) \[AgI:NO_{3}^{-}:A{{g}^{+}}\]
D) \[AgI:{{I}^{-}}:{{K}^{+}}\]
View Answer play_arrowquestion_answer106) In the Freundlich's adsorption isotherm equation \[\log \frac{x}{m}=\log k+\left( \frac{1}{n} \right)\log \,p,\] the value of n is
A) any value from 0 to 1
B) a negative integer
C) a positive integer
D) a positive or a negative fractional number
View Answer play_arrowquestion_answer107) The polymer used in the manufacture of 'orlon is
A) PTFE
B) PAN
C) PMMA
D) PVC
View Answer play_arrowquestion_answer108) Which one of the following is \['d'-\]block element?
A) Gd
B) Hs
C) Es
D) Cs
View Answer play_arrowquestion_answer109) The atom of smallest atomic radius among the following is
A) Na
B) K
C) Br
D) Li
View Answer play_arrowquestion_answer110) The \['d'\]orbital involved in the hybridisation in the\[PC{{l}_{5}}\] molecule is
A) \[3{{d}_{{{x}^{2}}-{{y}^{2}}}}\]
B) \[3{{d}_{{{z}^{2}}}}\]
C) \[3{{d}_{xy}}\]
D) \[4{{d}_{{{x}^{2}}-{{y}^{2}}}}\]
View Answer play_arrowquestion_answer111) The shape of \[\text{XeO}{{\text{F}}_{\text{2}}}\]on the basis of VSEPR theory is
A) sea saw
B) V-shaped
C) trigonal planar
D) T-shaped
View Answer play_arrowquestion_answer112) Among the following the molecule possessing highest dipole moment is
A) \[C{{O}_{2}}\]
B) \[B{{F}_{3}}\]
C) \[S{{O}_{2}}\]
D) Trans 2-butene
View Answer play_arrowquestion_answer113) Which one of the following molecules is paramagnetic?
A) \[{{F}_{2}}\]
B) \[{{B}_{2}}\]
C) \[L{{i}_{2}}\]
D) \[{{N}_{2}}\]
View Answer play_arrowquestion_answer114) Among the following the least thermally stable is
A) \[{{K}_{2}}C{{O}_{3}}\]
B) \[~N{{a}_{2}}C{{O}_{3}}\]
C) \[~BaC{{O}_{3}}\]
D) \[~L{{i}_{2}}C{{O}_{3}}\]
View Answer play_arrowquestion_answer115) Which one of the following has the highest Lewis acid strength?
A) \[B{{I}_{3}}\]
B) \[~BB{{r}_{3}}\]
C) \[~B{{F}_{3}}\]
D) \[~BC{{l}_{3}}\]
View Answer play_arrowquestion_answer116) The most powerful oxidising agent of the following is
A) \[{{I}_{2}}\]
B) \[{{F}_{2}}\]
C) \[B{{r}_{2}}\]
D) \[C{{l}_{2}}\]
View Answer play_arrowquestion_answer117) Which one of the following is non-reducing?
A) \[{{H}_{2}}S\]
B) \[~{{H}_{2}}Te\]
C) \[{{H}_{2}}Se\]
D) \[~{{H}_{2}}\text{O}\]
View Answer play_arrowquestion_answer118) The atom of which one of the following elements has the highest number of unpaired electrons?
A) \[{{\,}_{25}}Mn\]
B) \[{{\,}_{24}}Cr\]
C) \[{{\,}_{96}}Cm\]
D) \[{{~}_{26}}Fe\]
View Answer play_arrowquestion_answer119) The ion of least magnetic moment among the following is
A) \[T{{i}^{3+}}\]
B) \[N{{i}^{2+}}\]
C) \[C{{o}^{2+}}\]
D) \[M{{n}^{2+}}\]
View Answer play_arrowquestion_answer120) The composition of Bell metal is
A) \[Cu\text{ (}80%\text{)},\text{ }Zn\text{ (}20%\text{)}\]
B) \[~Cu\text{ (}60%\text{)},\text{ }Ni\text{ (}40%\text{)}\] .
C) \[~Cu\text{ (}90%\text{)},\text{ }Sn\text{ (}10%\text{)}\]
D) \[Cu\text{ (}80%\text{)},\text{ }Sn\text{ (}20%\text{)}\]
View Answer play_arrowquestion_answer121) The amphoteric oxide among the following is
A) \[C{{r}_{2}}{{O}_{3}}\]
B) \[M{{n}_{2}}{{O}_{7}}\]
C) \[{{V}_{2}}{{O}_{3}}\]
D) \[CrO\]
View Answer play_arrowquestion_answer122) The coordination compound of which one of the following compositions will produce two equivalents of AgCl on reaction with aqueous silver nitrate solution?
A) \[CoC{{l}_{3}}.3N{{H}_{3}}\]
B) \[~CoC{{l}_{3}}.6N{{H}_{3}}\]
C) \[CoC{{l}_{3}}.4N{{H}_{3}}\]
D) \[~CoC{{l}_{3}}.5N{{H}_{3}}\]
View Answer play_arrowquestion_answer123) The optically active coordination complex ion among the following is
A) trans\[{{[Co{{(en)}_{2}}C{{l}_{2}}]}^{+}}\]
B) \[cis{{[Co(en){{(N{{H}_{3}})}_{2}}C{{l}_{2}}]}^{+}}\]
C) \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
D) \[{{[Fe(C{{N}_{6}})]}^{3-}}\]
View Answer play_arrowquestion_answer124) Which one of the following complex ions has the highest magnetic moment?
