question_answer1) A solid cylinder is rolling down on an inclined plane of angle \[\theta ,\] The coefficient of static friction between the plane and cylinder is \[{{\mu }_{s}}\]. Then condition for the cylinder not to slip is
A) \[\tan \,\,\theta \ge \,3{{\mu }_{s}}\] done clear
B) \[\tan \,\,\theta >3{{\mu }_{s}}\] done clear
C) \[\tan \,\,\theta \le 3{{\mu }_{s}}\] done clear
D) \[\tan \,\,\theta <3{{\mu }_{s}}\] done clear
View Answer play_arrowquestion_answer2) The moment of inertia of a circular ring of mass \[1\text{ }kg\]about an axis passing through its centre and perpendicular to its plane is \[4\text{ }kg-{{m}^{2}}\]. The diameter of the ring is
A) \[2\,\,m\] done clear
B) \[4\,\,m\] done clear
C) \[5\,\,m\] done clear
D) \[6\,\,m\] done clear
View Answer play_arrowquestion_answer3) If g is the acceleration due to gravity on the surface of earth, its value at a height equal to double the radius of earth is
A) \[g\] done clear
B) \[\frac{g}{2}\] done clear
C) \[\frac{g}{3}\] done clear
D) \[\frac{g}{9}\] done clear
View Answer play_arrowquestion_answer4) On bombardment of \[{{U}^{235}}\] by slow neutrons, \[200\text{ }MeV\] energy is released. If the power output of atomic reactor is \[1.6\text{ }MW,\] then the rate of fission will be
A) \[5\times {{10}^{16}}/s\] done clear
B) \[10\times {{10}^{16}}/s\] done clear
C) \[15\times {{10}^{16}}/s\] done clear
D) \[20\times {{10}^{-16}}/s\] done clear
View Answer play_arrowquestion_answer5) A stress of \[3.18\times {{10}^{8}}\,N-{{m}^{-2}}\] is applied to a steel rod of length 1 m along its length. Its Young's modulus is \[2\times {{10}^{11}}\text{ }N-{{m}^{-2}}\]. Then, the elongation produced in the rod (in mm) is
A) \[3.18\] done clear
B) \[6.36\] done clear
C) \[5.18\] done clear
D) \[1.59\] done clear
View Answer play_arrowquestion_answer6) A liquid is allowed into a tube of truncated cone shape. Identify the correct statement from the following.
A) The speed is high at the wider end and low at the narrow end done clear
B) The speed is low at the wider end and high at the narrow end done clear
C) The speed is same at both ends in a stream line flow done clear
D) The liquid flows with uniform velocity in the tube done clear
View Answer play_arrowquestion_answer7) A sphere of radius R is gently dropped into liquid of viscosity \[\eta \] in a vertical uniform tube. It attains a terminal velocity v. Another sphere of radius 2R when dropped into the same liquid, will attain its terminal velocity
A) \[v\] done clear
B) \[2v\] done clear
C) \[4v\] done clear
D) \[9v\] done clear
View Answer play_arrowquestion_answer8) The excess pressure in a bubble of radius R of a gas in a liquid of surface tension S is
A) \[\frac{2\,S}{R}\] done clear
B) \[\frac{2\,R}{S}\] done clear
C) \[\frac{2\,S}{{{R}^{2}}}\] done clear
D) \[\frac{2{{R}^{2}}}{S}\] done clear
View Answer play_arrowquestion_answer9) The average kinetic energy of a gas molecule is
A) proportional to pressure of gas done clear
B) inversely proportional to volume of gas done clear
C) inversely proportional to absolute temperature of gas done clear
D) directly proportional to absolute temperature of gas done clear
View Answer play_arrowquestion_answer10) Ideal gas undergoes an adiabatic change in its state from \[({{p}_{1}},{{V}_{1}},{{T}_{1}})\] to \[({{p}_{2}},{{V}_{2}},{{T}_{2}})\]. The work done (W) in the process is (\[\mu =\] number of molecules, \[{{C}_{P}}\] and \[{{C}_{V}}\] are molar specific heats of gas)
A) \[W=\mu {{C}_{P}}({{T}_{1}}-{{T}_{2}})\] done clear
B) \[W=\mu {{C}_{V}}({{T}_{1}}-{{T}_{2}})\] done clear
C) \[W=\mu {{C}_{P}}({{T}_{1}}+{{T}_{2}})\] done clear
D) \[W=\mu {{C}_{V}}({{T}_{1}}+{{T}_{2}})\] done clear
View Answer play_arrowquestion_answer11) For an ideal gas
A) \[{{C}_{P}}\] is less than \[{{C}_{V}}\] done clear
B) \[{{C}_{P}}\] is equal to \[{{C}_{V}}\] done clear
C) \[{{C}_{P}}\] is greater than \[{{C}_{V}}\] done clear
D) \[{{C}_{P}}={{C}_{V}}=0\] done clear
View Answer play_arrowquestion_answer12) For a gas molecule with 6 degrees of freedom the law of equipartition of energy gives the following relation between the molecular specific heat \[({{C}_{V}})\] and gas constant (R)
A) \[{{C}_{V}}=\frac{R}{2}\] done clear
B) \[{{C}_{V}}=R\] done clear
C) \[{{C}_{V}}=2R\] done clear
D) \[{{C}_{V}}=3R\] done clear
View Answer play_arrowquestion_answer13) Wien's displacement law for emission of radiation can be written as
A) \[{{\lambda }_{\max }}\]max is proportional to absolute temperature (T) done clear
B) \[{{\lambda }_{\max }}\] is proportional to square of absolute temperature \[({{T}^{2}})\] done clear
C) \[{{\lambda }_{\max }}\] is inversely proportional to absolute temperature (T) done clear
D) \[{{\lambda }_{\max }}\] is inversely proportional to square of absolute temperature \[({{T}^{2}})\] (\[{{\lambda }_{\max }}\] = wavelength whose energy density is greatest) done clear
View Answer play_arrowquestion_answer14) The frequency of the fundamental note in a wire stretched under tension T is /. If the tension is increased to 25 T, then the frequency of the fundamental note will be
A) \[25\,f\] done clear
B) \[5\,f\] done clear
C) \[10\,f\] done clear
D) \[f\] done clear
View Answer play_arrowquestion_answer15) The frequency of fundamental note in an organ pipe is \[240\text{ }Hz.\] On blowing air, frequencies \[720\text{ }Hz\]and \[1200\text{ }Hz\]are heard. This indicates that organ pipe is
A) a pipe closed at one end done clear
B) a pipe open at both ends done clear
C) closed at both ends done clear
D) having holes like flute done clear
View Answer play_arrowquestion_answer16) If \[{{L}_{1}}\]and \[{{L}_{2}}\] are the lengths of the first and second resonating air columns in a resonance tube, then the wavelength of the note produced is
A) \[2({{L}_{2}}+{{L}_{1}})\] done clear
B) \[2({{L}_{2}}-{{L}_{1}})\] done clear
C) \[2\left( {{L}_{2}}-\frac{{{L}_{1}}}{2} \right)\] done clear
D) \[2\left( {{L}_{2}}+\frac{{{L}_{1}}}{2} \right)\] done clear
View Answer play_arrowquestion_answer17) Beats are produced by frequencies \[{{f}_{1}}\] and \[{{f}_{2}}({{f}_{1}}>{{f}_{2}})\]. The duration of time between two successive maxima or minima is equal to
A) \[\frac{1}{{{f}_{1}}+{{f}_{2}}}\] done clear
B) \[\frac{2}{{{f}_{1}}-{{f}_{2}}}\] done clear
C) \[\frac{2}{{{f}_{1}}+{{f}_{2}}}\] done clear
D) \[\frac{1}{{{f}_{1}}-{{f}_{2}}}\] done clear
View Answer play_arrowquestion_answer18) If a body is executing simple harmonic motion, then
A) at extreme positions, the total energy is zero done clear
B) at equilibrium position, the total energy is in the form of potential energy done clear
C) at equilibrium position, the total energy is in the form of kinetic energy done clear
D) at extreme position, the total energy is infinite done clear
View Answer play_arrowquestion_answer19) An electric dipole has a pair of equal and opposite point charges q and \[-q\] separated by a distance 2x. The axis of the dipole is defined as
A) direction from positive, charge to negative charge done clear
B) direction from negative charge to positive charge done clear
C) perpendicular to the line joining the two charges drawn at the centre and pointing upward direction done clear
D) perpendicular to the line joining the two charges drawn at the centre and pointing downward direction done clear
View Answer play_arrowquestion_answer20) The dipole moment of a dipole in an uniform external field \[\vec{E}\] is \[\vec{P}\]. Then, the torque \[(\tau )\] acting on the dipole is
A) \[\vec{\tau }=\vec{P}\times \vec{E}\] done clear
B) \[\vec{\tau }=\vec{P}.\vec{E}\] done clear
C) \[\vec{\tau }=2(\vec{P}+\vec{E})\] done clear
D) \[\vec{\tau }=(\vec{P}+\vec{E})\] done clear
View Answer play_arrowquestion_answer21) The electric flux through a closed surface area S enclosing charge Q is \[\phi \]. If the surface area is doubled, then the flux is
A) \[2\,\phi \] done clear
B) \[\phi /2\] done clear
C) \[\phi /4\] done clear
D) \[\phi \] done clear
View Answer play_arrowquestion_answer22) Consider a thin spherical shell of radius R consisting of uniform surface charge density \[\sigma \] The electric field at a point of distance x from its centre and outside the shell is
A) inversely proportional to \[\sigma \] done clear
B) directly proportional to \[{{x}^{2}}\] done clear
C) directly proportional to \[\sigma \] done clear
D) inversely proportional to \[{{x}^{2}}\] done clear
View Answer play_arrowquestion_answer23) The work done in bringing at a unit positive charge from infinity distance to a point at distance X from a positive charge Q is W. Then the potential \[\phi \] at that point is
A) \[\frac{WQ}{X}\] done clear
B) \[W\] done clear
C) \[\frac{W}{Q}\] done clear
D) \[WQ\] done clear
View Answer play_arrowquestion_answer24) The capacitance C of a capacitor is
A) independent of the charge and potential of the capacitor done clear
B) dependent on the charge and independent of potential done clear
C) independent of the geometrical configuration of the capacitor done clear
D) independent of the dielectric medium between the two conducting surfaces of the capacitor done clear
View Answer play_arrowquestion_answer25) Four capacitors are connected in a circuit as shown in the following figure. Calculate the effective capacitance between the points A and B.
