question_answer1) In beta minus decay a neutron transforms with the nucleus according to.
A) \[p\to n+{{e}^{+}}+v\] done clear
B) \[n\to p+{{e}^{-}}+\bar{v}\] done clear
C) \[n\to p+{{e}^{+}}+\bar{v}\] done clear
D) \[n\to p+{{e}^{+}}+v\] done clear
View Answer play_arrowquestion_answer2) The element with maximum value of binding energy per nucleon is
A) iron done clear
B) aluminium done clear
C) uranium done clear
D) hydrogen done clear
View Answer play_arrowquestion_answer3) If the particles listed below all have the same kinetic energy, which one would possess the shortest de-Broglie wavelength?
A) Deuteron done clear
B) \[\alpha \]-particle done clear
C) Proton done clear
D) Electron done clear
View Answer play_arrowquestion_answer4) Which of the following quantities for a nucleus is independent of its mass number?
A) Density done clear
B) Volume done clear
C) Mass done clear
D) Radius done clear
View Answer play_arrowquestion_answer5) The SI unit of activity of a radioactive sample is
A) Curie done clear
B) Rutherford done clear
C) Becquerel done clear
D) Mill curie done clear
View Answer play_arrowquestion_answer6) P-type semiconductor is obtained by doping
A) germanium with arsenic done clear
B) germanium with aluminium done clear
C) germanium with antimony done clear
D) germanium with phosphorus done clear
View Answer play_arrowquestion_answer7) A cubical block rests on an inclined plane of coefficient of friction \[\mu =1/\sqrt{3}\]. What should be the angle of inclination so that the block Just slides down the inclined plane?
A) \[{{30}^{o}}\] done clear
B) \[{{60}^{o}}\] done clear
C) \[{{45}^{o}}\] done clear
D) \[{{90}^{o}}\] done clear
View Answer play_arrowquestion_answer8) The acceleration of an object moving in a circle of radius R with uniform speed v is
A) \[\frac{{{v}^{2}}}{R}\] done clear
B) \[\frac{{{v}^{2}}}{2R}\] done clear
C) \[\frac{2{{v}^{2}}}{R}\] done clear
D) \[\frac{3{{v}^{2}}}{2R}\] done clear
View Answer play_arrowquestion_answer9) If a projectile is launched with velocity \[{{v}_{0}},\] making an angle \[\theta \] with x-axis, then its time of flight T is
A) \[T=\frac{v_{0}^{2}\sin 2\theta }{g}\] done clear
B) \[T=\frac{v_{0}^{2}\,\,{{\sin }^{2}}\theta }{2g}\] done clear
C) \[T=\frac{v_{0}^{2}}{g}\] done clear
D) \[T=\frac{2{{v}_{0}}\,\sin \,\theta }{g}\] done clear
View Answer play_arrowquestion_answer10) A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of\[12\text{ }m/s\]. If the mass of the ball is \[0.15\text{ }kg\]the impulse imparted to the ball is
A) \[36\text{ }Ns\] done clear
B) \[3.6\text{ }Ns\] done clear
C) \[0.36\text{ }Ns\] done clear
D) \[0.036\text{ }Ns\] done clear
View Answer play_arrowquestion_answer11) Which of the following statements' is correct regarding the photoelectric experiment?
A) The photocurrent increases with intensity of light done clear
B) Stopping potential increases with increase in intensity of incident light done clear
C) The photo current increases with increase in frequency done clear
D) All of the above done clear
View Answer play_arrowquestion_answer12) In a double-slit experiment, the two slits are separated by \[1\text{ }mm\]and the screen is placed \[1\text{ }m\]away. The fringe separation for blue green light of wavelength \[500\text{ }nm\]is
A) \[10\text{ }mm\] done clear
B) \[0.5\text{ }mm\] done clear
C) \[20\,\,mm\] done clear
D) \[15\,\,mm\] done clear
View Answer play_arrowquestion_answer13) Rainbow is a phenomenon due to
A) dispersion alone done clear
B) refraction alone done clear
C) reflection alone done clear
D) combined effect of dispersion, refraction and reflection done clear
View Answer play_arrowquestion_answer14) In the case of light waves from two coherent\[{{S}_{1}}\] and \[{{S}_{2}}\] there will be constructive interference at an arbitrary point p, if the path difference \[{{S}_{1}}P-{{S}_{2}}P\] is
A) \[\left( n+\frac{1}{2} \right)\lambda \] done clear
B) \[n\lambda \] done clear
C) \[\left( n-\frac{1}{2} \right)\lambda \] done clear
D) \[\frac{\lambda }{2}\] done clear
View Answer play_arrowquestion_answer15) The de-Broglie wavelength \[\lambda \]of an electron accelerated through a potential V(in volt) is
A) \[\frac{1.227}{\sqrt{V}}nm\] done clear
B) \[\frac{0.1227}{\sqrt{V}}nm\] done clear
C) \[\frac{0.01227}{\sqrt{V}}nm\] done clear
D) \[\frac{0.1227}{\sqrt{V}}\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
View Answer play_arrowquestion_answer16) A gardener pushes a lawn roller through a distance\[20\text{ }m\]. If he applies a force of \[20kg-wt\] in a direction inclined at \[60{}^\circ \] to the ground, the work done by him is
A) \[1960\text{ }J\] done clear
B) \[196\text{ }J\] done clear
C) \[1.96\text{ }J\] done clear
D) \[196\text{ }kJ\] done clear
View Answer play_arrowquestion_answer17) If two bodies stick together after collision and move as a single body, the collision is said to be
A) perfectly inelastic done clear
B) elastic done clear
C) inelastic done clear
D) perfectly elastic done clear
View Answer play_arrowquestion_answer18) If \[{{\mu }_{s}}\] is coefficient of static friction, the maximum speed \[{{v}_{\max }}\]with which a vehicle can negotiate an unbanked curved track having radius R and inclined at an angle \[\theta \] with respect to horizontal plane is
A) \[{{v}_{\max }}=\sqrt{Rg\,\,\tan \theta }\] done clear
B) \[{{v}_{\max }}=\sqrt{{{\mu }_{s}}\,\,Rg}\] done clear
C) \[\sqrt{Rg}\] done clear
D) \[\sqrt{\tan \theta /Rg}\] done clear
View Answer play_arrowquestion_answer19) For a moving particle (mass m, velocity v) having a momentum p, which one of the following correctly describes the kinetic energy of the particle?
A) \[\frac{{{p}^{2}}}{2m}\] done clear
B) \[\frac{p}{2m}\] done clear
C) \[\frac{{{v}^{2}}}{2m}\] done clear
D) \[\frac{v}{2m}\] done clear
View Answer play_arrowquestion_answer20) SI unit of power is
A) joule done clear
B) erg done clear
C) newton done clear
D) watt done clear
View Answer play_arrowquestion_answer21) Sun is visible a little before the actual sunrise and until a little after the actual sunset. This is due to
A) total internal reflection done clear
B) reflection done clear
C) refraction done clear
D) polarization done clear
View Answer play_arrowquestion_answer22) The part of the spectrum of the electro- magnetic radiation used to cook food is
A) Ultraviolet rays done clear
B) Cosmic rays done clear
C) X-rays done clear
D) Microwaves done clear
View Answer play_arrowquestion_answer23) An LCR series circuit is under resonance. \[{{I}_{m}}\] is current amplitude, \[{{V}_{m}}\] is voltage amplitude, R is the resistance, Z is the impedance, \[{{X}_{L}}\] is the inductive reactance and \[{{X}_{C}}\] is the capacitive reactance then,
A) \[{{I}_{m}}=\frac{{{V}_{m}}}{Z}\] done clear
B) \[{{I}_{m}}=\frac{{{V}_{m}}}{{{X}_{L}}}\] done clear
C) \[{{I}_{m}}=\frac{{{V}_{m}}}{{{X}_{C}}}\] done clear
D) \[{{I}_{m}}=\frac{{{V}_{m}}}{R}\] done clear
View Answer play_arrowquestion_answer24) A point source that emits waves uniformly in all directions, produces wave fronts that are
A) spherical done clear
B) elliptical done clear
C) cylindrical done clear
D) planar done clear
View Answer play_arrowquestion_answer25) In the case of an inductor
A) voltage lags the current by \[\pi /2\] done clear
B) voltage leads the current by \[\pi /2\] done clear
C) voltage leads the current by \[\pi /3\] done clear
D) voltage leads the current by \[\pi /4\] done clear
View Answer play_arrowquestion_answer26) For a stretched string of length L fixed at both ends, the frequency of the fundamental mode of vibration is (v is the velocity if travelling waves in the string)
A) \[\frac{v}{2L}\] done clear
B) \[\frac{v}{L}\] done clear
C) \[\frac{v}{4L}\] done clear
D) \[\frac{v}{3L}\] done clear
View Answer play_arrowquestion_answer27) The figure shows circular motion of a reference particle to represent simple harmonic motion. The amplitude of simple harmonic motion is
A) \[2\text{ }cm\] done clear
B) \[3\text{ }cm\] done clear
C) \[\text{4 }cm\] done clear
D) \[3\,m\] done clear
View Answer play_arrowquestion_answer28) In the case of a travelling wave, the reflection at a rigid boundary will take place with a phase change of
A) \[\frac{\pi }{2}\,rad\] done clear
B) \[\frac{\pi }{4}\,rad\] done clear
C) \[\pi \,\,rad\] done clear
D) \[\frac{\pi }{6}\,\,rad\] done clear
View Answer play_arrowquestion_answer29) If \[{{u}_{1}}\] and \[{{u}_{2}}\] are the frequencies of two tuning forks then the beat frequency is
A) \[\frac{{{u}_{1}}}{{{u}_{2}}}\] done clear
B) \[{{u}_{1}}+{{u}_{2}}\] done clear
C) \[\frac{{{u}_{2}}}{{{u}_{1}}}\] done clear
D) \[{{u}_{1}}-{{u}_{2}}\] done clear
View Answer play_arrowquestion_answer30) A metallic rod of length R is rotated with an angular frequency co with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius R, about an axis passing through the centre and perpendicular to the plane of the ring. There is a magnetic field B, perpendicular to the plane of the ring. The emf induced between the centre and the metallic ring is