A) \[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
B) \[{{[Fe{{(CN)}_{6}}]}^{3-}}\]
C) \[{{[Fe{{(CN)}_{6}}]}^{4-}}\]
D) \[{{[Zn{{(N{{H}_{3}})}_{6}}]}^{2+}}\]
View Answer play_arrowquestion_answer125) The non-existant metal carbonyl among the following is
A) \[Cr{{(CO)}_{6}}\]
B) \[Mn{{(CO)}_{5}}\]
C) \[Ni{{(CO)}_{4}}\]
D) \[Fe{{(CO)}_{5}}\]
View Answer play_arrowquestion_answer126) The auto reduction process is not used in the metallurgy of
A) Hg
B) Cu
C) Pb
D) Fe
View Answer play_arrowquestion_answer127) The incorrect statement among the following is
A) hydrogen is used to reduce \[\text{NiO}\]
B) zirconium is refined by van-Arkel method
C) the sulphide ore galena is concentrated by hydraulic washing process
D) in the metallurgy of iron, the flux used is \[\text{Si}{{\text{O}}_{2}}\]
View Answer play_arrowquestion_answer128) The percentage of carbon in cast iron is
A) \[5-10\]
B) \[~0.25-2.5\]
C) \[2.5-4.5\]
D) \[0.12-0.2\]
View Answer play_arrowquestion_answer129) The IUPAC name of the molecule \[C{{H}_{3}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,=\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-OH\]
A) 4-oxo-2, 3-dimethyl pent-2-en-l-oic acid
B) 2-carboxy-3 methyl pent-2-en-3-one
C) 4-carboxy-3 methyl pent-3-en-2-one
D) 2, 3-dimethyl-4-oxo pent-2-en-l-oic acid
View Answer play_arrowquestion_answer130) The ascending order of stability of the \[\bar{C}{{H}_{3}}(P),{{C}_{6}}{{H}_{5}}\bar{C}{{H}_{2}}(Q),\] \[{{(C{{H}_{3}})}_{2}}-CH(R)\]and \[{{H}_{2}}\bar{C}-CH=C{{H}_{2}}(S)\]is
A) \[P<R<S<Q\]
B) \[R<P<S<Q\]
C) \[R<P<Q<S\]
D) \[P<R<Q<S\]
View Answer play_arrowquestion_answer131) The descending order of stability, of the carbonium ions \[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{C}}\,{{H}_{2}}(I),p(C{{H}_{3}}O){{C}_{6}}{{H}_{4}}\overset{+}{\mathop{C}}\,{{H}_{2}}(II),p(N{{O}_{2}})\] \[{{C}_{6}}{{H}_{4}}\overset{+}{\mathop{C}}\,{{H}_{2}}(III)\]and \[p(C{{H}_{3}}){{C}_{6}}{{H}_{4}}\overset{+}{\mathop{C}}\,{{H}_{2}}(IV)\]
A) \[IV>II>I>III\]
B) \[II>IV>m>l\]
C) \[II>IV>I>III\]
D) \[IV>II>III>I\text{ }\]
View Answer play_arrowquestion_answer132) Which one of the following is aromatic?
A) Cyclopentadienyl cation
B) Cyclooctatetraene
C) Cycloheptatriene
D) Cycloheptatrienylcation
View Answer play_arrowquestion_answer133) The total number of acyclic structural and optical isomers possible for a hydrocarbon of molecular formula \[{{C}_{7}}{{H}_{16}}\]is
A) 12
B) 8
C) 10
D) 6
View Answer play_arrowquestion_answer134) The optical rotaion of an optically active compound is
A) directly proportional to the length of the polarimeter tube only
B) directly proportional to the molar concentration of the compound
C) independent of the length of the polarimeter tube and concentration of the compound
D) directly proportional to both the length of the polarimeter tube and the molar concentration of the compound
View Answer play_arrowquestion_answer135) The absolute configurations of the\[{{C}_{2}}\] and\[{{C}_{3}}\] atoms in the molecule with the structure is
A) \[2S,3S\]
B) \[2R,3S\]
C) \[2S,3R\]
D) \[2R,3R\]
View Answer play_arrowquestion_answer136) Hydration of which one of the following yields a ketone
A) Propyne
B) Ethene
C) Prppene
D) Ethyne
View Answer play_arrowquestion_answer137) The most easily hydrolysed molecule under \[{{\text{S}}_{\text{N}}}\text{1}\] conditions is
A) allyl chloride
B) ethyl chloride
C) isopropyl chloride
D) benzyl chloride
View Answer play_arrowquestion_answer138) The most acidic among the following is
A) p-cresol
B) o-cresol
C) p-nitrophenol
D) p-chlorophenol
View Answer play_arrowquestion_answer139) Which one of the following does not undergo iodoform reaction?
A) Secondary butyl alcohol
B) Iso-propyl alcohol
C) Diethyl ketone
D) Ethyl alcohol
View Answer play_arrowquestion_answer140) Glycerol on oxidation with bismuth nitrate forms
A) mesooxalic acid
B) glyceraldehyde
C) dihydroxy acotone
D) tartronic acid
View Answer play_arrowquestion_answer141) Among the following, the alkene on ozonolysis giving rise to only one aldehyde as the product is
A) 1-butene
B) propone
C) 2-butene
D) a-methyl-prop-1-ene
View Answer play_arrowquestion_answer142) Which one of the following does not form sodium bisulphite addition product with sodium bisulphite solution?