A) \[\frac{4}{3}\mu F\] done clear
B) \[\frac{24}{5}\mu F\] done clear
C) \[9\,\mu F\] done clear
D) \[5\,\mu F\] done clear
View Answer play_arrowquestion_answer26) Metals have
A) zero resistivity done clear
B) high resistivity done clear
C) low resistivity done clear
D) infinite resistivity done clear
View Answer play_arrowquestion_answer27) The electric potential inside a conducting sphere
A) increases from centre to surface done clear
B) decreases from centre to surface done clear
C) remains constant from centre to surface done clear
D) is zero at every point inside done clear
View Answer play_arrowquestion_answer28) Electron of mass m and charge e in external field ? experiences acceleration
A) \[\frac{e}{mE},\] in the opposite direction to the field done clear
B) \[\frac{eE}{m},\] in the direction of the field done clear
C) \[\frac{em}{E},\] m the direction of the field done clear
D) \[\frac{eE}{m},\] in the opposite direction of the field, done clear
View Answer play_arrowquestion_answer29) Kirchhoff?s second law for the analysis of circuit is based on
A) conservation of charge done clear
B) conservation of energy done clear
C) conservation of both charge and energy done clear
D) conservation of momentum of electron done clear
View Answer play_arrowquestion_answer30) In circuit shown below, the resistances are given in ohm and the battery is assumed ideal with emf equal to\[3\text{ }V\]. The voltage across the resistance \[{{R}_{4}}\] is
A) \[0.4V\] done clear
B) \[0.6V\] done clear
C) \[1.2\text{ }V\] done clear
D) \[1.5V\] done clear
View Answer play_arrowquestion_answer31) The direction of induced magnetic field \[d\,\,\vec{B}\] due to current element i d \[\vec{L},\] at a point of distance r from it, when a current i passes through a long conductor is in the direction
A) of position vector \[\vec{r}\] of the point done clear
B) of current element \[d\,\vec{L}\] done clear
C) perpendicular to both \[d\,\vec{L}\] and \[\vec{r}\] done clear
D) perpendicular to \[\vec{L}\] only done clear
View Answer play_arrowquestion_answer32) The magnetic force on a charged particle moving in the field does not work, because
A) kinetic energy of the charged particle does not change done clear
B) the charge of the particle remains same done clear
C) the magnetic force is parallel to velocity of the particle done clear
D) the magnetic force is parallel to magnetic field done clear
View Answer play_arrowquestion_answer33) To convert a moving coil galvanometer (MCG) into a voltmeter
A) a high resistance R is connected in parallel with MCG done clear
B) a low resistance r is connected in parallel with MCG done clear
C) a low resistance r is connected in series With MCG done clear
D) a high resistance R is connected in series with MCG done clear
View Answer play_arrowquestion_answer34) Identify the correct statement from the following.
A) Cyclotron frequency is dependent on speed of the charged particle done clear
B) Kinetic energy of charged particle in cyclotron does not dependent on its mass done clear
C) Cyclotron frequency does not depend on speed of charged particle done clear
D) Kinetic energy of charged particle in cyclotron is independent of its charge done clear
View Answer play_arrowquestion_answer35) Consider two straight parallel conductors A and B separated by a distance x and carrying individual currents \[{{i}_{A}}\] and \[{{i}_{B}}\] respectively. If the two conductors attract each other, it indicates that
A) the two currents are parallel in direction done clear
B) the two currents are anti-parallel in direction done clear
C) the magnetic lines of induction are parallel done clear
D) the magnetic lines of induction are parallel to length of conductors done clear
View Answer play_arrowquestion_answer36) The magnetic susceptibility of paramagnetic materials is
A) positive, but very high done clear
B) negative, but small done clear
C) negative but very high done clear
D) positive, but small done clear
View Answer play_arrowquestion_answer37) According to Lenz's law of electromagnetic induction
A) the induced emf is not in the direction opposing the change in magnetic flux done clear
B) the relative motion between the coil and magnet produces change in magnetic flux done clear
C) only the magnet should be moved towards coil done clear
D) only the coil should be moved towards magnet done clear
View Answer play_arrowquestion_answer38) According to phenomenon of mutual inductance
A) the mutual inductance does not dependent on geometry of the two coils involved done clear
B) the mutual inductance depends on the intrinsic magnetic property, like relative permeability of the material done clear
C) the mutual inductance is independent of the magnetic property of the material done clear
D) ratio of magnetic flux produced by the coil 1 at-the place of the coil 2 and the current in the coil 2 will be different from that of the ratio defined by interchanging the coils done clear
View Answer play_arrowquestion_answer39) The natural frequency \[({{\omega }_{0}})\] of oscillations in L-C circuit is given by
A) \[\frac{1}{2\pi }\frac{1}{\sqrt{LC}}\] done clear
B) \[\frac{1}{2\pi }\,\sqrt{LC}\] done clear
C) \[\frac{1}{\,\sqrt{LC}}\] done clear
D) \[\sqrt{LC}\] done clear
View Answer play_arrowquestion_answer40) In L-C-R series circuit the resonance condition in terms of capacitive reactance \[({{X}_{C}})\] and inductive reactance \[({{X}_{L}})\] is
A) \[{{X}_{C}}+{{X}_{L}}=0\] done clear
B) \[{{X}_{C}}=0\] done clear
C) \[{{X}_{L}}=0\] done clear
D) \[{{X}_{C}}-{{X}_{L}}=0\] done clear
View Answer play_arrowquestion_answer41) In step-up transformer, relation between number of turns in primary \[({{N}_{P}})\] and number of turns in secondary \[({{N}_{S}})\] coils is
A) \[{{N}_{s}}\] is greater than \[{{N}_{p}}\] done clear
B) \[{{N}_{p}}\] is greater than \[{{N}_{s}}\] done clear
C) \[{{N}_{s}}\] is equal to \[{{N}_{p}}\] done clear
D) \[{{N}_{p}}=2{{N}_{s}}\] done clear
View Answer play_arrowquestion_answer42) Two light sources are said to be of coherent nature
A) when they have same frequency and a varying phase difference done clear
B) when they have same frequency and a constant phase difference done clear
C) when they have constant phase difference and different frequencies done clear
D) when they have varying phase difference and different frequencies done clear
View Answer play_arrowquestion_answer43) In Young's double slit interference pattern the fringe width
A) can be changed only by changing the wavelength of incident light done clear
B) can be changed only by changing the separation between the two slits done clear
C) can be changed either by changing the wavelength or by changing the separation between two sources done clear
D) is a universal constant and hence cannot be changed done clear
View Answer play_arrowquestion_answer44) Colours in thin films are due to
A) diffraction phenomenon done clear
B) scattering phenomenon done clear
C) interference phenomenon done clear
D) polarization phenomenon done clear
View Answer play_arrowquestion_answer45) Brewster?s angle in terms of refractive index (n) of the medium
A) \[{{\tan }^{-1}}\,\sqrt{n}\] done clear
B) \[{{\sin }^{-1}}\,n\] done clear
C) \[{{\sin }^{-1}}\,\sqrt{n}\] done clear
D) \[{{\tan }^{-1}}\,n\] done clear
View Answer play_arrowquestion_answer46) The angle of incidence of light is equal to Brewster?s angle, then
A. reflected ray is perpendicular to refracted ray |
B. refracted ray is parallel to reflected ray |
C. reflected light is polarized having its electric vector in the plane of incidence |
D. refracted light is polarized |
A) [A] and [D] are true done clear
B) [A] and [B] are true done clear
C) [A] and [C] are true done clear
D) [B] and [C] are true done clear
View Answer play_arrowquestion_answer47) The working of optical fibres is based on