A) \[B\,\,\sin \,\,\omega t\] done clear
B) \[\frac{B{{R}^{2}}\omega }{2}\] done clear
C) \[2\,B{{R}^{2}}\omega \] done clear
D) \[B{{R}^{2}}\omega \] done clear
View Answer play_arrowquestion_answer31) The statement "Polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it" is known as
A) Faraday's law done clear
B) Gauss's law done clear
C) Coulomb's law done clear
D) Lenz's law done clear
View Answer play_arrowquestion_answer32) When the current changes form \[+2A\]to \[-3A\] in \[0.05,\]an emf of \[8\text{ }V\]is induced in a coil. The coefficient of self inductance of the coil is
A) \[0.2\text{ }H\] done clear
B) \[0.4\text{ }H\] done clear
C) \[0.8\text{ }H\] done clear
D) \[0.1\text{ }H\] done clear
View Answer play_arrowquestion_answer33) A car moving with a speed of \[50\text{ }km/h\]can be stopped by brakes, over a distance of \[6m\]. If the same car is moving at a speed of \[100\text{ }km/h,\] the stopping distance is
A) \[12\text{ }m\] done clear
B) \[18\text{ }m\] done clear
C) \[6\text{ }m\] done clear
D) \[24\text{ }m\] done clear
View Answer play_arrowquestion_answer34) The dimensions of impulse are
A) \[[ML{{T}^{-1}}]\] done clear
B) \[[M{{L}^{2}}{{T}^{-1}}]\] done clear
C) \[[M{{L}^{-1}}{{T}^{-1}}]\] done clear
D) \[[M{{T}^{-1}}]\] done clear
View Answer play_arrowquestion_answer35) Position-time graph for motion with zero acceleration is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer36) If the magnetic susceptibility of a material is large and positive. The material is
A) diamagnetic done clear
B) ferromagnetic done clear
C) paramagnetic done clear
D) perfect diamagnetic done clear
View Answer play_arrowquestion_answer37) A 100 turn closely wound circular coil of radius \[10\text{ }cm\]carries a current of \[3.2\text{ }A\]. The magnetic moment of the coil is, approximately
A) \[5\text{ }A{{m}^{2}}\] done clear
B) \[10\text{ }A{{m}^{2}}\] done clear
C) \[20\text{ }A{{m}^{2}}\] done clear
D) \[40\text{ }A{{m}^{2}}\] done clear
View Answer play_arrowquestion_answer38) The particle that cannot be accelerated by a cyclotron is
A) proton done clear
B) \[\alpha \]-particle done clear
C) electron done clear
D) deuteron nucleus done clear
View Answer play_arrowquestion_answer39) The material whose resistivity is insensitive to temperature is
A) silicon done clear
B) copper done clear
C) silver done clear
D) nichrome done clear
View Answer play_arrowquestion_answer40) The path of a charged particle in a uniform magnetic field, when the velocity and the magnetic field are perpendicular to each other is a
A) circle done clear
B) parabola done clear
C) helix done clear
D) straight line done clear
View Answer play_arrowquestion_answer41) A galvanometer can be converted into a voltmeter by connecting
A) low resistance in series done clear
B) high resistance in series done clear
C) low resistance in parallel done clear
D) high resistance in parallel done clear
View Answer play_arrowquestion_answer42) The angle which the total magnetic field of earth makes with the surface of the earth is called
A) declination done clear
B) magnetic meridian . done clear
C) geographic meridian done clear
D) inclination done clear
View Answer play_arrowquestion_answer43) A constant torque of \[3.14\text{ }Nm\] is exerted on a pivoted wheel. If the angular acceleration of the wheel is \[4\pi \text{ }rad/{{s}^{2}},\] then the moment of Inertia of the wheel is
A) \[0.25\text{ }kg-{{m}^{2}}\] done clear
B) \[2.5\text{ }kg-{{m}^{2}}\] done clear
C) \[4.5\text{ }kg-{{m}^{2}}\] done clear
D) \[25\text{ }kg-{{m}^{2}}\] done clear
View Answer play_arrowquestion_answer44) The temperature of the sink of a Carnot engine is \[{{27}^{o}}C\]and its efficiency is 25%. The temperature of the source is
A) \[{{227}^{o}}C\] done clear
B) \[{{27}^{o}}C\] done clear
C) \[{{327}^{o}}C\] done clear
D) \[{{127}^{o}}C\] done clear
View Answer play_arrowquestion_answer45) A thermodynamic process in which the system is insulated from the surroundings and no heat flows between the system and the surroundings is an
A) isothermal process done clear
B) adiabatic process done clear
C) isochoric process done clear
D) isobaric process done clear
View Answer play_arrowquestion_answer46) The moment of inertia of rod of mass M length I about an axis perpendicular to it through one end is
A) \[\frac{M{{l}^{2}}}{12}\] done clear
B) \[\frac{M{{l}^{2}}}{2}\] done clear
C) \[\frac{M{{l}^{2}}}{3}\] done clear
D) \[\frac{M{{l}^{2}}}{4}\] done clear
View Answer play_arrowquestion_answer47) In the diagram shown below, \[{{m}_{1}}\] and \[{{m}_{2}}\] are the masses of two particles and \[{{x}_{1}}\] and \[{{x}_{2}}\] are the respective distances from the origin O. The centre of mass of the system is
A) \[\frac{{{m}_{1}}{{x}_{2}}+{{m}_{2}}{{x}_{1}}}{{{m}_{1}}+{{m}_{2}}}\] done clear
B) \[\frac{{{m}_{1}}+{{x}_{2}}}{2}\] done clear
C) \[\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] done clear
D) \[\frac{{{m}_{1}}{{m}_{2}}+{{x}_{1}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] done clear
View Answer play_arrowquestion_answer48) Fractional increase in resistivity per unit increase in temperature is defined as
A) resistivity done clear
B) temperature coefficient of resistivity done clear
C) conductivity done clear
D) drift velocity done clear
View Answer play_arrowquestion_answer49) Magnitude of drift velocity per unit electric field is
A) current density done clear
B) current done clear
C) resistivity done clear
D) mobility done clear
View Answer play_arrowquestion_answer50) Four cells of identical emf E and internal resistance r are connected is series to a variable resistor. The following graph shows the variation of terminal voltage of the combination with current. The emf of each cell used is
A) \[1.4\,\,V\] done clear
B) \[5.6\,\,V\] done clear
C) \[2\,\,V\] done clear
D) \[1\,\,V\] done clear
View Answer play_arrowquestion_answer51) Kirchhoff?s 1st law for analysis of current at a junction in a circuit is based on
A) conservation of charge done clear
B) conservation of energy done clear
C) conservation of momentum done clear
D) Newton's 3rd law of motion done clear
View Answer play_arrowquestion_answer52) Water is used as a coolant in automobile radiators owing to its high
A) viscosity done clear
B) surface tension done clear
C) latent heat done clear
D) specific heat capacity done clear
View Answer play_arrowquestion_answer53) The SI unit of thermal conductivity is
A) \[Js{{m}^{-1}}{{K}^{-1}}\] done clear
B) \[{{W}^{-1}}{{m}^{-1}}{{K}^{-1}}\] done clear
C) \[W{{m}^{-1}}{{K}^{-1}}\] done clear
D) \[W{{m}^{-2}}{{K}^{-1}}\] done clear
View Answer play_arrowquestion_answer54) For a body immersed in a liquid, when the weight of the body is less than the up thrust then the body will
A) float partially immersed done clear
B) sink done clear
C) float fully immersed done clear
D) be of zero weight done clear
View Answer play_arrowquestion_answer55) If R is the radius of a soap bubble and S its surface tension, then the excess pressure inside is
A) \[\frac{2S}{R}\] done clear
B) \[\frac{3S}{R}\] done clear
C) \[\frac{4S}{R}\] done clear
D) \[\frac{S}{R}\] done clear
View Answer play_arrowquestion_answer56) An aeroplane of mass \[3\times {{10}^{4}}\,kg\] and total wing area of \[120\text{ }{{m}^{2}}\]is in a level flight at some height. The difference in pressure between the upper and lower surface of its wings in kpa is \[g=20m/{{s}^{2}}\])
A) \[2.5\] done clear
B) \[5\] done clear
C) \[10\] done clear
D) \[15\] done clear
View Answer play_arrowquestion_answer57) The rate of loss of heat of a body is directly proportional to the difference of temperature of the body and the surroundings. This statement is known as
A) Stefan's law done clear
B) Newton's law of cooling done clear
C) Wien's law done clear
D) Kirchhoff?s law done clear
View Answer play_arrowquestion_answer58) A parallel plate capacitor has two square plates with equal and opposite charges. The surface charge densities on the plates are \[+\sigma \] and \[-\sigma \] respectively. In the region between the plates the magnitude of the electric field is
A) \[\frac{\sigma }{2{{\varepsilon }_{0}}}\] done clear
B) \[\frac{\sigma }{{{\varepsilon }_{0}}}\] done clear
C) zero done clear
D) None of these done clear
View Answer play_arrowquestion_answer59) If the equivalent capacitance between P and Q of the combination of the capacitors shown in figure below is \[30\text{ }\mu \text{F}\], the capacitor C is
A) \[60\,\mu F\] done clear
B) \[30\,\mu F\] done clear
C) \[10\,\mu F\] done clear
D) \[5\,\mu F\] done clear
View Answer play_arrowquestion_answer60) A charge Q is placed at the origin. The electric potential due to this charge at a given point in space is V. The work done by an external force in bringing another charge q from infinity up to the point is