A) \[C{{H}_{2}}O\]
B) \[{{C}_{6}}{{H}_{5}}COC{{H}_{3}}\]
C) \[{{C}_{6}}{{H}_{5}}CHO\]
D) \[C{{H}_{3}}CHO\]
View Answer play_arrowquestion_answer143) The carboxylic acid of least strength among the following is
A) p-nitrobenzoic acid
B) p-methylbenzoic acid
C) p-chlprobenzoic acid
D) p-methoxybenzoic acid
View Answer play_arrowquestion_answer144) The most reactive of the following is
A) acetone
B) benzophenone
C) benzaldehyde
D) acetaldehyde
View Answer play_arrowquestion_answer145) Which of the following is not a resonating form of benzaldehyde?
A)
B)
C)
D)
View Answer play_arrowquestion_answer146) The compound that does' not undergo Hell-Volhard Zelinsky reaction is
A) ethanoicacid
B) propionic acid
C) \[iso-\]butyric acid
D) trichloroacetic acid
View Answer play_arrowquestion_answer147) Nitrobenzene can be converted into hydrazobenzene by reduction with
A) Zn and alcoholic NaOH
B) Zn and aqueous NaOH
C) \[\text{ }\!\!~\!\!\text{ N}{{\text{H}}_{\text{2}}}\text{N}{{\text{H}}_{\text{2}}}\] and alcoholic KOH
D) Zn and HCl
View Answer play_arrowquestion_answer148) Which of the following compounds gives carbylamine test?
A) N-methyl-o-methyl aniline
B) N, N-dimethyl aniline
C) 2, 4-diethyl aniline
D) p-methyl-N-methyl benzylamine
View Answer play_arrowquestion_answer149) By which of the following reagents, both the aldehyde and the primary alcoholic group of glucose are oxidized?
A) Tollen?s reagent
B) \[B{{r}_{2}}+{{H}_{2}}O\]
C) \[HN{{O}_{3}}\]
D) All of these
View Answer play_arrowquestion_answer150) Lactoflavin is
A) Vitamin \[{{B}_{1}}\]
B) Vitamin C
C) Vitamin \[{{B}_{2}}\]
D) Vitamin \[{{B}_{2}}\]
View Answer play_arrowquestion_answer151) If S is a set with 10 elements and \[A=\{(x,y):x,\,y\,\in S,\,x\ne y\},\] then the number of elements in A is
A) \[100\]
B) \[90\]
C) \[50\]
D) \[45\]
View Answer play_arrowquestion_answer152) The domain of the real function \[f(x)=\frac{1}{\sqrt{4-{{x}^{2}}}}\]is
A) the set of all real numbers
B) the set of all positive real numbers
C) \[(-2,\,2)\]
D) \[[-2,\,2]\]
View Answer play_arrowquestion_answer153) If \[(3+i)\,(z+\bar{z})-(2+i)(z-\bar{z})+14i\,=0,\] then \[z\bar{z}\] is equal to
A) \[5\]
B) \[8\]
C) \[10\]
D) \[40\]
View Answer play_arrowquestion_answer154) \[4+5{{\left( \frac{-1+i\sqrt{3}}{2} \right)}^{2008}}+3{{\left( \frac{-1+i\sqrt{3}}{2} \right)}^{2009}}\] is equal to
A) \[-i\sqrt{3}\]
B) \[i\sqrt{3}\]
C) \[1-i\sqrt{3}\]
D) \[-1+i\sqrt{3}\]
View Answer play_arrowquestion_answer155) If the equation \[(a+1){{x}^{2}}-(a+2)x+(a+3)=0\] has roots equal in magnitude but opposite in signs, then the roots of the equation are
A) \[\pm \,\,a\]
B) \[\pm \,\frac{1}{2}\,a\]
C) \[\pm \,\frac{3}{2}\,a\]
D) \[\pm \,2\,a\]
View Answer play_arrowquestion_answer156) If a and p are roots of the quadratic equation \[{{x}^{2}}+4x+3=0,\]then the equation whose roots are \[2\alpha \,\text{+}\,\beta \] and \[\alpha \,\text{+2}\,\beta \] is
A) \[{{x}^{2}}-12x+35=0\]
B) \[{{x}^{2}}+12x-33=0\]
C) \[{{x}^{2}}-12x-33=0\]
D) \[{{x}^{2}}+12x+35=0\]
View Answer play_arrowquestion_answer157) If the sum to 2 n terms of the \[AP\text{ }2,\text{ }5,\text{ }8,11,...\]is equal to the sum to n terms of the \[AP\text{ }57,\text{ }59,\text{ }61,\text{ }63,\text{ }...\text{ },\]then n is equal to
A) \[10\]
B) \[11\]
C) \[12\]
D) \[13\]
View Answer play_arrowquestion_answer158) If the third term of a GP is 3, then the product of its first 5 terms is
A) 15
B) \[81\]
C) \[243\]
D) Cannot be determined
View Answer play_arrowquestion_answer159) The term independent of x in the expansion of \[{{\left( \sqrt{\frac{x}{3}}+\frac{3}{2{{x}^{2}}} \right)}^{10}}\] is
A) \[\frac{5}{4}\]
B) \[\frac{7}{4}\]
C) \[\frac{9}{4}\]
D) \[45\]