A) dispersion of light done clear
B) total internal reflection done clear
C) polarization of light done clear
D) interference of light done clear
View Answer play_arrowquestion_answer48) First Bohr radius of an atom with \[Z=82\]is R. Radius of its third orbit is
A) \[9\,\,R\] done clear
B) \[6\,\,R\] done clear
C) \[3\,R\] done clear
D) \[R\] done clear
View Answer play_arrowquestion_answer49) The de-Broglie wavelength associated with a particle moving with momentum (p) and mass (m) is
A) \[\frac{h}{p}\] done clear
B) \[\frac{h}{mp}\] done clear
C) \[\frac{h}{{{p}^{2}}}\] done clear
D) \[\frac{{{h}^{2}}}{{{p}^{2}}}\] done clear
View Answer play_arrowquestion_answer50) The angular momentum (L) of an electron moving in a stable orbit around nucleus is
A) half integral multiple of \[\frac{h}{2\pi }\] done clear
B) integral multiple of h done clear
C) integral multiple of \[\frac{h}{2\pi }\] done clear
D) half integral multiple of h done clear
View Answer play_arrowquestion_answer51) According to Moseley's law of X-rays the frequency (v) of a particular characteristic X-ray and the atomic number (Z) of the element depend on each other as
A) \[\sqrt{v}=k{{Z}^{2}}\] done clear
B) \[\sqrt{v}=\frac{h}{{{Z}^{2}}}\] done clear
C) \[v=kZ\] done clear
D) \[\sqrt{v}=kZ\] done clear
View Answer play_arrowquestion_answer52) If \[\lambda \] is decay constant and N the number of radioactive nuclei of an element, then the decay rate (R) of that element is
A) \[\lambda {{N}^{2}}\] done clear
B) \[\lambda N\] done clear
C) \[\frac{\lambda }{N}\] done clear
D) \[{{\lambda }^{2}}N\] done clear
View Answer play_arrowquestion_answer53) The ratio of half-life times of two elements A and B is \[\frac{{{T}_{A}}}{{{T}_{B}}}\] The ratio of respective decay constants \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}\] is
A) \[\frac{{{T}_{B}}}{{{T}_{A}}}\] done clear
B) \[\frac{{{T}_{A}}}{{{T}_{B}}}\] done clear
C) \[\frac{{{T}_{A}}+{{T}_{B}}}{{{T}_{A}}}\] done clear
D) \[\frac{{{T}_{A}}-{{T}_{B}}}{{{T}_{A}}}\] done clear
View Answer play_arrowquestion_answer54) For a nuclear to be in critical condition, the value of neutron multiplication factor (k) must be
A) \[k>1\] done clear
B) \[k<1\] done clear
C) \[k=1\] done clear
D) \[k=0\] done clear
View Answer play_arrowquestion_answer55) If \[{{n}_{E}}\] and \[{{n}_{H}}\] represent the number of free electrons and holes respectively in a semiconducting material, then for n-type semiconducting material
A) \[{{n}_{E}}<<{{n}_{H}}\] done clear
B) \[{{n}_{E}}>>{{n}_{H}}\] done clear
C) \[{{n}_{E}}={{n}_{H}}\] done clear
D) \[{{n}_{E}}={{n}_{H}}=0\] done clear
View Answer play_arrowquestion_answer56) An intrinsic semiconductor at \[0\text{ }K\]temperature behaves like
A) conductor done clear
B) p-type semiconductor done clear
C) n-typesemiconductor done clear
D) insulator done clear
View Answer play_arrowquestion_answer57) When a p-n junction diode is connected in forward bias its barrier potential
A) decreases and less current flows in the circuit done clear
B) decreases and more current flows in the circuit done clear
C) increases and more current flows in the circuit done clear
D) decreases and no current flows in the circuit done clear
View Answer play_arrowquestion_answer58) The main cause of zener breakdown is
A) the base semiconductor being germanium done clear
B) production of electron-hole pairs due to thermal excitation done clear
C) low doping done clear
D) high doping done clear
View Answer play_arrowquestion_answer59) The depletion layer in a silicon diode is \[1\,\mu m\] wide and its knee potential is \[0.6\text{ }V,\] then the electric field in the depletion layer will be
A) \[0.6\text{ }V/m\] done clear
B) \[6\times {{10}^{4}}\,V/m\] done clear
C) \[6\times {{10}^{5}}\,V/m\] done clear
D) zero done clear
View Answer play_arrowquestion_answer60) Identify the true statement for OR gate
A) Output Y will be 1 when input A or B or both are 1 done clear
B) Output Y will be 0 when the either of the inputs A or B is 1 done clear
C) Output Y will be 1 only when both the inputs A and Bare 1 done clear
D) Output Y will be 1 only when either of the inputs A and B are 1 done clear
View Answer play_arrowquestion_answer61) Dimensional formula for force is
A) \[[M{{L}^{2}}{{T}^{-2}}]\] done clear
B) \[[ML{{T}^{-2}}]\] done clear
C) \[[M{{L}^{-1}}{{T}^{-2}}]\] done clear
D) \[[M{{L}^{2}}{{T}^{-2}}]\] done clear
View Answer play_arrowquestion_answer62) X is a vector with magnitude A, then the unit vector a in the direction of vector A is
A) \[A\,\vec{A}\] done clear
B) \[\vec{A}.\,\vec{A}\] done clear
C) \[\vec{A}\times \,\vec{A}\] done clear
D) \[\frac{|\vec{A}|}{A}\] done clear
View Answer play_arrowquestion_answer63) A body is under the action of two mutually perpendicular forces of \[3\text{ }N\]and\[4\text{ }N\]. The resultant force acting on the body is
A) \[7\,N\] done clear
B) \[1\,N\] done clear
C) \[5\,N\] done clear
D) zero done clear
View Answer play_arrowquestion_answer64) If the scalar and vector products of two vectors X and S are equal in magnitude, then the angle between the two vectors is
A) \[{{45}^{o}}\] done clear
B) \[{{90}^{o}}\] done clear
C) \[{{180}^{o}}\] done clear
D) \[{{360}^{o}}\] done clear
View Answer play_arrowquestion_answer65) A body is moving along a straight line path with constant velocity. At an instant of time the distance travelled by it is 5 and its displacement is D, then
A) \[D<s\] done clear
B) \[D>s\] done clear
C) \[D=s\] done clear
D) \[D\le s\] done clear
View Answer play_arrowquestion_answer66) A body is projected at an angle \[\theta \] with respect to horizontal direction with velocity u. The maximum range of the body is
A) \[R=\frac{{{u}^{2}}\,\sin \,\,2\theta }{g}\] done clear
B) \[R=\frac{{{u}^{2}}\,{{\sin }^{2}}\theta }{2g}\] done clear
C) \[R=\frac{{{u}^{2}}}{g}\] done clear
D) \[R={{u}^{2}}\,\,\sin \,\,\theta \] done clear
View Answer play_arrowquestion_answer67) A body moving along a circular path of radius R with velocity v, has centripetal acceleration a. If its velocity is made equal to 2v, then its centripetal acceleration is
A) \[4\,a\] done clear
B) \[2\,a\] done clear
C) \[\frac{a}{4}\] done clear
D) \[\frac{a}{2}\] done clear
View Answer play_arrowquestion_answer68) A cyclist is travelling with velocity v on a banked curved road of radius R. The angle \[\theta \] through which the cyclist leans inwards is given by
A) \[\tan \,\theta =\frac{Rg}{{{v}^{2}}}\] done clear
B) \[\tan \,\theta ={{v}^{2}}\,Rg\] done clear
C) \[\tan \,\theta =\frac{{{v}^{2}}\,g}{R}\] done clear
D) \[\tan \,\theta =\frac{{{v}^{2}}}{Rg}\] done clear
View Answer play_arrowquestion_answer69) A body starts from rest and moves with uniform acceleration. Which of the following graphs represent its motion?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer70) A gun fires N bullets per second, each of mass m with velocity v. The force exerted by the bullets on the gun is
A) \[vNm\] done clear
B) \[\frac{mv}{N}\] done clear
C) \[mv{{N}^{2}}\] done clear
D) \[\frac{m{{v}^{2}}}{N}\] done clear
View Answer play_arrowquestion_answer71) The rate of mass of the gas emitted from rear of a rocket is initially\[0.1\text{ }kg/s\]. If the speed of the gas relative to the rocket is \[50\text{ }m/s\]and mass of the rocket is\[2\text{ }kg\], then the acceleration of the rocket (in\[m/{{s}^{2}}\]) is
A) \[5\] done clear
B) \[5.2\] done clear
C) \[2.5\] done clear
D) \[25\] done clear
View Answer play_arrowquestion_answer72) The area under the displacement-force curve gives
A) distance travelled done clear
B) total force done clear
C) momentum done clear
D) work done done clear
View Answer play_arrowquestion_answer73) Identify the correct statement for the rotational motion of a rigid body.