A) \[\frac{V}{q}\] done clear
B) \[Vq\] done clear
C) \[V+q\] done clear
D) \[V\] done clear
View Answer play_arrowquestion_answer61) A capacitor of capacitance \[{{C}_{1}}\] is charged to a potential V and then connected in parallel to an uncharged capacitor of capacitance \[{{C}_{2}}\].The final potential difference across each capacitor will be
A) \[\frac{{{C}_{1}}V}{{{C}_{1}}+{{C}_{2}}}\] done clear
B) \[\frac{{{C}_{2}}V}{{{C}_{1}}+{{C}_{2}}}\] done clear
C) \[1+\frac{{{C}_{2}}}{{{C}_{1}}}\] done clear
D) \[1-\frac{{{C}_{2}}}{{{C}_{1}}}\] done clear
View Answer play_arrowquestion_answer62) In the case of a sphere falling through a viscous medium, it attains terminal velocity when
A) viscous force plus buoyant force becomes equal to force of gravity done clear
B) viscous force is zero done clear
C) viscous force plus force of gravity becomes equal to buoyant force done clear
D) buoyant force become equal to force of gravity done clear
View Answer play_arrowquestion_answer63) A radio wave that travels in a straight line from the transmitting antenna to the receiving antenna is knows as
A) sky wave done clear
B) ground wave done clear
C) space wave done clear
D) ionosphere wave done clear
View Answer play_arrowquestion_answer64) The output y of the circuit shown is
A) \[y=A.B\] done clear
B) \[y=\overline{A}.\overline{B}\] done clear
C) \[y=\overline{A.B}\] done clear
D) \[y=A+B\] done clear
View Answer play_arrowquestion_answer65) The ratio of tensile stress to the longitudinal strain is defined as
A) Bulk modulus done clear
B) Young's modulus done clear
C) Shear modulus done clear
D) Compressibility done clear
View Answer play_arrowquestion_answer66) In the case of hollow metallic sphere, without any change inside the sphere, electric potential (V) changes with respect to distance (r) from the centre as
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer67) An electric charge of \[8.85\times {{10}^{-13}}C\] is placed at the centre of a sphere of radius \[1\text{ }m\]. The electric flux through the sphere is
A) \[0.2\,\,N{{C}^{-1}}\,{{m}^{2}}\] done clear
B) \[0.1\,\,N{{C}^{-1}}\,{{m}^{2}}\] done clear
C) \[0.3\,\,N{{C}^{-1}}\,{{m}^{2}}\] done clear
D) \[0.01\,\,N{{C}^{-1}}\,{{m}^{2}}\] done clear
View Answer play_arrowquestion_answer68) An electric dipole is placed in an uniform electric field with the dipole axis making an angle \[\theta \] with the direction of the electric field. The orientation of the dipole for stable equilibrium is
A) \[\frac{\pi }{6}\] done clear
B) \[\frac{\pi }{3}\] done clear
C) \[0\] done clear
D) \[\frac{\pi }{2}\] done clear
View Answer play_arrowquestion_answer69) The escape velocity of a body on the surface of earth is \[11.2\text{ }km/s\]. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become
A) \[5.6\,\,km/s\] done clear
B) \[11.2\,\,km/s\] done clear
C) \[44.8\,\,km/s\] done clear
D) \[22.4\,\,km/s\] done clear
View Answer play_arrowquestion_answer70) Consider earth to be a sphere of mass M and radius R. The acceleration due to gravity at a depth d below the earth's surface \[({{g}_{d}})\] is
A) \[{{g}_{d}}=g\left\{ 1-\frac{d}{R} \right\}\] done clear
B) \[{{g}_{d}}=g\left\{ 1-\frac{2d}{R} \right\}\] done clear
C) \[{{g}_{d}}=g\] done clear
D) \[{{g}_{d}}=g\left\{ 1+\frac{d}{R} \right\}\] done clear
View Answer play_arrowquestion_answer71) An orbiting satellite has
A) only kinetic energy done clear
B) only potential energy done clear
C) kinetic and potential energies done clear
D) zero energy done clear
View Answer play_arrowquestion_answer72) \[x(t)=A\,\,\cos (\omega t+\phi )\]is the equation of simple harmonic motion. In this equation \[\phi \]is called
A) phase constant done clear
B) frequency done clear
C) amplitude done clear
D) displacement done clear
View Answer play_arrowquestion_answer73) The transfer characteristics of a base biased transistor has the operation regions, namely, cut-off, active region and saturation region. For using the transistor as an amplifier it has to operate in the
A) active region done clear
B) cut-off region done clear
C) sturation region done clear
D) cut-off and saturation done clear
View Answer play_arrowquestion_answer74) In which, of the following figures, the p-n diode is forward biased?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer75) The pn-junction which generates an emf when solar radiation falls on it, with no external bias applied, is a
A) light emitting diode done clear
B) Photodiode done clear
C) solar cell done clear
D) zener diode done clear
View Answer play_arrowquestion_answer76) In which of the following compounds, carbon exhibits a valency of 4 but oxidation state -2?
A) \[C{{H}_{3}}Cl\] done clear
B) \[CHC{{l}_{3}}\] done clear
C) \[C{{H}_{2}}C{{l}_{2}}\] done clear
D) \[HCHO\] done clear
View Answer play_arrowquestion_answer77) Which one of the following is correct?
A) Equivalent conductance decreases with dilution done clear
B) Specific conductance increases with dilution done clear
C) Specific conductance decreases with dilution done clear
D) Equivalent conductance increases with increasing concentration done clear
View Answer play_arrowquestion_answer78) A cell is constituted by coupling the two electrodes \[\text{Sn/S}{{\text{n}}^{\text{2+}}}\]and \[Cu/C{{u}^{2+}}.\] If \[{{E}^{o}}(S{{n}^{2+}},Sn),{{E}^{o}}(C{{u}^{2+}},Cu)\]and \[{{E}^{o}}\](cell) are \[-0.14\,V,0.34\,V\]and 0.48 V respectively, the correct representation of the cell is
A) \[Sn(s)|S{{n}^{2+}}(0.1\,M)||C{{u}^{2+}}(1.0\,M)|Cu(s)\] done clear
B) \[Sn(s)|S{{n}^{2+}}(1.0\,M)||C{{u}^{+}}(1.0\,M)|Cu(s)\] done clear
C) \[Sn(s)|S{{n}^{2+}}(1.0\,M)||C{{u}^{2+}}(1.0\,M)|Cu(s)\] done clear
D) \[Cu(s)|C{{u}^{2+}}(1.0\,M)||S{{n}^{2+}}(1.0\,M)|Sn(s)\] done clear
View Answer play_arrowquestion_answer79) Chemically unreactive three different gases A, B and C of molecular masses 16, 32 and 64 are enclosed in a vessel at constant temperature till equilibrium is reached. Which of the following statements is true?
A) Gas A will be at the top of the vessel done clear
B) Gas C will be at the top of the vessel done clear
C) Gas C will be at the bottom of the vessel done clear
D) Gases will form homogeneous mixture done clear
View Answer play_arrowquestion_answer80) Among the following which one is a linear molecule having zero dipole moment?
A) \[{{H}_{2}}O\] done clear
B) \[HCl\] done clear
C) \[C{{O}_{2}}\] done clear
D) \[{{H}_{2}}S\] done clear
View Answer play_arrowquestion_answer81) The bond order of\[{{\text{C}}_{\text{2}}}\]molecule is
A) 1 done clear
B) 2 done clear
C) 0 done clear
D) 3 done clear
View Answer play_arrowquestion_answer82) Among the following, the compound that is readily soluble in water is
A) \[BeS{{O}_{4}}\] done clear
B) \[CaS{{O}_{4}}\] done clear
C) \[SrS{{O}_{4}}\] done clear
D) \[BaS{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer83) The oxyacid of sulphur that contains a lone pair of electrons on sulphur is
A) sulphurous acid done clear
B) sulphuric acid done clear
C) peroxodisulphuric acid done clear
D) pyrosulphuric acid done clear
View Answer play_arrowquestion_answer84) The hybridization involved in\[\text{PC}{{\text{l}}_{\text{5}}}\] is
A) \[s{{p}^{3}}d\] done clear
B) \[s{{p}^{3}}{{d}^{2}}\] done clear
C) \[{{d}^{2}}s{{p}^{2}}\] done clear
D) \[s{{p}^{3}}\] done clear
View Answer play_arrowquestion_answer85) In which of the following molecules the central atom has two lone pairs of electrons?
A) \[S{{F}_{4}}\] done clear
B) \[Br{{F}_{5}}\] done clear
C) \[S{{O}_{2}}\] done clear
D) \[Xe{{F}_{4}}\] done clear
View Answer play_arrowquestion_answer86) The correct order of reducing character of alkali metals is
A) \[Rb<K<Na<Li\] done clear
B) \[Li<Na<K<Rb\] done clear
C) \[Na<K<Rb<Li\] done clear
D) \[Rb<Na<K<Li\] done clear
View Answer play_arrowquestion_answer87) The paramagnetic oxides of nitrogen are
A) dinitrogen monoxide and nitrogen monoxide done clear
B) nitrogen monoxide and nitrogen dioxide done clear
C) nitrogen dioxide and dinitrogen trioxide done clear
D) dinitrogen trioxide and dinitrogen tetroxide done clear
View Answer play_arrowquestion_answer88) Pick out the wrong statement
A) The standard free energy of formation of elements is zero done clear
B) A process that leads to increase in free energy will be spontaneous done clear
C) A process accompanied by decrease in entropy will be non-spontaneous under normal conditions. done clear
D) Enthalpy of combustion is always negative done clear
View Answer play_arrowquestion_answer89) The standard enthalpy of formation of \[{{C}_{2}}{{H}_{4}}(g),C{{O}_{2}}(g)\] and\[{{H}_{2}}O(l)\]are\[~52,-394\] and \[-284\,kJ\,mo{{l}^{-1}}\]respectively. Then the amount of heat evolved by burning 7 g of \[{{C}_{2}}{{H}_{4}}(g)\]is
A) 1412 kJ done clear
B) 9884 kJ done clear
C) 353 kJ done clear
D) 706 kJ done clear
View Answer play_arrowquestion_answer90) Which one among the following pairs does not represent, example for intensive property?