View Answer play_arrowquestion_answer160) \[\frac{^{8}{{C}_{0}}}{6}{{-}^{8}}{{C}_{1}}{{+}^{8}}{{C}_{2}}.6{{-}^{8}}{{C}_{3}}{{.6}^{2}}+....{{+}^{8}}{{C}_{8}}{{.6}^{7}}\] is equal to
A) \[0\]
B) \[{{6}^{7}}\]
C) \[{{6}^{8}}\]
D) \[\frac{{{5}^{8}}}{6}\]
View Answer play_arrowquestion_answer161) The number of ways in which 5 boys and 5 girls can be seated for a photograph so that no two girls sit next to each other is
A) \[6!\,5!\]
B) \[{{(5!)}^{2}}\]
C) \[\frac{10!}{(5!)}\]
D) \[\frac{10!}{{{(5!)}^{2}}}\]
View Answer play_arrowquestion_answer162) The number of diagonals of a polygon of 20 sides is
A) \[210\]
B) \[190\]
C) \[180\]
D) \[170\]
View Answer play_arrowquestion_answer163) The sum of the series \[\left( 1+\frac{{{({{\log }_{e}}\,n)}^{2}}}{2!}+\frac{{{({{\log }_{e}}n)}^{4}}}{4!}+... \right)\]is
A) \[n+\frac{1}{n}\]
B) \[\frac{n'}{2}+\frac{1}{2n}\]
C) \[{{\log }_{e}}\frac{1}{1-{{({{\log }_{e}}n)}^{2}}}\]
D) \[\frac{1}{2}{{\log }_{e}}\,\frac{1}{1-{{({{\log }_{e}}\,n)}^{2}}}\]
View Answer play_arrowquestion_answer164) If \[{{x}_{1}},{{x}_{2}},......{{x}_{18}}\] are observations such, that \[\sum\limits_{j=1}^{18}{({{x}_{j}}-8)=9}\] and \[\sum\limits_{j=1}^{18}{{{({{x}_{j}}-8)}^{2}}=45,}\] then the standard deviation of these observations is
A) \[\sqrt{\frac{81}{34}}\]
B) \[5\]
C) \[\sqrt{5}\]
D) \[\frac{3}{2}\]
View Answer play_arrowquestion_answer165) If \[(3,\,\,3)\] is a vertex of a triangle and \[(-3,\,\,6)\] and \[(9,\,\,6)\] are the mid points of the two sides through this vertex, then the centroid of the triangle is
A) \[(3,\,\,7)\]
B) \[(1,\,\,7)\]
C) \[(-3,\,\,7)\]
D) \[(-1,\,\,7)\]
View Answer play_arrowquestion_answer166) If the lines \[x+2ay+a=0,\,\,\,\,x+3by+b=0\] and \[x+4\,cy+c=0\] are concurrent, where a, b, c are non-zero real numbers, then
A) \[\frac{1}{a},\frac{1}{b},\frac{1}{c}\]are in an AP
B) \[\frac{1}{a},\frac{1}{b},\frac{1}{c}\] are in a GP
C) a, b, c are in an AP
D) a, b, c are in a GP
View Answer play_arrowquestion_answer167) If the - equation \[6{{x}^{2}}+11xy-10{{y}^{2}}+x+31y+c=0\]represent a pair of straight lines, then the value of c is
A) \[\frac{125}{367}\]
B) \[-\frac{125}{367}\]
C) \[15\]
D) \[-15\]
View Answer play_arrowquestion_answer168) If the equation \[\lambda \,\,{{x}^{2}}+(2\lambda -3){{y}^{2}}-4x-1=0\] represents a circle, then its radius is
A) \[\frac{\sqrt{11}}{3}\]
B) \[\frac{\sqrt{13}}{3}\]
C) \[\frac{\sqrt{7}}{3}\]
D) \[\frac{1}{3}\]
View Answer play_arrowquestion_answer169) The equation of the circle passing through the point \[(1,\,\,1)\] and through the points of intersection of the circles \[{{x}^{2}}+{{y}^{2}}=6\] and \[{{x}^{2}}+\text{ }{{y}^{2}}-6y+8=0\]is
A) \[{{x}^{2}}+{{y}^{2}}+3y-13=0\]
B) \[{{x}^{2}}+{{y}^{2}}-3y+1=0\]
C) \[{{x}^{2}}+{{y}^{2}}-3x+1=0\]
D) \[5{{x}^{2}}+5{{y}^{2}}+6y+16=0\]
View Answer play_arrowquestion_answer170) If \[x+y=k\]is a tangent to the parabola \[{{y}^{2}}=12x,\]then k is equal to
A) \[9\]
B) \[-9\]
C) \[3\]
D) \[-3\]
View Answer play_arrowquestion_answer171) If in a hyperbola, the distance between the foci is 10 and the transverse axis has length 8, then the length of its latuserectum is
A) \[9\]
B) \[\frac{9}{2}\]
C) \[\frac{5}{4}\]
D) \[2\]
View Answer play_arrowquestion_answer172) If \[\tan \theta =\frac{1}{\sqrt{7}},\]then \[\frac{(\text{cose}{{\text{c}}^{2}}\,\theta -{{\sec }^{2}}\theta )}{(\text{cose}{{\text{c}}^{2}}\,\theta +{{\sec }^{2}}\theta )}\] is equal to
A) \[\frac{1}{2}\]
B) \[\frac{3}{4}\]
C) \[\frac{5}{4}\]
D) \[2\]
View Answer play_arrowquestion_answer173) When \[\theta \] varies over the real numbers, the maximum value of \[\cos \,\,\theta -\cos \,2\theta \] is
A) \[2\]
B) \[\frac{7}{8}\]
C) \[\frac{5}{4}\]
D) \[2\]
View Answer play_arrowquestion_answer174) \[\sin \,\,{{47}^{o}}+\sin {{61}^{o}}-\sin {{11}^{o}}-\sin {{25}^{o}}\] is equal to