A) Individual particles of the body do not undergo accelerated motion done clear
B) The centre of mass of the body remains unchanged done clear
C) The centre of mass of the body moves uniformly in a circular path done clear
D) Individual particles and centre of mass the body undergo an accelerated motion done clear
View Answer play_arrowquestion_answer74) The moment of inertia about an axis of a body which is rotating with angular velocity 1 rad/s is numerically equal to
A) one-fourth of its rotational kinetic energy done clear
B) half of the rotational kinetic energy done clear
C) rotational kinetic energy done clear
D) twice the rotational kinetic energy done clear
View Answer play_arrowquestion_answer75) The moment of inertia of a circular disc of radius\[2\text{ }m\]and mass \[2\text{ }kg,\] about an axis passing through its centre of mass is\[2\text{ }kg-{{m}^{2}}\]. Its moment of inertia about an axis parallel to this axis and passing through its edge (in\[kg-{{m}^{2}}\]) is
A) \[10\] done clear
B) \[8\] done clear
C) \[6\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer76) The phenomenon observed when a beam of light is passed through a colloidal solution, is
A) cataphoresis done clear
B) delectrophoresis done clear
C) coagulation done clear
D) Tyndall effect done clear
View Answer play_arrowquestion_answer77) In case of condensation of polymers
A) high molecular weight polymers are formed all at once done clear
B) lower molecular weight polymers are formed all at once done clear
C) molecular weight of polymer rises throughout the reaction done clear
D) have no Specific relation to their molecular weight done clear
View Answer play_arrowquestion_answer78) The element with the lowest ionization potential is
A) Na done clear
B) K done clear
C) Rb done clear
D) Cs done clear
View Answer play_arrowquestion_answer79) Differentiating electron in inner transition elements enters the ......... orbital.
A) s done clear
B) p done clear
C) d done clear
D) \[f\] done clear
View Answer play_arrowquestion_answer80) Which one of the following is a non-polar molecule?
A) \[CC{{l}_{4}}\] done clear
B) \[CHC{{l}_{3}}\] done clear
C) \[C{{H}_{2}}C{{l}_{2}}\] done clear
D) \[C{{H}_{3}}Cl\] done clear
View Answer play_arrowquestion_answer81) The nature of the bond in diamond is
A) ionic done clear
B) covalent done clear
C) metallic done clear
D) coordinate covalent done clear
View Answer play_arrowquestion_answer82) According to VSEPR theory the repulsion between different pair (lone or bond) of electrons obey the order
A) \[lp-bp-lp-lp>bp-bp\] done clear
B) \[lp-bp>bp-bp>lp-lp\] done clear
C) \[lp-lp>lp-bp>lp-bp\] done clear
D) \[bp-bp>lp-lp>lp-bp\] done clear
View Answer play_arrowquestion_answer83) From the molecular orbital theory, one can show that the bond order in \[{{F}_{2}}\]molecule as
A) 2 done clear
B) 1 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer84) Which of the following metal oxides is most basic?
A) \[ZnO\] done clear
B) \[~A{{l}_{2}}{{O}_{3}}\] done clear
C) \[A{{s}_{2}}{{O}_{3}}\] done clear
D) \[{{K}_{2}}O\] done clear
View Answer play_arrowquestion_answer85) In the laboratory \[{{\text{H}}_{\text{2}}}\text{S}\]gas is prepared by using black lumps and dil.\[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{.}\] The black lumps are
A) \[~FeS{{O}_{4}}\] done clear
B) \[~Mn{{O}_{2}}\] done clear
C) \[FeS\] done clear
D) \[FeS{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer86) The order of electron affinity of halogens is
A) \[F>Cl>Br>I\] done clear
B) \[Cl>F>Br>I\] done clear
C) \[Cl>F>I>Br\] done clear
D) \[Br>Cl>F>I\] done clear
View Answer play_arrowquestion_answer87) When chlorine reacts with dil. \[\text{NaOH}\]under cold conditions, the oxidation state of chlorine changes from zero to
A) - 1 and + 5 done clear
B) + 1 and + 4 done clear
C) + 5 and +3 done clear
D) - 1 and + 1 done clear
View Answer play_arrowquestion_answer88) The highest oxidation state exhibited by transition metals is
A) + 7 done clear
B) + 8 done clear
C) + 6 done clear
D) + 5 done clear
View Answer play_arrowquestion_answer89) Which one of the following statements is not true with regard to transition elements?
A) They readily form complex compounds done clear
B) They show variable oxidation states done clear
C) All their ions are colourless done clear
D) Their ions contain partially filled d-electrons done clear
View Answer play_arrowquestion_answer90) The catalyst used in the manufacture of ammonia is
A) \[{{V}_{2}}{{O}_{5}}\] done clear
B) \[Pt\] done clear
C) \[Fe\] done clear
D) \[Ni{{(CO)}_{4}}\] done clear
View Answer play_arrowquestion_answer91) The most stable oxidation state of lanthanides is
A) + 2 done clear
B) + 4 done clear
C) 0 done clear
D) + 3 done clear
View Answer play_arrowquestion_answer92) The number of ions formed when hexamine copper (II) sulphate is dissolved in water is
A) 1 done clear
B) 2 done clear
C) 4 done clear
D) 6 done clear
View Answer play_arrowquestion_answer93) The number of unpaired electrons in the square planar \[{{[Pt{{(CN)}_{4}}]}^{2-}}\]ion is
A) 2 done clear
B) 1 done clear
C) 0 done clear
D) 3 done clear
View Answer play_arrowquestion_answer94) In metal carbonyl (organometallic) complexes, the M-C bond is
A) ionic done clear
B) covalent with ionic character done clear
C) covalent done clear
D) coordinate covalent done clear
View Answer play_arrowquestion_answer95) The complexes\[[PrC{{l}_{2}}{{(N{{H}_{3}})}_{4}}]B{{r}_{2}}\] and \[[PtB{{r}_{2}}{{(N{{H}_{3}})}_{4}}]C{{l}_{2}}\]are examples for isomerism
A) geometrical done clear
B) optical done clear
C) ionisation done clear
D) linkage done clear
View Answer play_arrowquestion_answer96) The metallurgical process in which a metal is obtained in a fused state is called
A) smelting done clear
B) roasting done clear
C) calcination done clear
D) froth floatation done clear
View Answer play_arrowquestion_answer97) Metallic silver may be obtained from \[\text{AgCl}\]by
A) heating it in the current of \[{{\text{H}}_{\text{2}}}\] done clear
B) fusing it with sand done clear
C) treating with carbon monoxide done clear
D) fusing it with \[\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\] done clear
View Answer play_arrowquestion_answer98) Which one of the following metals is extracted by a carbon reduction process?