A) temperature and density done clear
B) pressure and molar volume done clear
C) molar heat capacity and density done clear
D) heat capacity and enthalpy done clear
View Answer play_arrowquestion_answer91) The values of \[\Delta H\]and \[\Delta S\]for a reaction are \[30\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\]and-\[100\,J{{K}^{-1}}\,mo{{l}^{-1}}\] respectively. Then the temperature above which the reaction will become spontaneous is
A) 300 K done clear
B) 30 K done clear
C) 100 K done clear
D) \[~300{{\,}^{o}}C\] done clear
View Answer play_arrowquestion_answer92) Three Faradays of electricity are passed through molten\[\text{A}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}\text{,}\]aqueous solution of \[\text{CuS}{{\text{O}}_{\text{4}}}\]and molten NaCI taken in three different electrolytic cells. Then the mole ratio of Al, Cu and Na deposited on the cathode will be
A) 3:4:6 done clear
B) 2:1:6 done clear
C) 3: 2: 1 done clear
D) 2: 3 : 6 done clear
View Answer play_arrowquestion_answer93) Which of the esters shown, after reduction with \[\text{LiAl}{{\text{H}}_{\text{4}}}\]and aqueous workup, will yield two molecules of only a single alcohol?
A) \[{{C}_{6}}{{H}_{5}}COO{{C}_{6}}{{H}_{5}}\] done clear
B) \[C{{H}_{3}}C{{H}_{2}}COOC{{H}_{2}}C{{H}_{3}}\] done clear
C) \[{{C}_{6}}{{H}_{5}}COOC{{H}_{2}}{{C}_{6}}{{H}_{5}}\] done clear
D) \[C{{H}_{3}}COOC{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer94) Ethyl methyl ketone on treatment with a solution of sodium hypochlorite gives chloroform and
A) sodium ethanoate done clear
B) sodium propanoate done clear
C) sodium methanoate done clear
D) sodium ethoxide done clear
View Answer play_arrowquestion_answer95) What are the products of the following reaction \[{{C}_{6}}{{H}_{5}}OC{{H}_{2}}C{{H}_{2}}OH\xrightarrow[\text{Hear}]{\text{excess}\,\text{HBr}}\]
A) \[{{C}_{6}}{{H}_{5}}OH+BrC{{H}_{2}}C{{H}_{2}}Br\] done clear
B) \[{{C}_{6}}{{H}_{5}}OH+HOC{{H}_{2}}C{{H}_{2}}OH\] done clear
C) \[{{C}_{6}}{{H}_{5}}Br+HOC{{H}_{2}}C{{H}_{2}}OH\] done clear
D) \[{{C}_{6}}{{H}_{5}}OH+BrC{{H}_{2}}C{{H}_{2}}OH\] done clear
View Answer play_arrowquestion_answer96) The compound that gives both iodoform and Fehling's tests is
A) ethanol done clear
B) propanone done clear
C) 2-butanol done clear
D) ethanol done clear
View Answer play_arrowquestion_answer97) The equilibrium constant value\[{{K}_{p}}\]for the equilibrium \[{{H}_{2}}(g)+{{I}_{2}}(g)\rightleftharpoons 2HI(g)\] changes with
A) total pressure done clear
B) temperature done clear
C) catalyst done clear
D) the amounts of \[{{\text{H}}_{\text{2}}}\]and\[{{\text{I}}_{\text{2}}}\]present done clear
View Answer play_arrowquestion_answer98) Among the following, the one which can act as both Bronsted acid as well as Bronsted base is
A) \[{{H}_{3}}P{{O}_{4}}\] done clear
B) \[AlC{{l}_{3}}\] done clear
C) \[C{{H}_{3}}CO{{O}^{-}}\] done clear
D) \[{{H}_{2}}O\] done clear
View Answer play_arrowquestion_answer99) The reaction \[A+B\to C+D+40\,kJ\]has an .activation energy of 18 kJ. Then the activation energy for the reaction\[C+D\to A+B\] is
A) 58 kJ done clear
B) \[~-\text{ }40\text{ }kJ\] done clear
C) \[~-\text{ }18\text{ }kJ\] done clear
D) \[~22\text{ }kJ\] done clear
View Answer play_arrowquestion_answer100) One gram atom of a radioactive isotope \[({{t}_{1/2}}=10\,h)\]that emits alpha particle was placed in a sealed container. The time taken for 0.875 g atom of helium to accumulate in the container is
A) 10 h done clear
B) 20 h done clear
C) 30 h done clear
D) 40 h done clear
View Answer play_arrowquestion_answer101) In which one of the following reactions, the yield of the products decreases by increasing the pressure?
A) \[2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g)\] done clear
B) \[{{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)\] done clear
C) \[PC{{l}_{5}}(g)PC{{l}_{3}}(g)+C{{l}_{2}}(g)\] done clear
D) \[{{N}_{2}}(g)+{{O}_{2}}(g)2NO(g)\] done clear
View Answer play_arrowquestion_answer102) The pH of the solution formed by mixing 20 mL of \[\text{0}\text{.05 M }{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]with 5.0 mL of \[\text{0}\text{.45 M NaOH}\]at 298 K is
A) 6 done clear
B) 2 done clear
C) 12 done clear
D) 7 done clear
View Answer play_arrowquestion_answer103) Zeise's salt is
A) \[[Fe{{({{C}_{5}}{{H}_{5}})}_{2}}]\] done clear
B) \[[Pb{{({{C}_{2}}{{H}_{5}})}_{4}}]\] done clear
C) \[K[PtC{{l}_{3}}({{C}_{2}}{{H}_{4}})]\] done clear
D) \[[Ni{{(CO)}_{4}}]\] done clear
View Answer play_arrowquestion_answer104) The metal used to recover copper from a solution of copper sulphate is
A) Na done clear
B) Fe done clear
C) Hg done clear
D) Ag done clear
View Answer play_arrowquestion_answer105) Which of the following is a correct name according to IUPAC rules?
A) 2, 3-diethylhexane done clear
B) 3-ethyl-2-methylpentane done clear
C) 3, 4-dimethylpentane done clear
D) 2-ethyl-2-methylpentane done clear
View Answer play_arrowquestion_answer106) The formula of siderite is
A) \[F{{e}_{2}}{{O}_{3}}\] done clear
B) \[F{{e}_{3}}{{O}_{4}}\] done clear
C) \[Fe{{S}_{2}}\] done clear
D) \[FeC{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer107) When 'blue vitriol? is heated at 373 K, the product formed is
A) \[CuS{{O}_{4}}.3{{H}_{2}}O\] done clear
B) \[CuO+S{{O}_{3}}\] done clear
C) \[CuS{{O}_{4}}.{{H}_{2}}O\] done clear
D) \[CuS{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer108) An alkane with a molecular formula \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{14}}}\]reacts with chlorine in the presence of light and heat to give two constitutionally isomeric monochlorides of molecular formula \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{13}}}\text{Cl}\text{.}\]What is the most reasonable starting alkane?
A) \[n-\]hexane done clear
B) 2, 2-dimethylbutane done clear
C) 2, 3-dimethylbutane done clear
D) 3-methylpentane done clear
View Answer play_arrowquestion_answer109) Which of the following statements are correct with respect to the effect of trifluoromethyl group\[(-C{{F}_{3}}),\]on an electrophilic aromatic substitution?
A) The \[\text{C}{{\text{F}}_{\text{3}}}\]group will deactivate the ring done clear
B) The\[\text{C}{{\text{F}}_{\text{3}}}\] group will activate the ring done clear
C) The \[\text{C}{{\text{F}}_{\text{3}}}\]group will be ortho, para director done clear
D) The \[\text{C}{{\text{F}}_{\text{3}}}\]group will be a meta director done clear
View Answer play_arrowquestion_answer110) Which of the following compound is chiral?
A) 3-pentanol done clear
B) 1-pentanol done clear
C) 3-methyl-l-butanol done clear
D) 3-methyl-2-butanol done clear
View Answer play_arrowquestion_answer111) Which one among the following is most reactive towards electrophilic substitution reaction?
A) Aniline done clear
B) Nitrobenzene done clear
C) Benzoicacid done clear
D) Acetanilide done clear
View Answer play_arrowquestion_answer112) Which one of the following is not aromatic?
A) Cyclopentadienyl anion done clear
B) Cycloheptatrienyl cation done clear
C) Cyclooctatetraene done clear
D) Thiophene done clear
View Answer play_arrowquestion_answer113) The separation of racemic mixture into the pure enantiomers is termed as
A) racemiscition done clear
B) resolution done clear
C) equilibration done clear
D) isomerization done clear
View Answer play_arrowquestion_answer114) In a reaction \[2A+B\to {{A}_{2}}B,\]the reactant B will disappear at
A) half the rate as A will decrease done clear
B) the same rate as A will decrease done clear
C) twice the rate as A will decrease done clear
D) half the rate as \[{{A}_{2}}B\]will form done clear
View Answer play_arrowquestion_answer115) Which one of the following liquid pairs will exhibit a positive deviation from Raoult?s law?