A) \[\sin \,{{7}^{o}}\]
B) \[\cos \,{{7}^{o}}\]
C) \[\sin \,{{36}^{o}}\]
D) \[\cos \,{{36}^{o}}\]
View Answer play_arrowquestion_answer175) In \[\Delta \,\,ABC\] if \[si{{n}^{2}}A+si{{n}^{2}}B+si{{n}^{2}}C=2,\]then the triangle is
A) right angled, but need not be isosceles
B) right angled and isosceles
C) isosceles, but need not be right angled
D) equilateral
View Answer play_arrowquestion_answer176) In \[\Delta \,\,ABC,\]if \[s=\frac{a+b+c}{2},\]then \[\left( b\,\,{{\cos }^{2}}\,\frac{C}{2}+c\,\,{{\cos }^{2}}\,\frac{B}{2} \right)\] is equal to
A) \[s\]
B) \[2s\]
C) \[4\,s\]
D) \[3\,s\]
View Answer play_arrowquestion_answer177) The number of solutions of the equation \[\sin \,x\,\,\cos \,\,3x=\sin \,3x\,\,\cos \,5x\]in \[\left[ 0,\frac{\pi }{2} \right]\] is
A) \[3\]
B) \[4\]
C) \[5\]
D) \[6\]
View Answer play_arrowquestion_answer178) The most general values of \[\theta \] satisfying \[\tan \theta +\tan \left( \frac{3\pi }{4}+\theta \right)=2\] are given by
A) \[2n\pi \pm \frac{\pi }{3},\,n\in Z\]
B) \[n\pi \pm \frac{\pi }{3},\,n\in Z\]
C) \[2n\pi \pm \frac{\pi }{6},\,n\in Z\]
D) \[n\pi \pm \frac{\pi }{6},\,n\in Z\]
View Answer play_arrowquestion_answer179) The value of \[{{\cos }^{-1}}\,\left( \sin \,\frac{7\pi }{6} \right)\] is equal to
A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{6}\]
C) \[\frac{2\pi }{3}\]
D) \[-\frac{\pi }{3}\]
View Answer play_arrowquestion_answer180) If \[{{\tan }^{-1}}\,2\] and \[{{\tan }^{-1}}\,3\] are two angles of a triangle, then the third angle is
A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrowquestion_answer181) The value of \[\left| \begin{matrix} {{\log }_{5}}\,\,729 & {{\log }_{3}}\,5 \\ {{\log }_{5}}\,27 & {{\log }_{9}}\,25 \\ \end{matrix} \right|\,.\,\,\left| \begin{matrix} {{\log }_{3}}\,5 & {{\log }_{27}}\,\,5 \\ {{\log }_{5}}\,9 & {{\log }_{5}}\,9 \\ \end{matrix} \right|\] is equal to
A) \[1\]
B) \[6\]
C) \[{{\log }_{5}}\,9\]
D) \[{{\log }_{3}}5.\,{{\log }_{5}}\,81\,\]
View Answer play_arrowquestion_answer182) If a, b, c are all distinct and if \[\left| \begin{matrix} 1-{{a}^{3}} & {{a}^{2}} & a \\ 1-{{b}^{3}} & {{b}^{2}} & b \\ 1-{{c}^{3}} & {{c}^{2}} & c \\ \end{matrix} \right|=0,\] then
A) \[abc=1\]
B) \[abc=-1\]
C) \[a+b+c=0\]
D) \[a+b+c=\pm 1\]
View Answer play_arrowquestion_answer183) If the system of homogeneous equations \[2x-y+z=0,\,\,x-2y+z=0,\,\,\lambda \,\,x-y+2z=0\] has infinitely many solutions, then
A) \[\lambda =5\]
B) \[\lambda =-5\]
C) \[\lambda \ne \pm 5\]
D) None of these
View Answer play_arrowquestion_answer184) If X and Y are \[2\times 2\] matrices such that \[2X+3Y=O\] and \[X+2Y=I,\]where \[O\] and \[I\] denote the \[2\times 2\] zero matrix and the \[2\times 2\] identity matrix, then X is equal to
A) \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 2 & 0 \\ 0 & 2 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -3 & 0 \\ 0 & -3 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer185) For \[0<\theta <\pi ,\] if \[A=\left[ \begin{matrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right],\]then
A) \[{{A}^{T}}=A\]
B) \[{{A}^{T}}=-A\]
C) \[{{A}^{2}}=I\]
D) \[{{A}^{T}}={{A}^{-1}}\]
View Answer play_arrowquestion_answer186) The matrix \[\left[ \begin{matrix} \lambda & 1 & 0 \\ 0 & 2 & 3 \\ 0 & 0 & \lambda \\ \end{matrix} \right]\] is non-singular
A) for all real values of \[\lambda \]
B) only when \[\lambda =\pm \frac{1}{\sqrt{2}}\]
C) only when \[\lambda \ne 0\]
D) only when \[\lambda =0\]
View Answer play_arrowquestion_answer187) A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are respectively, \[4\hat{i}+3\hat{j}-\hat{k}\]and \[-3\hat{i}+\hat{j}+\hat{k},\] then\[\overrightarrow{DE}\] is equal to
A) \[7\hat{i}+2\hat{j}-2k\]