A) Copper done clear
B) Iron done clear
C) Aluminium done clear
D) Magnesium done clear
View Answer play_arrowquestion_answer99) IUPAC name of \[C{{H}_{3}}-\underset{Cl}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}-CHO\]is \[Cl\]
A) 3-chlorobutanol done clear
B) 3-chlorobutanaldehyde done clear
C) 3-chlorobutanal done clear
D) 2-chlorobutanol done clear
View Answer play_arrowquestion_answer100) Di-chloroacetic acid is a stronger acid than acetic acid. This is due to occurrence of
A) mesomeric effect done clear
B) hyperconjugation done clear
C) inductive effect done clear
D) steric effect done clear
View Answer play_arrowquestion_answer101) Dehydration of alcohol is an example of which type of reaction?
A) Substitution done clear
B) Elimination done clear
C) Addition done clear
D) Rearrangement done clear
View Answer play_arrowquestion_answer102) Number of monochloro derivatives obtained when neo-pentane is chlorinated, is
A) one done clear
B) two done clear
C) three done clear
D) four done clear
View Answer play_arrowquestion_answer103) Which of the following alkenes gives only acetaldehyde on ozonolysis?
A) Ethene done clear
B) Propene done clear
C) 1-butene done clear
D) 2-butene done clear
View Answer play_arrowquestion_answer104) 1-butyne on hydration gives
A) butan-1, 2-diol done clear
B) butan-1-ol done clear
C) butan-2-ol done clear
D) butan-2-one done clear
View Answer play_arrowquestion_answer105) Least stable conformer of cyclohexane is
A) chair done clear
B) boat done clear
C) twist boat done clear
D) planar hexagon done clear
View Answer play_arrowquestion_answer106) Which one of the following monoenes does not exhibit geometric isomerism?
A) \[{{C}_{4}}{{H}_{8}}\] done clear
B) \[{{C}_{3}}{{H}_{6}}\] done clear
C) \[{{C}_{5}}{{H}_{10}}\] done clear
D) \[{{C}_{8}}{{H}_{16}}\] done clear
View Answer play_arrowquestion_answer107) Which one of the following chlorohydrocarbons readily undergoes solvolysis?
A) \[C{{H}_{2}}=CHCl\] done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer108) Conversion of chlorobenzene to phenol involves
A) electrophilic substitution done clear
B) nucleophilic substitution done clear
C) free radical substituion done clear
D) electrophilic addition done clear
View Answer play_arrowquestion_answer109) is
A) an ester done clear
B) an anhydride done clear
C) acetal done clear
D) hemiacetal done clear
View Answer play_arrowquestion_answer110) Which one of the following does not give iodoform?
A) done clear
B) \[C{{H}_{3}}OH\] done clear
C) \[C{{H}_{3}}C{{H}_{2}}OH\] done clear
D) \[C{{H}_{3}}-\underset{OH}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer111) The products obtained when anisole is heated in a sealed tube with HI are
A) done clear
B) done clear
C) done clear
D) \[C{{H}_{3}}OH+C{{H}_{3}}I\] done clear
View Answer play_arrowquestion_answer112) Which of the following diacid readily gives anhydride on heating?
A) Fumaric done clear
B) Maleic acid done clear
C) Malic acid done clear
D) Terephthalic acid done clear
View Answer play_arrowquestion_answer113) Hydroxamic acid test is employed to detect
A) ketones done clear
B) aldehydes done clear
C) esters done clear
D) amides done clear
View Answer play_arrowquestion_answer114) Picric acid is a stronger acid than acetic acid and benzoic acid. It contains
A) \[-\text{S}{{\text{O}}_{\text{3}}}\text{H}\]group done clear
B) two\[-COOH\] groups done clear
C) phenolic group done clear
D) three \[-COOH\]groups done clear
View Answer play_arrowquestion_answer115) Benzamide can be converted into benzonitrile with
A) \[{{H}_{3}}{{O}^{+}}\] done clear
B) \[O{{H}^{-}}/{{H}_{2}}O\] done clear
C) KCN done clear
D) \[{{P}_{2}}{{O}_{5}}\] done clear
View Answer play_arrowquestion_answer116) The most basic compound in the following is
A) \[N{{H}_{3}}\] done clear
B) \[~C{{H}_{3}}N{{H}_{2}}\] done clear
C) \[HN{{(C{{H}_{3}})}_{2}}\] done clear
D) \[N{{(C{{H}_{3}})}_{3}}\] done clear
View Answer play_arrowquestion_answer117) The compound with foul odour among the following is-
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer118) Nitration of nitrobenzene at \[125{}^\circ C\] with mixed acids gives
A) meto-dinitrobenzene done clear
B) ortho-dinitrobenzene done clear
C) para-dinitrobenzene done clear
D) 1, 3, 5-trinitro benzene done clear
View Answer play_arrowquestion_answer119) The \[\alpha -\]amino acid which does not give purple colour in the ninhydrin test is
A) proline done clear
B) glycine done clear
C) lysine done clear
D) aspartic acid done clear
View Answer play_arrowquestion_answer120) The anomeric carbon in \[\text{D}\,\text{(+)}\]glucose is
A) \[C-1\]carbon done clear
B) \[C-2\]carbon done clear
C) \[C-5\]carbon done clear
D) \[C-6\] carbon done clear
View Answer play_arrowquestion_answer121) The stoichiometry of the following reaction is \[{{K}_{2}}{{S}_{2}}{{O}_{8}}(aq)+2KI(aq)\to 2{{K}_{2}}S{{O}_{4}}(aq)+{{I}_{2}}(aq)\]
A) 2:2 done clear
B) 1:1 done clear
C) 1:2 done clear
D) 2:1 done clear
View Answer play_arrowquestion_answer122) Of two oxides of iron, the first contained 22% and the second contained 30% of oxygen by weight. The ratio of weights of iron in the two oxides that combine with the same weight of oxygen, is
A) 3:2 done clear
B) 2:1 done clear
C) 1:2 done clear
D) 1:1 done clear
View Answer play_arrowquestion_answer123) The scientist who proposed the atomic model based on the quantization of energy for the first time is
A) Max Planck done clear
B) Niels Bohr done clear
C) de-Broglie done clear
D) Heisenberg done clear
View Answer play_arrowquestion_answer124) Which one of the following is the set of correct quantum numbers of an electron in 3d orbital?
A) \[~n=3,l=0,m=0,s=-\text{ }1/2\] done clear
B) \[~n=2,l=3,m=0,s=+1/2\] done clear
C) \[~n=3,l=1,m=0,s=-1/2\] done clear
D) \[~n=3,l=2,m=1,s=+\,1/2\] done clear
View Answer play_arrowquestion_answer125) Electron density in the YZ plane of \[3{{d}_{{{x}^{2}}-{{y}^{2}}}}\] orbital is
A) zero done clear
B) 0.50 done clear
C) 0.75 done clear
D) 0.90 done clear
View Answer play_arrowquestion_answer126) The half-life period of a radioactive isotope is 4.8 min. Starting with 1 mg of the isotope, how much of it would remain after 10 min?
A) 0.5 mg done clear
B) 0.726 mg done clear
C) 0.126 mg done clear
D) 0.236 mg done clear
View Answer play_arrowquestion_answer127) The number of beta particles emitted in the radioactive decay series from \[^{238}{{U}_{92}}\]to \[^{206}P{{b}_{82}}\]is
A) 10 done clear
B) 8 done clear
C) 6 done clear
D) 2 done clear
View Answer play_arrowquestion_answer128) What happens to the yield on application of high pressure in the Habefs synthesis of ammonia?
A) Increases done clear
B) Decreases done clear
C) Unaffected done clear
D) Reaction stops done clear
View Answer play_arrowquestion_answer129) In the reaction\[{{H}_{2}}(g)+C{{l}_{2}}(g)\rightleftharpoons 2HCl(g)\]
A) \[{{K}_{p}}\ne {{K}_{c}}\] done clear
B) \[{{K}_{p}}={{K}_{c}}\] done clear
C) \[{{K}_{p}}>{{K}_{c}}\] done clear
D) \[{{K}_{p}}<{{K}_{c}}\] done clear
View Answer play_arrowquestion_answer130) pH of an aqueous solution containing \[{{10}^{-8}}mol/L\]of \[HCl\]is
A) 8 done clear
B) 10 done clear
C) 6.96 done clear
D) 12 done clear
View Answer play_arrowquestion_answer131) An aqueous solution contains \[N{{i}^{2+}},C{{o}^{2+}}\]and\[P{{b}^{2+}}\]ions at equal concentrations. The solubility product of \[\text{NiS, PbS}\]and \[\text{CoS}\]in water at \[\text{25}{{\,}^{\text{o}}}\text{C}\]are \[\text{1}\text{.4}\times \text{1}{{\text{0}}^{-24}},\]and\[3\times {{10}^{-26}},\]respectively. Indicate which of these ions will be precipitated first and last when sulphide concentration is progressively increased from zero?