A) \[n-\]hexane and n-heptane done clear
B) ethanol and chloroform done clear
C) phenol and aniline done clear
D) chloroform and acetone done clear
View Answer play_arrowquestion_answer116) The van't Hoff factor ?i? for a dilute aqueous solution of sucrose is
A) zero done clear
B) 1.0 done clear
C) 1.5 done clear
D) 2.0 done clear
View Answer play_arrowquestion_answer117) The unit of rate constant for a zero order reaction is
A) \[{{s}^{-1}}\] done clear
B) \[\text{mol}\,\text{L}{{\text{s}}^{-1}}\] done clear
C) \[mol\,{{L}^{-1}}{{s}^{-1}}\] done clear
D) no unit done clear
View Answer play_arrowquestion_answer118) When a solution containing non-volatile solute is diluted with water
A) its osmotic pressure increases done clear
B) its boiling point increases done clear
C) its freezing point decreases done clear
D) its vapour pressure increases done clear
View Answer play_arrowquestion_answer119) What happens when blood cells are placed in pure water?
A) The fluid in blood cells rapidly moves into water done clear
B) The water molecules rapidly move into blood cells done clear
C) The blood cells dissolve in water done clear
D) No change takes place done clear
View Answer play_arrowquestion_answer120) Mendius reaction converts an alkyi cyanide to
A) a primary amine done clear
B) an aldehyde done clear
C) a ketone done clear
D) an oxime done clear
View Answer play_arrowquestion_answer121) Which one of the following amines cannot be prepared by Gabriel's synthesis?
A) Butylamine done clear
B) Isobutylamine done clear
C) 2-phenylethylamine done clear
D) N-methylbenzylamine done clear
View Answer play_arrowquestion_answer122) Which one of the following is not an aldose?
A) Glucose done clear
B) Ribose done clear
C) Fructose done clear
D) Mannose done clear
View Answer play_arrowquestion_answer123) Which one of the following is a secondary amine?
A) 2-butanamine done clear
B) N-methylpiperidine done clear
C) N-methyl-2-pentanamine done clear
D) p-anisidine done clear
View Answer play_arrowquestion_answer124) The weakest base among the following is
A) dimethylamine done clear
B) aniline done clear
C) methylamine done clear
D) ethylamine done clear
View Answer play_arrowquestion_answer125) Which one of the following is not a green house gas?
A) Methane done clear
B) Ozone done clear
C) Carbon dioxide done clear
D) Nitrogen done clear
View Answer play_arrowquestion_answer126) The lanthanide element that has the electronic configuration, \[[Xe]4{{f}^{7}}5{{d}^{1}}6{{s}^{2}}\]is
A) lutetium done clear
B) terbium done clear
C) ytterbium done clear
D) gadolinium done clear
View Answer play_arrowquestion_answer127) The transition metal ion that has 'spin-only magnetic moment value of 5.96 is
A) \[M{{n}^{2+}}\] done clear
B) \[F{{e}^{2+}}\] done clear
C) \[{{V}^{2+}}\] done clear
D) \[C{{u}^{2+}}\] done clear
View Answer play_arrowquestion_answer128) Square planar complexes of the type MABXL (where A, B, X and L are unidentates) show
A) two \[cis\]and one trans isomer done clear
B) two trans and one \[cis\] isomer done clear
C) two \[cis\]and two trans isomer done clear
D) one \[cis\]and one trans isomer done clear
View Answer play_arrowquestion_answer129) The alloy of copper that contains zinc is
A) monel metal done clear
B) bronze done clear
C) bell metal done clear
D) brass done clear
View Answer play_arrowquestion_answer130) All \[\text{Cu (II)}\]halides are known except the iodide. The reason for is that
A) iodide is a bulky ion done clear
B) \[\text{C}{{\text{u}}^{\text{2+}}}\]oxidizes iodide to iodine done clear
C) \[\text{C}{{\text{u}}^{\text{2+}}}\] (aq) has much more negative hydration enthalpy done clear
D) \[\text{C}{{\text{u}}^{\text{2+}}}\]ion has smaller size done clear
View Answer play_arrowquestion_answer131) Among the following the ambidentate ligand is
A) \[{{H}_{2}}NC{{H}_{2}}C{{H}_{2}}N{{H}_{2}}\] done clear
B) \[CO_{3}^{2-}\] done clear
C) \[NO_{2}^{-}\] done clear
D) \[{{C}_{2}}O_{4}^{2-}\] done clear
View Answer play_arrowquestion_answer132) Among the following, which one is paramagnetic and has tetrahedral geometry?
A) \[{{[Ni{{(CN)}_{4}}]}^{2-}}\] done clear
B) \[{{[NiC{{l}_{4}}]}^{2-}}\] done clear
C) \[[Ni{{(CO)}_{4}}]\] done clear
D) \[{{[CoC{{l}_{2}}{{(en)}_{2}}]}^{+}}\] done clear
View Answer play_arrowquestion_answer133) The de-Broglie wavelength of a ball of mass 10 g moving with a velocity of \[10\,\text{m}{{\text{s}}^{-1}}\]is \[[h=6.626\times {{10}^{-34}}Js]\]
A) \[6.626\times {{10}^{-33}}\,m\] done clear
B) \[6.626\times {{10}^{-29}}\,m\] done clear
C) \[6.626\times {{10}^{-31}}\,m\] done clear
D) \[6.626\times {{10}^{-36}}\,m\] done clear
View Answer play_arrowquestion_answer134) The electrons identified by quantum numbers n and I, (i) \[n=4,l=1,\](ii)\[~n=4,l=0\] (iii) \[n=3,l=2\]and (iv) \[n=3,l=1\]can be placed in order of increasing energy as
A) (i) < (ii) < (iii) < (iv) done clear
B) (iv) < (iii) < (ii) < (i) done clear
C) (iv) < (ii) < (iii) < (i) done clear
D) (iv) < (i) < (ii) < (iii) done clear
View Answer play_arrowquestion_answer135) A radioactive element\[_{\text{92}}^{\text{238}}\text{M}\]emits one alpha particle followed by two beta particles. Then the daughter element formed is
A) an isotope done clear
B) an isobar done clear
C) an isotone done clear
D) an isodiaphere done clear
View Answer play_arrowquestion_answer136) When 6.3 g of sodium bicarbonate are added to 30.0 g of acetic acid solution, the residual solution is found to weigh 33.0 g. The mass of carbon dioxide released in the reaction is
A) 3.0 g done clear
B) 0.91 g done clear
C) 1.91 g done clear
D) 3.3 g done clear
View Answer play_arrowquestion_answer137) Two oxides of a metal contain 36.4% and 53.4% of oxygen by mass respectively. If the formula of the first oxide is \[{{\text{M}}_{\text{2}}}\text{O,}\]then that of the second is
A) \[{{M}_{2}}{{O}_{3}}\] done clear
B) \[MO\] done clear
C) \[M{{O}_{2}}\] done clear
D) \[{{M}_{2}}{{O}_{5}}\] done clear
View Answer play_arrowquestion_answer138) In a volumetric experiment, it was found that a solution of\[\text{KMn}{{\text{O}}_{\text{4}}}\]is reduced to\[\text{MnS}{{\text{O}}_{\text{4}}}\text{.}\]If the normality of the solution is 1.0 N, then the molarity of the solution will be
A) 0.5 M done clear
B) 0.2 M done clear
C) 1.0 M done clear
D) 0.4 M done clear
View Answer play_arrowquestion_answer139) Which of the following pair of gases will diffuse at the same rate through a porous plug?
A) \[CO,N{{O}_{2}}\] done clear
B) \[NO,{{C}_{2}}{{H}_{6}}\] done clear
C) \[N{{O}_{2}},C{{O}_{2}}\] done clear
D) \[N{{H}_{3}},P{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer140) Freundlich adsorption isotherm equation is
A) \[\log \frac{m}{x}=\log K+\frac{1}{m}\log p\] done clear
B) \[\log \frac{x}{m}=\log K+n\log p\] done clear
C) \[\log \frac{m}{x}=\log K+n\log p\] done clear
D) \[\log \frac{x}{m}=\log K+\frac{1}{n}\log p\] done clear
View Answer play_arrowquestion_answer141) Which one of the following is a copolymer formed by condensation polymerization?
A) Terylene done clear
B) Buna-S done clear
C) Buna-N done clear
D) Neoprene done clear
View Answer play_arrowquestion_answer142) Which of the following is the largest is size?
A) \[C{{l}^{-}}\] done clear
B) \[{{S}^{2-}}\] done clear
C) \[N{{a}^{+}}\] done clear
D) \[{{F}^{-}}\] done clear
View Answer play_arrowquestion_answer143) In zinc blende structure, the coordination number of the cation is
A) 4 done clear
B) 6 done clear
C) 8 done clear
D) 12 done clear
View Answer play_arrowquestion_answer144) The best coagulant for the precipitation of \[\text{Fe(OH}{{\text{)}}_{\text{3}}}\]is
A) \[N{{a}_{2}}HP{{O}_{3}}\] done clear
B) \[NaN{{O}_{3}}\] done clear
C) \[N{{a}_{3}}P{{O}_{4}}\] done clear
D) \[N{{a}_{2}}S{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer145) The second ionization energies of Li, Be, B and C are in the order
A) \[Li>C>B>Be\] done clear
B) \[Li>B>C>Be\] done clear
C) \[B>C>Be>Li\] done clear
D) \[Be>C>B>Li\] done clear
View Answer play_arrowquestion_answer146) Chloroform on heating with silver powder gives
A) ethene done clear
B) ethyne done clear
C) methane done clear
D) ehane done clear
View Answer play_arrowquestion_answer147) The decreasing order of acidity among the compounds, ethanol (I) 2, 2, 2-trifluoroethanol (II), trifiuroacetic acid (III) and acetic acid (IV) is
A) \[III>II>IV>I\] done clear
B) \[IV>III>II>I\] done clear
C) \[~I>II>III>IV\] done clear
D) \[III>IV>II>I\] done clear
View Answer play_arrowquestion_answer148) Which of the following is most acidic?