B) \[-7\hat{i}-2\hat{j}+\text{ }2\hat{k}\]
C) \[3\hat{i}-\hat{j}-\hat{k}\]
D) \[-4\hat{i}-3\hat{j}+2\hat{k}\]
View Answer play_arrowquestion_answer188) If the position vectors of the vertices of triangle ABC are \[3\hat{i}+\hat{j}+2\hat{k},\,\,\,\hat{i}-2\hat{j}+7\hat{k}\]and \[-2\hat{i}+3\hat{j}+5\hat{k},\] then the triangle ABC is
A) right angled and isosceles
B) right angled, but not isosceles
C) isosceles but not right angled
D) equilateral
View Answer play_arrowquestion_answer189) If \[4|\vec{a}|=12|\vec{b}|=3|\vec{c}|=12\] and \[\vec{a}+\vec{b}+\vec{c}=\vec{0},\] then \[\vec{a}\,\,.\,\,\vec{b}+\vec{b}\,.\,\,\vec{c}+\vec{c}\,.\,\,\vec{a}\] is equal to
A) \[-8\]
B) \[8\]
C) \[-13\]
D) \[13\]
View Answer play_arrowquestion_answer190) If \[2\text{ }\vec{a}+3\text{ }\vec{b}+\vec{c}=0,\] then \[\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}\]is equal to
A) \[6\,(\vec{b}\times \vec{c})\]
B) \[3\,(\vec{b}\times \vec{c})\]
C) \[2\,(\vec{b}\times \vec{c})\]
D) \[\vec{0}\]
View Answer play_arrowquestion_answer191) If \[\hat{i}-\hat{k},\,\lambda \hat{i}+\hat{j}+(1-\lambda )\hat{k}\] and \[\mu \hat{i}+\lambda \hat{j}+(1+\lambda -\mu )\hat{k}\]are three coterminal edges of a parallelopiped, then its volume depends on
A) only \[\lambda \]
B) only \[\mu \]
C) both \[\lambda \] and \[\mu \]
D) neither \[\lambda \] nor\[\mu \]
View Answer play_arrowquestion_answer192) \[\vec{u}\] and \[\vec{v}\] are unit vectors such that \[\vec{u}\,\,.\vec{v}\]. If \[\vec{r}\]is any vector coplanar with \[\vec{u}\] and \[\vec{v}\] then the magnitude of the \[\vec{u}\] vector \[\vec{v},\] is
A) \[0\]
B) \[1\]
C) \[|\vec{r}|\]
D) \[2|\vec{r}|\]
View Answer play_arrowquestion_answer193) The point on the x-axis equidistant from the points \[(4,3,1)\]and \[(-2,\,-6,\,-2)\] is
A) \[(0,\,-1,0)\]
B) \[(0,\,1,-6)\]
C) \[\left( -\frac{3}{2},0,0 \right)\]
D) \[\left( -\frac{1}{2},0,0 \right)\]
View Answer play_arrowquestion_answer194) A line makes an obtuse angle with the positive x-axis and angles \[\frac{\pi }{4}\] and \[\frac{\pi }{3}\] with the positive y and z axes respectively. Its direction cosine are
A) \[\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{2}\]
B) \[\frac{1}{\sqrt{2}},-\frac{1}{2},\frac{1}{2}\]
C) \[-\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]
D) \[\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]
View Answer play_arrowquestion_answer195) The shortest distance between the straight line \[\frac{x-6}{1}=\frac{2-y}{2}=\frac{z-2}{2}\] and \[\frac{x+4}{3}-\frac{y}{-2}=\frac{1-z}{2}\] is
A) \[9\]
B) \[\frac{19}{3}\]
C) \[\frac{16}{3}\]
D) \[4\]
E) None of these
View Answer play_arrowquestion_answer196) The image of the point \[(6,3,9)\]in the straight line \[x-2=\frac{1-y}{2}=\frac{z}{2}\]is
A) \[\left( \frac{28}{9},\frac{83}{9},\frac{11}{9} \right)\]
B) \[(28,83,11)\]
C) \[(4,-3,4)\]
D) \[(2,-9,-1)\]
View Answer play_arrowquestion_answer197) The equation of the plane passing through the point \[(1,1,1)\] and containing the line of intersection of the planes \[x+y+z=6\] and \[2x+3y+4z=12\] is
A) \[x+y+z=3\]
B) \[x+2y+3z=6\]
C) \[2x+3y+4z=9\]
D) \[3x+4y+5z=18\]
View Answer play_arrowquestion_answer198) The shortest distance from the plane \[2x-y+2z=25\] to the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2x-4y+2z-3=0\] is
A) \[6\]
B) \[9\]
C) \[12\]
D) \[24\]
View Answer play_arrowquestion_answer199) If \[\vec{a}\] is a constant vector and p is a real constant with \[|\vec{a}{{|}^{2}}>p,\] then the locus of a point with position vector \[|\vec{r}|\] such that \[|\vec{r}{{|}^{2}}-2\,\,\vec{r}.\,\vec{a}\,+\,\,p=O\]is
A) a sphere
B) an ellipse
C) a circle
D) a plane