A) NiS and PbS done clear
B) NiS and CoS done clear
C) CoS and NiS done clear
D) PbS and NiS done clear
View Answer play_arrowquestion_answer132) A reaction involving A, B and C as reactants is found to obey the rate law, rate \[=k{{[A]}^{x}}{{[B]}^{y}}{{[C]}^{z}}.\]When the concentrations of A, B and C are doubled separately, the rate is also found to increase two, zero and four times respectively. The overall order of the reaction is
A) 1 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer133) The units of the rate of a second order reaction are
A) \[\text{tim}{{\text{e}}^{-1}}\] done clear
B) \[\text{mol}\,{{\text{L}}^{-1}}\,\text{tim}{{\text{e}}^{-1}}\] done clear
C) \[\text{L}\,\text{mol}{{\,}^{-1}}\,\text{tim}{{\text{e}}^{-1}}\] done clear
D) \[{{\text{L}}^{2}}\,\text{mol}{{\,}^{-2}}\,\text{tim}{{\text{e}}^{-1}}\] done clear
View Answer play_arrowquestion_answer134) Activation energy of a reaction
A) is independent of temperature done clear
B) increases with temperature done clear
C) gets doubled for every 10 degree rise in temperature done clear
D) decreases with temperature done clear
View Answer play_arrowquestion_answer135) Which one of the following concentration units is independent of temperature?
A) Normality done clear
B) Molarity done clear
C) Molality done clear
D) ppm done clear
View Answer play_arrowquestion_answer136) Maximum lowering of vapour pressure is observed in the case of
A) 0.1 M glucose done clear
B) \[0.1\text{ }M\text{ }BaC{{l}_{2}}\] done clear
C) \[\text{ }\!\!~\!\!\text{ 0}\text{.1 M MgS}{{\text{O}}_{\text{4}}}\] done clear
D) \[\text{ }\!\!~\!\!\text{ 0}\text{.1 NaCl}\] done clear
View Answer play_arrowquestion_answer137) A solution containing 4 g of polyvinyl chloride polymer in one litre of dioxane was found to have an osmotic pressure of \[\text{4}\text{.1}\times {{10}^{-4}}\text{atm}\]at \[\text{27}{{\,}^{\text{o}}}\text{C}\text{.}\] The approximate molecular weight of the polymer is
A) 1500 done clear
B) 10,000 done clear
C) \[\text{2}\text{.4}\times \text{1}{{\text{0}}^{5}}\] done clear
D) \[\text{2}\times \text{1}{{\text{0}}^{12}}\] done clear
View Answer play_arrowquestion_answer138) Abnormal colligative properties are observed only when the dissolved non-volatile solute in a given dilute solution
A) is a non-electrolyte done clear
B) offers an intense colour done clear
C) associates or dissociates done clear
D) offers no colour done clear
View Answer play_arrowquestion_answer139) We believe in the laws of thermodynamics because they are
A) theoretical done clear
B) derived based on mathematical analysis done clear
C) empirical and nobody disproved done clear
D) mere statements done clear
View Answer play_arrowquestion_answer140) The latent heat of fusion of ice at \[0{{\,}^{o}}C\]is\[\text{80}\,\text{cal/g}\text{.}\]Entropy change \[\text{(}\Delta S\text{)}\] accompanying the melting of 1 g of ice at \[0{{\,}^{o}}C\]would be (units:\[cal/g/K\])
A) 273 done clear
B) 8.0 done clear
C) 0.0 done clear
D) 0.293 done clear
View Answer play_arrowquestion_answer141) \[\Delta H\] for the reaction, \[C(graphite)+2{{H}_{2}}(g)\xrightarrow{{}}C{{H}_{4}}(g)\]at \[298\,K\]and 1 atm is\[~-\text{ }17900\text{ cal}\text{.}\] The \[\Delta E\]for the above conversion would be
A) \[-\text{ }17900\text{ cal}\] done clear
B) \[\text{ }\!\!~\!\!\text{ 17900 cal}\] done clear
C) \[\text{17308 cal}\] done clear
D) \[~-\text{ }17308\text{ cal}\] done clear
View Answer play_arrowquestion_answer142) Which one of the following is spontaneous at all temperatures?
A) \[{{H}_{2}}(g)\xrightarrow{{}}2{{H}_{\text{atom}}}\] \[\Delta {{H}^{o}}=436\,kJ,\Delta {{S}^{o}}=90.7\,\text{eu}\] done clear
B) \[\frac{1}{2}{{N}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}NO(g);\] \[\Delta {{H}^{o}}=90.3\,kJ,\Delta {{S}^{o}}=3.0\,\text{eu}\] done clear
C) \[2N{{O}_{2}}(g)\xrightarrow{{}}{{N}_{2}}{{O}_{4}}(g)\] \[\Delta {{H}^{o}}=-56.0\,kJ\,\Delta {{S}^{o}}=-17.7\text{eu}\] done clear
D) \[{{H}_{2}}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l)+\frac{1}{2}{{O}_{2}}(g)\] \[\Delta {{H}^{o}}=-98.3\,kJ\Delta {{S}^{o}}=80.0\,\text{eu}\] done clear
View Answer play_arrowquestion_answer143) During a redox titration involving a solution containing \[\text{F}{{\text{e}}^{\text{2+}}}\]ions against\[\text{MnO}_{4}^{-}\]in the presence of excess of \[{{\text{H}}^{\text{+}}}\]ions, the number of electrons that gets transferred is.