A) Methane done clear
B) Ethane done clear
C) Ethyne done clear
D) Ethene done clear
View Answer play_arrowquestion_answer149) 1-chlorobutane on reaction with alcoholic potash gives
A) 1-butanol done clear
B) 2-butene done clear
C) 1-butene done clear
D) 2-butanol done clear
View Answer play_arrowquestion_answer150) Phenol on heating with alcoholic KOH and chloroform -undergoes
A) Reimer-Tiemann reaction done clear
B) Kolbe reaction done clear
C) Gattermann reaction done clear
D) Cannizzaro reaction done clear
View Answer play_arrowquestion_answer151) The ratio in which ZX-plane divides the line segment AB joining the points \[A(4,2,3)\] and \[B(-2,4,5)\] is equal to
A) \[1:2\] internally done clear
B) \[1:2\] externally done clear
C) \[-1:2\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer152) The projection of a line segment OP through origin O, on the coordinate axes are 8, 5, 6. Then, the length of the line segment OP is equal to
A) \[5\] done clear
B) \[5\sqrt{5}\] done clear
C) \[10\sqrt{5}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer153) The length of the perpendicular distance of the point \[(-1,\,4,\,0)\] from the line \[\frac{x}{1}=\frac{y}{3}=\frac{z}{1}\] is equal to
A) \[\sqrt{6}\] done clear
B) \[\sqrt{5}\] done clear
C) \[2\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer154) The number of lines making equal angles with the coordinate axes in three dimensional geometry is equal to
A) 3 done clear
B) 4 done clear
C) 2 done clear
D) None of these done clear
View Answer play_arrowquestion_answer155) Suppose \[P(2,\,y,\,z)\] lies on the line through \[A(3,-1,4)\] and \[B(-4,2,1)\]. Then, the value of z is equal to
A) \[\frac{-1}{2}\] done clear
B) \[\frac{19}{4}\] done clear
C) \[\frac{-19}{4}\] done clear
D) \[\frac{25}{7}\] done clear
View Answer play_arrowquestion_answer156) The equation of the plane perpendicular to the Z-axis and passing through \[(2,-3,5)\] is
A) \[x-2=0\] done clear
B) \[y+3=0\] done clear
C) \[z-5=0\] done clear
D) \[2x-3y+5z+4=0\] done clear
View Answer play_arrowquestion_answer157) The value of \[\sum\limits_{n=0}^{\infty }{\frac{{{n}^{2}}+4}{n\,!}}\]is equal to
A) \[6\,e\] done clear
B) \[5\,e\] done clear
C) \[4\,e\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer158) The three distinct points \[A(at_{1}^{2},\,2a{{t}_{1}}),\,\,B(at_{2}^{2},\,\,2a{{t}_{2}})\]and \[C(0,\,a)\](where a is a real number) are collinear, if
A) \[{{t}_{1}}{{t}_{2}}=-1\] done clear
B) \[{{t}_{1}}{{t}_{2}}=1\] done clear
C) \[2{{t}_{1}}{{t}_{2}}={{t}_{1}}+{{t}_{2}}\] done clear
D) \[{{t}_{1}}+{{t}_{2}}=a\] done clear
View Answer play_arrowquestion_answer159) The equation of the line passing through \[(0,0)\]and intersection of \[3x-4y=2\]and \[x+2y=-4\]is
A) \[7x=6y\] done clear
B) \[6x=7y\] done clear
C) \[5x=8y\] done clear
D) \[x=0\] done clear
View Answer play_arrowquestion_answer160) The value of k for which the equation \[{{x}^{2}}-4xy-{{y}^{2}}+6x+2y+k=0\] represents a pair of straight lines is
A) \[k=4\] done clear
B) \[k=-1\] done clear
C) \[k=\frac{-4}{5}\] done clear
D) \[k=\frac{-22}{5}\] done clear
View Answer play_arrowquestion_answer161) If the values observed are \[1,\text{ }2,\text{ }3,\text{ }...,\text{ }n\]each with frequency 1 and n is even, then the mean deviation from mean equals to
A) \[n\] done clear
B) \[\frac{n}{2}\] done clear
C) \[\frac{n}{4}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer162) A line segment of 8 units in length moves so that its end points are always on the coordinate axes. Then, the equation of locus of its mid-point is
A) \[{{x}^{2}}+{{y}^{2}}=4\] done clear
B) \[{{x}^{2}}+{{y}^{2}}=16\] done clear
C) \[{{x}^{2}}+{{y}^{2}}=8\] done clear
D) \[|x|+|y|=8\] done clear
View Answer play_arrowquestion_answer163) The number of straight lines which can be drawn through the point \[(-2,\,\,\,2)\] so that its distance from \[(-3,\,\,1)\] will be equal 6 units is
A) one done clear
B) two done clear
C) infinite done clear
D) zero done clear
View Answer play_arrowquestion_answer164) The maximum and minimum magnitude of resultants of two forces are \[{{P}_{1}}\] and \[{{P}_{2}}\]respectively. The magnitude of the resultant when two forces are at right angles is equal to
A) \[2\sqrt{{{P}_{1}}{{P}_{2}}}\] done clear
B) \[\sqrt{P_{1}^{2}\,+P_{2}^{2}}\] done clear
C) \[\frac{\sqrt{P_{1}^{2}\,+P_{2}^{2}}}{2}\] done clear
D) \[\sqrt{\frac{P_{1}^{2}\,+P_{2}^{2}}{2}}\] done clear
View Answer play_arrowquestion_answer165) The distance travelled by a bus in t seconds after the brakes are applied is \[1+2t-2{{t}^{2}}m.\] The distance travelled by the bus before it stops is equal to
A) \[0.5\text{ }m\] done clear
B) \[1\,\,m\] done clear
C) \[1.5\,\,m\] done clear
D) \[2.5\,\,m\] done clear
View Answer play_arrowquestion_answer166) Two balls are projected from the same point in directions inclined at \[{{45}^{o}}\] and \[{{60}^{o}}\] to the horizontal respectively. If they attain the same height, the ratio of their velocities of projection is equal to
A) \[\sqrt{3}:1\] done clear
B) \[3:1\] done clear
C) \[3:2\] done clear
D) \[3:2\] done clear
View Answer play_arrowquestion_answer167) A force 2 unite acts along the line \[x-4=y-5.\] The moment of the force about the point \[(1,\,\,1)\] along Z-axis is equal to
A) \[0\] done clear
B) \[\frac{1}{\sqrt{2}}\] done clear
C) \[\sqrt{2}\] done clear
D) \[2\sqrt{2}\] done clear
View Answer play_arrowquestion_answer168) A particle is thrown vertically upwards with velocity \[24.5\text{ }cm/min\]. It will return to the original position after
A) \[1\,s\] done clear
B) \[3\,\,s\] done clear
C) \[1.5\,\,s\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer169) The area of the triangle whose vertices are the points \[(a(a+1),\,a+1),\,\,((a+1)\,(a+2),\]\[a+2)\] and \[((a+2)\,(a+3),\,(a+3)\]is equal to
A) \[-1\] done clear
B) \[1\] done clear
C) \[1/2\] done clear
D) \[a(a+1)\,(a+2)\,(a+3)\] done clear
View Answer play_arrowquestion_answer170) If A is a \[2\times 2\] matrix and \[|A|=2,\] then the matrix represented by A (adj A) is equal to
A) \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} 2 & 0 \\ 0 & 2 \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} 1/2 & 0 \\ 0 & 1/2 \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} 0 & 2 \\ 2 & 0 \\ \end{matrix} \right]\] done clear
View Answer play_arrowquestion_answer171) . Let a and b be the position vector of A and B respectively. The position vector of a point C on AB produced, such that \[AC=4\text{ }AB\]is equal to
A) \[\frac{4b-a}{3}\] done clear
B) \[4b-3a\] done clear
C) \[4a-3b\] done clear
D) \[\frac{4a-b}{3}\] done clear
View Answer play_arrowquestion_answer172) The matrix product satisfies \[[5\,\,\,\,6\,\,\,\,\,2].\,\,{{A}^{T}}=[4\,\,8\,\,\,1\,\,\,7\,\,\,8],\] where \[{{A}^{T}}\]denotes the transpose of the matrix A. Then, the order of the matrix A equals to
A) \[1\times 2\] done clear
B) \[5\times 1\] done clear
C) \[3\times 5\] done clear
D) \[5\times 3\] done clear
View Answer play_arrowquestion_answer173) Let A and B both be \[3\times 3\] matrices. Then, \[{{(AB)}^{T}}=BA,\]if
A) A is skew-symmetric and B is symmetric done clear
B) B is skew-symmetric and A is symmetric done clear
C) A and B are skew-symmetric done clear
D) None of the above done clear
View Answer play_arrowquestion_answer174) Let \[A=\{1,\,2\},\] \[B=\{\{1\},\,\,\,\{2\}\},\] \[C=\{\{1\}\,\,\{1,\,\,2\}\}.\] Then, which of the following relation is true?