View Answer play_arrowquestion_answer200) Consider the switching circuit given below The logical expression corresponding to the complementary to the above circuit is
A) \[a'b'c'\]
B) \[a+b+c'\]
C) \[a\,.\,b\,.\,c'\]
D) \[a'+b'+c\]
View Answer play_arrowquestion_answer201) A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. The probability that they match is
A) \[\frac{4}{9}\]
B) \[\frac{5}{8}\]
C) \[\frac{5}{9}\]
D) \[\frac{5}{12}\]
View Answer play_arrowquestion_answer202) Events A, B, C are mutually exclusive events such that \[P(A)=\frac{(3x+1)}{3},\,\,P(B)=\frac{(1-x)}{4}\] and \[P(C)=\frac{(1-2x)}{2}\].The set of possible values of x are in the interval
A) \[\left[ \frac{1}{3},\frac{1}{2} \right]\]
B) \[\left[ \frac{1}{3},\frac{2}{3} \right]\]
C) \[\left[ \frac{1}{3},\frac{13}{3} \right]\]
D) \[[0,\,1]\]
View Answer play_arrowquestion_answer203) \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{{{e}^{{{x}^{2}}}}-\cos \,x}{{{x}^{2}}}\]is equal to
A) \[0\]
B) \[1/2\]
C) \[1\]
D) \[3/2\]
View Answer play_arrowquestion_answer204) If \[0<a<b,\]then \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{a}^{n}}+{{b}^{n}}}{{{a}^{n}}-{{b}^{n}}}\]
A) equals 0
B) equals - 1
C) equals 1
D) does not exist
View Answer play_arrowquestion_answer205) The function \[f(x)\] is defined as \[f(x)=\frac{2x-{{\sin }^{-1}}x}{2x+{{\tan }^{-1}}x'}\], if \[x\ne 0\]. The value to be assigned to f at \[x=0\]so that the function is continuous there, is
A) \[-\frac{1}{3}\]
B) \[1\]
C) \[\frac{2}{3}\]
D) \[\frac{1}{3}\]
View Answer play_arrowquestion_answer206) The function \[f(x)=\left\{ \begin{matrix} |x-3|, & if & x\ge 1 \\ \frac{{{x}^{2}}}{4}-\frac{3x}{2}+\frac{13}{4}, & if & x<1 \\ \end{matrix} \right.\]is
A) continuous and differentiable at \[x=3\]
B) continuous at \[x=3,\] but not differentiable at \[x=3\]
C) continuous and differentiable everywhere
D) continuous at \[x=1,\]but not differentiable at \[x=1,\]
View Answer play_arrowquestion_answer207) If \[f(x)={{x}^{n}},\] then \[f(1)+\frac{f'(1)}{1!}+\frac{f'\,'(1)}{2!}+....+\frac{{{f}^{n}}(1)}{n!}\]is equal to
A) \[\frac{n(n+1)}{2}\]
B) \[{{2}^{n}}\]
C) \[{{2}^{(n+1)}}\]
D) \[{{2}^{(n-1)}}\]
View Answer play_arrowquestion_answer208) If \[y=\log \,(\sin \,({{x}^{2}})),\] \[0<0<\frac{\pi }{2},\] then \[\frac{dy}{dx}\] at\[x=\frac{\sqrt{\pi }}{2}\]is
A) \[0\]
B) \[1\]
C) \[\frac{\pi }{4}\]
D) \[\sqrt{\pi }\]
View Answer play_arrowquestion_answer209) Let \[x={{\log }_{e}}\,t,t>0\] and \[y+1={{t}^{2}}.\] Then, \[\frac{{{d}^{2}}x}{d{{y}^{2}}}\]is equal to
A) \[4{{e}^{2x}}\]
B) \[-\frac{1}{2}\,{{e}^{-4x}}\]
C) \[-\frac{3}{4}\,{{e}^{-5x}}\]
D) \[4{{e}^{x}}\]
View Answer play_arrowquestion_answer210) \[f(x)={{\tan }^{-1}}\,(\sin x+\cos x),\,\,-\frac{\pi }{2}\le x\le \frac{\pi }{2},\]is increasing in
A) \[\left( -\frac{\pi }{4},\frac{\pi }{4} \right)\]
B) \[\left( 0,\frac{\pi }{2} \right)\]
C) \[\left( -\frac{\pi }{2},-\frac{\pi }{4} \right)\]
D) \[\left( \frac{\pi }{4},\frac{\pi }{2} \right)\]
View Answer play_arrowquestion_answer211) For the function \[f(x)=x{{e}^{x}}\]the point
A) \[x=0\]is a maximum
B) \[x=0\]is a minimum
C) \[x=-1\] is a maximum
D) \[x=-1\] is a minimum
View Answer play_arrowquestion_answer212) Let \[f(x)={{x}^{3}}.\]. Use mean value theorem to write \[\frac{f(x+h)-f(x)}{h}=f'(x+\theta h)\] , with \[0<\theta <1\]. If \[x\ne 0,\]then \[\underset{h\to 0}{\mathop{\lim }}\,\,\,\theta \] is equal to
A) \[-1\]
B) \[-0.5\]
C) \[0.5\]
D) \[1\]
View Answer play_arrowquestion_answer213) If \[f\,(x)=\underset{y\to x}{\mathop{lim}}\,\,\frac{{{\sin }^{2}}y-{{\sin }^{2}}x}{{{y}^{2}}-{{x}^{2}}},\]then \[\int{4x\,\,f(x)\,\,dx}\]is equal to
A) \[\cos \,\,2x+c\]
B) \[2\,\cos \,\,2x+c\]
C) \[-\,\cos \,\,2x+c\]
D) \[-2\,\cos \,\,2x+c\]
View Answer play_arrowquestion_answer214) \[\int_{0}^{a}{\sqrt{\frac{a-x}{x}}\,\,dx}\]is equal to