A) 6 done clear
B) 5 done clear
C) 4 done clear
D) 2 done clear
View Answer play_arrowquestion_answer144) The oxidation state of sulphur in sodium tetrathionate \[\text{(N}{{\text{a}}_{2}}{{\text{S}}_{4}}{{\text{O}}_{6}}\text{)}\]is
A) 2 done clear
B) 0 done clear
C) 2.5 done clear
D) 3.5 done clear
View Answer play_arrowquestion_answer145) Galvanic cell is a device in which
A) chemical energy is converted into electrical energy done clear
B) electrical energy is converted into chemical energy done clear
C) chemical energy is seen in the form of heat done clear
D) thermal energy from an outside source is used to drive the cell reaction done clear
View Answer play_arrowquestion_answer146) The relationship between Gibbs' free energy change\[(\Delta G)\]and emf\[(E)\]of a reversible electrochemical cell is given by
A) \[\Delta G=nFE\] done clear
B) \[\Delta G=nF/E\] done clear
C) \[\Delta G=-nFE\] done clear
D) \[\Delta G=E/nF\] done clear
View Answer play_arrowquestion_answer147) The units of van der Waals' constants a, b respectively, are
A) \[\text{L}\,\,\text{at}{{\text{m}}^{\text{2}}}\,\text{mo}{{\text{l}}^{-1}}\]and \[\text{mo}{{\text{l}}^{-1}}\] done clear
B) \[\text{L}\,\,\text{atm}\,\text{mo}{{\text{l}}^{2}}\]and \[\text{mol L}\] done clear
C) \[{{\text{L}}^{2}}\,\,\text{atm}\,\text{mo}{{\text{l}}^{-2}}\]and \[\text{mo}{{\text{l}}^{-1}}\text{ L}\] done clear
D) \[{{\text{L}}^{-2}}\,\,\text{at}{{\text{m}}^{-1}}\,\text{mo}{{\text{l}}^{-1}}\]and \[\text{L}\,\text{mo}{{\text{l}}^{-2}}\] done clear
View Answer play_arrowquestion_answer148) Identify the pair of gases that have equal rates of diffusion
A) CO, NO done clear
B) Np.CO done clear
C) \[{{N}_{2}}O,C{{O}_{2}}\] done clear
D) \[~C{{O}_{2}},N{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer149) For AX ionic crystal to exist in bcc structure, the ratio of radii \[\left( \frac{{{r}_{cation}}}{{{r}_{anion}}} \right)\] should be
A) between 0.41 and 0.73 done clear
B) greater than 0.73 done clear
C) less than 0.41 done clear
D) equal to 1.0 done clear
View Answer play_arrowquestion_answer150) Identify the correct statement for the adsorption of a real gas on charcoal at 1 atm and \[\text{15}{{\,}^{\text{o}}}\text{C}\text{.}\]
A) gases which are small in molecular size are adsorbed more done clear
B) decrease in pressure increases the extent of adsorption done clear
C) gases which are easily liquefiable are adsorbed more in quantity done clear
D) gas which has a behaviour similar to an inert gas is adsorbed more done clear
View Answer play_arrowquestion_answer151) The probability that number selected at random from the number 1, 2, 3, 4, 5, 6, 7, 8, ..., 100 is a prime, is
A) \[0.4\] done clear
B) \[0.25\] done clear
C) \[0.45\] done clear
D) \[0.43\] done clear
View Answer play_arrowquestion_answer152) \[\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{m}}-1}{{{x}^{n}}-1}\]is equal to
A) \[\frac{n}{m}\] done clear
B) \[\frac{m}{n}\] done clear
C) \[\frac{2m}{n}\] done clear
D) \[\frac{2n}{m}\] done clear
View Answer play_arrowquestion_answer153) \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{{{e}^{5x}}-{{e}^{4x}}}{x}\]is equal to
A) \[1\] done clear
B) \[2\] done clear
C) \[4\] done clear
D) \[5\] done clear
View Answer play_arrowquestion_answer154) If the function s\[f:R\to R\] given by \[f(x)=\left\{ \begin{matrix} x+a, & if & x\le 1 \\ 3-{{x}^{2}}, & if & x>1 \\ \end{matrix} \right.\] is continuous at \[x=1,\] then a is equal to
A) \[4\] done clear
B) \[3\] done clear
C) \[2\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer155) If n[A] denotes the number of elements in the Set A and if \[n(A)=4,\,n(B)=5,\] and \[(A\cap B)=3,\]then \[n[(A\times B)\cap (B\times A)]\] is equal to
A) \[8\] done clear
B) \[9\] done clear
C) \[10\] done clear
D) \[11\] done clear
View Answer play_arrowquestion_answer156) The function \[f:R\to R\] given by \[f(x)={{x}^{3}}-1\] is
A) a one-one function done clear
B) an onto function done clear
C) a bijection done clear
D) neither one-one nor onto done clear
View Answer play_arrowquestion_answer157) If \[\omega \] is a non-real cube root of unity, then \[1+\omega +{{\omega }^{2}}+....+{{\omega }^{101}}\] is equal to
A) \[1\] done clear
B) \[\omega \] done clear
C) \[{{\omega }^{2}}\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer158) The square roots of \[-7-24\sqrt{-1}\] are
A) \[\pm (4+3\sqrt{-1})\] done clear
B) \[\pm (3+4\sqrt{-1})\] done clear
C) \[\pm (3-4\sqrt{-1})\] done clear
D) \[\pm (4-3\sqrt{-1})\] done clear
View Answer play_arrowquestion_answer159) A value of k for which the quadratic equation \[{{x}^{2}}-2x(1+3k)+7(2k+3)=0\]has equal roots, is
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer160) If \[\alpha ,\beta \] are the roots of the equation \[{{x}^{2}}+ax+b=0,\] then \[\frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}}\]is equal to
A) \[\frac{{{a}^{2}}-2b}{{{b}^{2}}}\] done clear
B) \[\frac{{{b}^{2}}-2a}{{{b}^{2}}}\] done clear
C) \[\frac{{{a}^{2}}+2b}{{{b}^{2}}}\] done clear
D) \[\frac{{{b}^{2}}+2a}{{{b}^{2}}}\] done clear
View Answer play_arrowquestion_answer161) If \[|a|<1,\] then \[1+2a+3{{a}^{2}}+4{{a}^{3}}+.....\] is equal to
A) \[\frac{1}{1-a}\] done clear
B) \[\frac{1}{1+a}\] done clear
C) \[\frac{1}{1+{{a}^{2}}}\] done clear
D) \[\frac{1}{{{(1-a)}^{2}}}\] done clear
View Answer play_arrowquestion_answer162) If pth term of an arithmetic progression is q and the qth term is p, then 10th term is
A) \[p-q+10\] done clear
B) \[p+q+11\] done clear
C) \[p+q-9\] done clear
D) \[p+q-10\] done clear
View Answer play_arrowquestion_answer163) If \[{{C}_{0}},{{C}_{1}},{{C}_{2}},.....{{C}_{n}}\] denotes the binomial coefficients in the expansion of \[{{(1+x)}^{n}},\]then \[{{C}_{0}}+\frac{{{C}_{1}}}{2}+\frac{{{C}_{2}}}{3}+....+\frac{{{C}_{n}}}{n+1}\] is equal to
A) \[\frac{{{2}^{n+1}}-1}{n+1}\] done clear
B) \[\frac{{{2}^{n}}-1}{n}\] done clear
C) \[\frac{{{2}^{n-1}}-1}{n-1}\] done clear
D) \[\frac{{{2}^{n+1}}-1}{n+2}\] done clear
View Answer play_arrowquestion_answer164) The coefficient of \[{{x}^{r}}\] in the expansion of \[{{(1-x)}^{-2}}\]is
A) \[r\] done clear
B) \[r+1\] done clear
C) \[r+3\] done clear
D) \[r-1\] done clear
View Answer play_arrowquestion_answer165) The number of permutations of 4 letters that can be made out of the letters of the word EXAMINATION is
A) \[2454\] done clear
B) \[2452\] done clear
C) \[2450\] done clear
D) \[1806\] done clear
View Answer play_arrowquestion_answer166) \[\frac{1}{3!}+\frac{2}{5!}+\frac{3}{7!}+...\] is equal to
A) \[\frac{{{e}^{-1}}}{2}\] done clear
B) \[e\] done clear
C) \[\frac{e}{4}\] done clear
D) \[\frac{e}{6}\] done clear
View Answer play_arrowquestion_answer167) \[\frac{x-y}{x}+\frac{1}{2}{{\left( \frac{x-y}{x} \right)}^{2}}+\frac{1}{3}{{\left( \frac{x-y}{x} \right)}^{3}}+....\] is equal to
A) \[{{\log }_{e}}\,(x-y)\] done clear
B) \[{{\log }_{e}}\,(x+y)\] done clear
C) \[{{\log }_{e}}\,\left( \frac{x}{y} \right)\] done clear
D) \[{{\log }_{e}}\,\,xy\] done clear
View Answer play_arrowquestion_answer168) The standard deviation of the first n natural numbers is
A) \[\frac{\sqrt{{{n}^{2}}+1}}{12}\] done clear
B) \[\frac{{{n}^{2}}-1}{12}\] done clear