A) \[A=B\] done clear
B) \[B\subseteq C\] done clear
C) \[A\in C\] done clear
D) \[A\subset C\] done clear
View Answer play_arrowquestion_answer175) If \[f(x)=3-x,-4\le x\le 4,\]then the domain of \[{{\log }_{e}}\,(f\,(x))\] is
A) \[[-4,\,\,4]\] done clear
B) \[(-\,\infty ,\,\,3]\] done clear
C) \[(-\,\infty ,\,\,3)\] done clear
D) \[[-4,\,\,\,3)\] done clear
View Answer play_arrowquestion_answer176) If \[\omega \] denotes the imaginary cube roots of unity. Then, the roots of the equation \[{{(x+1)}^{3}}+8=0\] are
A) \[-3,\,1+2\omega ,\,1+2{{\omega }^{2}}\] done clear
B) \[-3,\,1-2\,\omega ,\,1-2{{\omega }^{2}}\] done clear
C) \[-3,-1+2\omega ,-1+2{{\omega }^{2}}\] done clear
D) \[-3,-1-2\omega ,-1-2{{\omega }^{2}}\] done clear
View Answer play_arrowquestion_answer177) The function \[f:[0,\,\,\infty )\to [0,\,\,\infty )\] defined by \[f\,(x)=\frac{2x}{1+2x}\]is
A) one-one and onto done clear
B) one-one but not onto done clear
C) not one-one but onto done clear
D) neither one-one nor onto done clear
View Answer play_arrowquestion_answer178) If \[{{z}_{r}}=\cos \,\left( \frac{\pi }{{{3}^{r}}} \right)+i\,\,\sin \left( \frac{\pi }{{{3}^{r}}} \right),\]then \[{{z}_{1}}.{{z}_{2}}.{{z}_{3}}....\] to \[\infty \] is equal to
A) \[-1\] done clear
B) \[0\] done clear
C) \[-\,\,i\] done clear
D) \[i\] done clear
View Answer play_arrowquestion_answer179) If \[\sin \,\,\theta \]and \[\cos \,\,\theta \] are the roots of the equation \[a{{x}^{2}}+bx+c=0,\,\,\,\,\,a\ne 0,\] then the relation between the coefficients of the equation is
A) \[{{a}^{2}}-{{b}^{2}}+2ac=0\] done clear
B) \[{{a}^{2}}+{{b}^{2}}+2ac=0\] done clear
C) \[\,{{a}^{2}}-{{b}^{2}}-2ac=0\] done clear
D) \[{{a}^{2}}+{{b}^{2}}-2ac=0\] done clear
View Answer play_arrowquestion_answer180) If \[f(x)\,=kx\,-\,\cos \,x\] is monotonically increasing for all \[x\in R,\] then
A) \[k>-1\] done clear
B) \[k>-1\] done clear
C) \[k>1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer181) The value of the integral \[\int{\frac{1}{{{e}^{2s}}+{{e}^{-2x}}}}\,\,dx\] is equal to
A) \[2\,{{\tan }^{-1}}\,({{e}^{2x}})+C\] done clear
B) \[{{\tan }^{-1}}\,({{e}^{2x}})+C\] done clear
C) \[\frac{1}{2}{{\tan }^{-1}}\,({{e}^{2x}})+C\] done clear
D) \[\frac{-1}{{{({{e}^{2x}}+{{e}^{-2x}})}^{2}}}+C\] done clear
View Answer play_arrowquestion_answer182) The value of \[\int_{4}^{8}{\frac{\sqrt{x}}{\sqrt{x}+\sqrt{12}-x}}\,\,dx\] is equal to
A) \[4\] done clear
B) \[2\] done clear
C) \[1\] done clear
D) \[1/2\] done clear
View Answer play_arrowquestion_answer183) If \[f(x)=2{{x}^{2}}-|x|+4,\,\,\,x\in [-1,2]\] Then, for some \[c\,\in \,(-1,\,2),\,\,f'(c)\] is equal to
A) \[\frac{f(2)-f(0)}{2-0}\] done clear
B) \[\frac{f(2)-f(-1)}{2-(-1)}\] done clear
C) \[\frac{f(1)-f(-1)}{1-(-1)}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer184) The value of the integral \[\int{\frac{-x\,\,{{e}^{x}}}{{{(x+1)}^{2}}}}\,\,\,dx\] is equal to
A) \[\frac{-{{e}^{x}}}{(x+1)}+C\] done clear
B) \[\frac{{{e}^{x}}}{{{(x+1)}^{2}}}+C\] done clear
C) \[\frac{{{e}^{x}}}{(x+1)}+C\] done clear
D) \[\frac{-{{e}^{x}}}{x+1}+C\] done clear
View Answer play_arrowquestion_answer185) If the straight line \[y=2x+c\]is a tangent to the ellipse \[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=1,\] then c equals to
A) \[\pm \,\,4\] done clear
B) \[\pm \,\,6\] done clear
C) \[\pm \,\,8\] done clear
D) \[\pm \,\,1\] done clear
View Answer play_arrowquestion_answer186) The value of \[\cos \frac{\pi }{7}.\,\cos \frac{2\pi }{7}.\,\cos \frac{4\pi }{7}\] is equal to
A) \[\frac{1}{2}\] done clear
B) \[-\frac{1}{4}\] done clear
C) \[\frac{1}{8}\] done clear
D) \[-\frac{1}{8}\] done clear
View Answer play_arrowquestion_answer187) The rational number among the following real numbers is
A) \[\sin \,\,{{15}^{o}}\] done clear
B) \[\cos \,\,{{15}^{o}}\] done clear
C) \[sin\,{{15}^{o}}.\,\cos \,{{15}^{o}}\] done clear
D) \[sin\,{{15}^{o}}.\,\cos \,{{75}^{o}}\] done clear
View Answer play_arrowquestion_answer188) Suppose the straight line \[x+y=5\]touches the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\]. Then, the coordinates of the point of contact are
A) \[(3,2)\] done clear
B) \[(2,3)\] done clear
C) \[(4,1)\] done clear
D) \[(1,4)\] done clear
View Answer play_arrowquestion_answer189) \[f(x)=|\sin \,2x|+|\cos \,2x|\] is a periodic function with period
A) \[\pi \] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\frac{\pi }{4}\] done clear
D) \[\frac{\pi }{8}\] done clear
View Answer play_arrowquestion_answer190) Let C be right angle of a \[\Delta \,ABC,\] then \[\frac{{{\sin }^{2}}A}{{{\sin }^{2}}B}-\frac{{{\cos }^{2}}A}{{{\cos }^{2}}B}\] is equal to
A) \[\frac{{{a}^{2}}-{{b}^{2}}}{ab}\] done clear
B) \[\frac{{{a}^{4}}-{{b}^{4}}}{{{a}^{2}}{{b}^{2}}}\] done clear
C) \[\frac{{{a}^{4}}+{{b}^{4}}}{{{a}^{2}}{{b}^{2}}}\] done clear
D) \[\frac{{{a}^{2}}+{{b}^{2}}}{ab}\] done clear
View Answer play_arrowquestion_answer191) In a \[\Delta \,ABC,\]\[a=8cm,\text{ }b=10cm\] and\[c=12cm\] The relation between angles of the triangle is
A) \[C=A+B\] done clear
B) \[C=2B\] done clear
C) \[C=2A\] done clear
D) \[C=3A\] done clear
View Answer play_arrowquestion_answer192) The area bounded by the curve \[y=1+{{\log }_{e}}\,\,x,\] the x-axis and the straight line x = e is equal to (in square units)
A) \[3e-2\] done clear
B) \[e\] done clear
C) \[e-\frac{1}{e}\] done clear
D) \[e+\frac{1}{e}\] done clear
View Answer play_arrowquestion_answer193) The general solution of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{2x}}+{{e}^{-x}}\] is
A) \[4{{e}^{2x}}+{{e}^{-x}}+{{C}_{1}}x+{{C}_{2}}\] done clear
B) \[\frac{1}{4}{{e}^{2x}}-{{e}^{-x}}+C\] done clear
C) \[\frac{1}{4}{{e}^{2x}}+{{e}^{-x}}+{{C}_{1}}x+{{C}_{2}}\] done clear
D) \[\frac{1}{4}{{e}^{2x}}-{{e}^{-x}}+{{C}_{1}}x+{{C}_{2}}\] done clear
View Answer play_arrowquestion_answer194) \[\int_{-3}^{2}{[f(x)+f(-x)]\,\,.\,\,[g(x)-g(-x)]\,\,dx}\] is equal to
A) \[0\] done clear
B) \[2\int_{-3}^{3}{f\,(x)dx}\] done clear
C) \[2\int_{0}^{3}{f\,(x)\,\,g\,\,(x)\,\,dx}\] done clear
D) \[2\int_{0}^{3}{[f(x)-g(x)]\,dx}\] done clear
View Answer play_arrowquestion_answer195) The degree of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\frac{5y+\frac{dy}{dx}}{\sqrt{\frac{{{d}^{2}}y}{d{{x}^{2}}}}}\]is equal to
A) \[2\] done clear
B) \[3\] done clear
C) \[4\] done clear
D) \[5/2\] done clear
View Answer play_arrowquestion_answer196) Three forces P, Q and R acting at a point 0 in the plane. The measure of \[\angle POQ\] and \[\angle QOR\] are \[{{120}^{o}}\] and \[{{90}^{o}}\] respectively. Then, the equilibrium forces P, Q and R are in the ratio
A) \[3:1:2\] done clear
B) \[2:1:3\] done clear
C) \[\sqrt{3}:1:2\] done clear
D) \[2:1:\sqrt{3}\] done clear
View Answer play_arrowquestion_answer197) The position vector of two given points A and B are \[4i-3j-k\]and \[5i-5j+k\]respectively. If y is the angle between AB and z-axis, then \[\cos \,\gamma \] is equal to
A) \[1/3\] done clear
B) \[2/3\] done clear
C) \[-2/3\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer198) Let a, b and c be the unit vectors, such that \[b\,.\,c=a\,.\,c=0\]. If the angle between a and b is \[\pi /3\], then c equals to
A) \[\pm \frac{2}{\sqrt{3}}\,(a\times b)\] done clear
B) \[\pm \frac{\sqrt{3}}{2}\,(a\times b)\] done clear
C) \[\pm \,2\,\,(a\times b)\] done clear
D) \[\pm \,\,\frac{1}{2}\,(a\times b)\] done clear
View Answer play_arrowquestion_answer199) The sum of two vectors a and b is a vector c, such that \[|a|=|b|=|c|=2.\] Then, the magnitude of \[a-b\] is equal to