A) \[\frac{\pi a}{2}\]
B) \[\frac{\pi a}{4}\]
C) \[\frac{\pi {{a}^{2}}}{4}\]
D) \[\frac{a}{2}\]
View Answer play_arrowquestion_answer215) \[\int_{0}^{x}{\log \,(\cot \,x\,+\,\tan t)\,dt}\]is equal to
A) \[x\,\log \,(\sin \,x)\]
B) \[-x\,\log \,(\sin \,x)\]
C) \[x\,\log \,(cos\,x)\]
D) \[-x\,\log \,(cos\,x)\]
View Answer play_arrowquestion_answer216) The equation of the tangent to the curve \[y=\int_{{{x}^{2}}}^{{{x}^{3}}}{\frac{dt}{\sqrt{{{t}^{2}}+1}}}\] at \[x=1\] is
A) \[y=\sqrt{3}x+1\]
B) \[x=\sqrt{3}y+1\]
C) \[x=\sqrt{2}y+1\]
D) \[y=\sqrt{3}(x+1)+1\]
View Answer play_arrowquestion_answer217) The area of the region bounded by the curves \[y={{2}^{x}}\] and \[y=2x-{{x}^{2}}\]between the ordinates \[x=0\]and \[x=2\]is
A) \[\frac{2}{\log \,2}-\frac{4}{3}\]
B) \[\frac{3}{\log \,2}-\frac{4}{3}\]
C) \[\frac{1}{\log \,2}-\frac{4}{3}\]
D) \[\frac{4}{\log \,2}-\frac{3}{2}\]
View Answer play_arrowquestion_answer218) If c is a positive constant, then the differential equation of the family of the curves \[{{y}^{2}}=2c(x+\sqrt{c})\]has
A) order 1 and degree 3
B) order 1 and degree 2
C) order 2 and degree 1
D) order 3 and degree 1
View Answer play_arrowquestion_answer219) The solution of the differential equation \[(1+{{y}^{2}})+(x-{{e}^{{{\tan }^{-1}}y}})\frac{dy}{dx}=0\]is
A) \[2x{{e}^{{{\tan }^{-1}}y}}={{e}^{2\,{{\tan }^{-1}}y}}+c\]
B) \[x{{e}^{{{\tan }^{-1}}y}}={{\tan }^{-1}}y+c\]
C) \[x{{e}^{2\,{{\tan }^{-1}}y}}={{e}^{{{\tan }^{-1}}y}}+c\]
D) \[(x-2)=c{{e}^{-{{\tan }^{-1}}}}y\]
View Answer play_arrowquestion_answer220) P and Q are two like parallel forces. If Q is moved parallel to itself through a distance x, then the resultant of P and Q moves through a distance
A) \[Q(P+Q)X\]
B) \[\frac{QX}{(P+Q)}\]
C) \[\frac{PX}{(P+Q)}\]
D) \[\frac{(P+Q)X}{(P-Q)}\]
View Answer play_arrowquestion_answer221) The greatest and the least magnitudes of the resultant of two forces of constant magnitudes are F and G. when the forces act at an angle \[2\alpha ,\] the magnitude of the resultant is equal to
A) \[\sqrt{{{F}^{2}}\,{{\cos }^{2}}\,\alpha \,+{{G}^{2}}\,{{\sin }^{2}}\alpha }\]
B) \[\sqrt{{{F}^{2}}\,{{\sin }^{2}}\alpha +{{G}^{2}}\,{{\cos }^{2}}\alpha }\]
C) \[\sqrt{{{F}^{2}}+{{G}^{2}}}\]
D) \[\sqrt{{{F}^{2}}-{{G}^{2}}}\]
View Answer play_arrowquestion_answer222) The magnitude of moment of a couple in certain direction is G and in a direction orthogonal to this direction (anti-clockwise) is H. The magnitude of moment of couple in anti-clockwise direction at an angle \[\theta \] to the critical direction is given by
A) \[G\,\cos \,\theta -H\,\sin \theta \]
B) \[-G\,\cos \,\theta +H\,\sin \theta \]
C) \[G\,\cos \,\theta +H\,\sin \theta \]
D) \[G\,sin\,\theta +H\,\cos \theta \]
View Answer play_arrowquestion_answer223) The amount of force that is needed to accelerate a truck of mass \[36000\,kg\]from rest to a velocity of \[60\,km/h\]in \[20\,s\] is
A) \[6\,kN\]
B) \[30\,kN\]
C) \[60\,kN\]
D) \[30000\,kN\]
View Answer play_arrowquestion_answer224) A body id falling freely under gravity starting from a point O.it passes through two points A and B. If \[OA=\,2AB,\] then the ratio of time takes by the body to cover the distance OA and AB is
A) \[2\,\pm \,\sqrt{6}\]
B) \[\sqrt{2}\]
C) \[2+\sqrt{2}\]
D) \[2+\sqrt{6}\]
View Answer play_arrowquestion_answer225) A particle is projected from a point on the horizontal plane so as to just clear two walls each of height \[20\,m\]at distance \[30\,m\] and \[170\,m\] respectively from the point of projection. If \[\alpha \] is the angle projection then
A) \[40\,\,\tan \,\alpha =51\]
B) \[40\,\,\cot \,\alpha =51\]
C) \[30\,\,tan\,\alpha =23\]
D) \[30\,\,\cot \,\alpha =23\]
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