A) \[\sqrt{3}\] done clear
B) \[2\] done clear
C) \[2\sqrt{3}\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer200) The vectors \[2i-j+k,\,\,i+2j-3k\]and \[3i+\lambda j+5k\] are coplanar, if \[\lambda \] equals to
A) \[1\] done clear
B) \[-1\] done clear
C) \[-4\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer201) For the non-zero vectors a, b and c, the relation \[a.\,(b\times c)=0\] is true, if
A) \[b\bot \,\,c\] done clear
B) \[a\bot \,\,b\] done clear
C) \[a||\,\,c\] done clear
D) \[a\bot \,c\] done clear
View Answer play_arrowquestion_answer202) If \[{{S}_{1}},{{S}_{2}}\] and \[{{S}_{3}}\] are the sum of n, \[2n\]and \[3n\] terms respectively of an arithmetic progression, then
A) \[{{S}_{3}}=2\,\,({{S}_{1}}+{{S}_{2}})\] done clear
B) \[{{S}_{3}}={{S}_{1}}+{{S}_{2}}\] done clear
C) \[{{S}_{3}}=3\,({{S}_{2}}-{{S}_{1}})\] done clear
D) \[{{S}_{3}}=3\,({{S}_{2}}+{{S}_{1}})\] done clear
View Answer play_arrowquestion_answer203) The coefficient of \[{{p}^{n}}{{q}^{n}}\] in the expansion of \[{{[(1+p)\,\,(1+q)\,\,(p\,+q)]}^{n}}\] is
A) \[\sum\limits_{k=0}^{n}{{{[C\,\,(n,\,\,k)]}^{2}}}\] done clear
B) \[\sum\limits_{k=0}^{n}{{{[C\,\,(n,\,\,k+2)]}^{2}}}\] done clear
C) \[\sum\limits_{k=0}^{n}{{{[C\,\,(n,\,\,k+3)]}^{2}}}\] done clear
D) \[\sum\limits_{k=0}^{n3}{{{[C\,\,(n,\,\,k)]}^{2}}}\] done clear
View Answer play_arrowquestion_answer204) The number of even numbers of three digits which can be formed with digits \[0,1,\text{ }2,\text{ }3,4\] and 5 (no digit being used more than once) is
A) \[60\] done clear
B) \[92\] done clear
C) \[52\] done clear
D) \[48\] done clear
View Answer play_arrowquestion_answer205) If \[{{4}^{x}}={{16}^{y}}={{64}^{z}},\]then
A) \[x,\text{ }y,\text{ }z\]are in GP done clear
B) \[x,\text{ }y,\text{ }z\]are in AP done clear
C) \[\frac{1}{x},\frac{1}{y},\frac{1}{z}\] tare in GP done clear
D) \[\frac{1}{x},\frac{1}{y},\frac{1}{z}\] are in AP done clear
View Answer play_arrowquestion_answer206) The constant terms is the expansion of \[{{\left( \sqrt{x}-\frac{c}{{{x}^{2}}} \right)}^{10}}\]is \[180,\]then the value of c equals to
A) \[\pm \,\,2\] done clear
B) \[\pm \,\,3\] done clear
C) \[\pm \,\,4\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer207) A student is allowed to select at best n books from a collection of \[(2n\,+1)\] books. If the total number of ways in which he can select a book is 255, then the value of n equals to
A) \[6\] done clear
B) \[5\] done clear
C) \[4\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer208) If \[f(x)=\frac{1}{2-x},\] then \[f\,\,(f(x))\] is discontinous at
A) \[x=2,4\] done clear
B) \[x=4,\,3/2\] done clear
C) \[x=2,3/2\] done clear
D) \[x=4\] done clear
View Answer play_arrowquestion_answer209) If \[g(x)\] is the inverse of \[f(x)\] and \[f'(x)=\cos x,\] then \[g'(x)\] is equal to
A) \[\sec \,\,x\] done clear
B) \[\sec \,\,(g\,\,(x))\] done clear
C) \[\cos \,(g\,(x))\] done clear
D) \[-\sin \,\,(g\,(x)\,)\] done clear
View Answer play_arrowquestion_answer210) The derivative of \[\text{cose}{{\text{c}}^{-1}},\,\,\,\,\left( \frac{1}{2x\,\sqrt{1-{{x}^{2}}}} \right)\] with respect to \[\sqrt{1-{{x}^{2}}}\] is
A) \[\frac{1}{\sqrt{1-{{x}^{2}}}}\] done clear
B) \[\frac{2}{x}\] done clear
C) \[-\frac{2}{x}\] done clear
D) \[\frac{-1}{\sqrt{1-{{x}^{2}}}}\] done clear
View Answer play_arrowquestion_answer211) If \[f(x)=|x-2|\,{{\log }_{10}}\,(x-1),\] then \[f\] is differentiable in
A) \[R-\{\,1,\,\,\,11\}\] done clear
B) \[R-\{\,2,\,\,\,11\}\] done clear
C) \[R-\{\,11\}\] done clear
D) \[R-\{\,1,\,\,2\}\] done clear
View Answer play_arrowquestion_answer212) If \[x\ne 0\] and \[y={{\log }_{e}}\,|2x|,\] then \[\frac{dy}{dx}\] is equal to
A) \[\frac{1}{x}\] done clear
B) \[-\frac{1}{x}\] done clear
C) \[\pm \,\frac{1}{2x}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer213) The curves \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{2}=1\] and \[{{y}^{2}}=8x\]intersect at right angles, if \[{{a}^{2}}\]is equal to
A) \[1/2\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer214) The plane \[2x-2y+z+5=0\] is a tangent to the sphere \[{{(x-2)}^{2}}+{{(y-2)}^{2}}+{{(z-1)}^{2}}={{r}^{2}},\] if r equals
A) \[1\] done clear
B) \[2\] done clear
C) \[4\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer215) A bag has four pair of balls of four distinct colours. If four balls are picked at random (without replacement), the probability that there is atleast one pair among them have the same colour is
A) \[\frac{1}{7\,\,!}\] done clear
B) \[\frac{8}{35}\] done clear
C) \[\frac{19}{35}\] done clear
D) \[\frac{27}{35}\] done clear
View Answer play_arrowquestion_answer216) Suppose \[f(x)=\frac{k}{{{2}^{x}}}\] is a probability distribution of a random variable X that can take on the values \[x=0,1,\text{ }2,\text{ }3,\text{ }4\]. Then, k is equal to
A) \[\frac{16}{15}\] done clear
B) \[\frac{15}{16}\] done clear
C) \[\frac{31}{16}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer217) The contrapositive statement of the proposition \[p\to \tilde{\ }q\] is
A) \[\tilde{\ }p\to q\] done clear
B) \[\tilde{\ }q\to p\] done clear
C) \[q\to \tilde{\ }p\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer218) If A and B are mutually exclusive events, such that \[P(A)=0.25,\,\,\,\,\,\,P(B)=0.4,\] then \[P({{A}^{c}}\,\cap {{B}^{c}})\]is equal to
A) \[0.45\] done clear
B) \[0.55\] done clear
C) \[0.9\] done clear
D) \[0.35\] done clear
View Answer play_arrowquestion_answer219) Let \[f(x)=\frac{3}{1+{{3}^{\tan \,x}}}\]. Then, which of the following is true?
A) \[\underset{x\to \frac{{{\pi }^{-}}}{2}}{\mathop{\lim }}\,\,\,f(x)\,=3\] done clear
B) \[\underset{x\to \frac{{{\pi }^{+}}}{2}}{\mathop{\lim }}\,\,\,f(x)\,=0\] done clear
C) \[\underset{x\to \frac{{{\pi }^{+}}}{2}}{\mathop{\lim }}\,\,\,f(x)\,=3\] done clear
D) \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\,\,f(x)\] exists done clear
View Answer play_arrowquestion_answer220) The general solution of \[\cos \,x\,.\,\cos \,6x=-1\]is
A) \[x=(2n+1)\frac{\pi }{7},\,n\in Z\] done clear
B) \[x=(2n+1)\frac{\pi }{5},\,n\in Z\] done clear
C) \[x=(2n+1)\frac{\pi }{35},\,n\in Z\] done clear
D) \[x=(2n+1)\,\pi ,\,n\in Z\] done clear
View Answer play_arrowquestion_answer221) The value of \[\tan \left[ {{\cos }^{-1}}\left( \frac{3}{5} \right)+{{\tan }^{-1}}\left( \frac{2}{3} \right) \right]\] is
A) \[6\] done clear
B) \[17/6\] done clear
C) \[6/17\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer222) If A is a square matrix of order 3 and a is a real number, then determinant \[|\alpha \,\,\,A|\] is equal to
A) \[{{\alpha }^{2}}\,|\,\,A|\] done clear
B) \[\alpha \,|\,\,A|\] done clear
C) \[{{\alpha }^{3}}\,|\,\,A|\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer223) The number of solution of the equation \[\sin x+\sin 5x=\sin 3x\] tying in the interval \[[0,\,\pi ]\] is
A) \[4\] done clear
B) \[6\] done clear
C) \[5\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer224) The ' value of \[\sin \,\left[ {{\tan }^{-1}}\,\,\left( \frac{1-{{x}^{2}}}{2x} \right)+{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right) \right]\] is
A) \[1\] done clear
B) \[0\] done clear
C) \[-1\] done clear
D) \[\frac{\pi }{2}\] done clear
View Answer play_arrowquestion_answer225) The system of equations \[2x-y+z=0,\]\[ax-y+2z=0\]and \[x-2y+z=0\] has non-zero solution, if a is equal to
A) \[1\] done clear
B) \[2\] done clear
C) \[4\] done clear
D) \[5\] done clear
View Answer play_arrow
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