C) \[\sqrt{\frac{{{n}^{2}}-1}{12}}\] done clear
D) \[\frac{{{n}^{2}}+1}{12}\] done clear
View Answer play_arrowquestion_answer169) A point P moves so that the sum of its distances from \[(-ae,\,0)\]and \[(ae,\,0)\] is\[2a\]. Then the locus of P is
A) \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1\] done clear
B) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1\] done clear
C) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1+{{e}^{2}})}=1\] done clear
D) \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}(1+{{e}^{2}})}=1\] done clear
View Answer play_arrowquestion_answer170) The length of the perpendicular from the origin to the line \[\frac{x\,\,\sin \alpha }{b}-\frac{y\,\cos \,\alpha }{a}-1=0\] is
A) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,{{\cos }^{2}}\alpha -{{b}^{2}}\,{{\sin }^{2}}\alpha }}\] done clear
B) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,{{\cos }^{2}}\alpha +{{b}^{2}}\,{{\sin }^{2}}\alpha }}\] done clear
C) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,si{{n}^{2}}\alpha -{{b}^{2}}\,{{\cos }^{2}}\alpha }}\] done clear
D) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,si{{n}^{2}}\alpha +{{b}^{2}}\,{{\cos }^{2}}\alpha }}\] done clear
View Answer play_arrowquestion_answer171) The distance between the parallel lines \[y=x+a,\,\,y=x+b\]is
A) \[\frac{|b-a|}{\sqrt{2}}\] done clear
B) \[|a-b|\] done clear
C) \[|a+b|\] done clear
D) \[\frac{|a+b|}{\sqrt{2}}\] done clear
View Answer play_arrowquestion_answer172) The line passing through the point of intersection of \[x+y=2,\,x-y=0\] and is parallel to \[x+2y=5\]is
A) \[x+2y=1\] done clear
B) \[x+2y=2\] done clear
C) \[x+2y=4\] done clear
D) \[x+2y=3\] done clear
View Answer play_arrowquestion_answer173) If the line \[y=7x-25\]meets the circle \[{{x}^{2}}+{{y}^{2}}=25\]in the points A, B then the distance between A and B is
A) \[\sqrt{10}\] done clear
B) \[10\] done clear
C) \[5\sqrt{2}\] done clear
D) \[5\] done clear
View Answer play_arrowquestion_answer174) One of the directrices of the ellipse \[8{{x}^{2}}+6{{y}^{2}}-16x+12y+13=0\]is
A) \[3y-3=\sqrt{6}\] done clear
B) \[3y+3=\sqrt{6}\] done clear
C) \[y+1=\sqrt{3}\] done clear
D) \[y-1=-\sqrt{3}\] done clear
View Answer play_arrowquestion_answer175) If OAB is an equilateral triangle inscribed in the parabola \[{{y}^{2}}=4ax\] with O as the vertex, then the length of the side of the\[\Delta \,\,OAB\] is
A) \[8\,a\,\sqrt{3}\] done clear
B) \[4\,a\,\sqrt{3}\] done clear
C) \[2\,a\,\sqrt{3}\] done clear
D) \[a\,\sqrt{3}\] done clear
View Answer play_arrowquestion_answer176) If \[x\,\sin \theta =y\,\cos \theta =\frac{2z\,\tan \theta }{1-{{\tan }^{2}}\theta },\] then \[4{{z}^{2}}({{x}^{2}}+{{y}^{2}})\] is equal to
A) \[{{({{x}^{2}}+{{y}^{2}})}^{3}}\] done clear
B) \[{{({{x}^{2}}-{{y}^{2}})}^{3}}\] done clear
C) \[{{({{x}^{2}}-{{y}^{2}})}^{2}}\] done clear
D) \[{{({{x}^{2}}+{{y}^{2}})}^{2}}\] done clear
View Answer play_arrowquestion_answer177) \[\tan {{25}^{o}}+\tan {{20}^{o}}+\tan {{25}^{o}}\,\tan {{20}^{o}}\] is equal to
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer178) If \[\cos x=3\cos y,\] then \[2\tan \frac{y-x}{2}\] is equal to
A) \[\cot \left( \frac{y-x}{2} \right)\] done clear
B) \[\cot \left( \frac{x+y}{4} \right)\] done clear
C) \[\cot \left( \frac{y-x}{4} \right)\] done clear
D) \[\cot \left( \frac{y-x}{4} \right)\] done clear
View Answer play_arrowquestion_answer179) In any \[\Delta \,ABC\] under usual notation, \[a(b\,\cos \,C-c\,\cos B)\] is equal to
A) \[{{b}^{2}}-{{c}^{2}}\] done clear
B) \[{{c}^{2}}-{{b}^{2}}\] done clear
C) \[\frac{{{b}^{2}}-{{c}^{2}}}{2}\] done clear
D) \[\frac{{{c}^{2}}-{{b}^{2}}}{2}\] done clear
View Answer play_arrowquestion_answer180) If \[4\,\sin \,A=4\,\sin B=3\,\sin \,C\] in a triangle ABC, then \[\cos \,\,C\] is equal to
A) \[1/3\] done clear
B) \[1/9\] done clear
C) \[1/27\] done clear
D) \[~1/18\] done clear
View Answer play_arrowquestion_answer181) If \[\cos \,x\ne \frac{1}{2},\] then the solutions of \[\cos \,x+\cos \,2x+\cos \,3x=0\]are
A) \[2n\pi \pm \frac{\pi }{4},n\in Z\] done clear
B) \[2n\pi \pm \frac{\pi }{3},n\in Z\] done clear
C) \[2n\pi \pm \frac{\pi }{6},n\in Z\] done clear
D) \[2n\pi \pm \frac{\pi }{2},n\in Z\] done clear
View Answer play_arrowquestion_answer182) \[{{\tan }^{-1}}\,\frac{x}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\]is equal to
A) \[2{{\sin }^{-1}}\frac{x}{a}\] done clear
B) \[{{\sin }^{-1}}\frac{2x}{a}\] done clear
C) \[{{\sin }^{-1}}\frac{x}{a}\] done clear
D) \[{{\cos }^{-1}}\frac{x}{a}\] done clear
View Answer play_arrowquestion_answer183) The solution of \[{{\tan }^{-1}}\,2\theta +{{\tan }^{-1}}3\theta =\frac{\pi }{4}\] is
A) \[\frac{1}{\sqrt{3}}\] done clear
B) \[\frac{1}{3}\] done clear
C) \[\frac{1}{6}\] done clear
D) \[\frac{1}{\sqrt{6}}\] done clear
View Answer play_arrowquestion_answer184) The number of solutions of \[\sin x=\sin 2x\]between \[\frac{-\pi }{2}\] and \[\frac{\pi }{2}\] is
A) \[3\] done clear
B) \[2\] done clear
C) \[1\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer185) If \[y=\frac{3a{{t}^{2}}}{1+{{t}^{3}}},\,x=\frac{3at}{1+{{t}^{3}}},\] then \[\frac{dy}{dx}\] is equal to
A) \[\frac{t(2-{{t}^{3}})}{(1-2{{t}^{3}})}\] done clear
B) \[\frac{t(2+{{t}^{3}})}{(1-2{{t}^{3}})}\] done clear
C) \[\frac{t(2-{{t}^{3}})}{(1+2{{t}^{3}})}\] done clear
D) \[\frac{t(2+{{t}^{3}})}{(1+2{{t}^{3}})}\] done clear
View Answer play_arrowquestion_answer186) If \[y={{\sec }^{-1}}\left( \frac{1}{\sqrt{1-{{x}^{2}}}} \right),\] then \[\frac{dy}{dx}\] is equal to
A) \[\frac{1}{\sqrt{1-{{x}^{2}}}}\] done clear
B) \[\frac{2}{\sqrt{1-{{x}^{2}}}}\] done clear
C) \[\frac{1}{\sqrt{1+{{x}^{2}}}}\] done clear
D) \[\frac{2}{\sqrt{1+{{x}^{2}}}}\] done clear
View Answer play_arrowquestion_answer187) The point on the curve \[y={{x}^{3}}\]at which the tangent to the curve is parallel to the x axis, is
A) \[(2,2)\] done clear
B) \[(3,3)\] done clear
C) \[(4,4)\] done clear
D) \[(0,0)\] done clear
View Answer play_arrowquestion_answer188) The equation of normal to the curve \[{{x}^{2}}y={{x}^{2}}-3x+6\] at the point with abscissa \[x=3\]is
A) \[3x+27y=79\] done clear
B) \[27\text{ }x-3y=79\] done clear
C) \[27x+3y=79\] done clear
D) \[3x-27y=79\] done clear
View Answer play_arrowquestion_answer189) The function \[f(x)=2{{x}^{3}}+3{{x}^{2}}-12x+1\] decreases in the interval
A) \[(2,3)\] done clear
B) \[(1,2)\] done clear
C) \[(-2,1)\] done clear
D) \[(-3,-2)\] done clear
View Answer play_arrowquestion_answer190) The function \[f(x)={{x}^{2}}{{e}^{-x}}\] increases in the interval
A) \[(0,2)\] done clear
B) \[(2,3)\] done clear
C) \[(3,4)\] done clear
D) \[(4,5)\] done clear
View Answer play_arrowquestion_answer191) The number of real roots of \[f(x)=0,\]where \[f(x)=(x-1)(x-2)(x-3)(x-4)\] lying the interval \[(1,3)\] is
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer192) If \[{{x}^{y}}={{y}^{x}},\] then \[\frac{dy}{dx}\] is equal to
A) \[\frac{{{y}^{2}}-xy\,\log \,y}{{{x}^{2}}-xy\,\log \,x}\] done clear
B) \[\frac{{{y}^{2}}+xy\,\log \,y}{{{x}^{2}}+xy\,\log \,x}\] done clear
C) \[\frac{{{y}^{2}}-xy\,\log \,x}{{{x}^{2}}-xy\,\log \,y}\] done clear
D) \[\frac{{{y}^{2}}+xy\,\log \,y}{{{x}^{2}}-xy\,\log \,x}\] done clear
View Answer play_arrowquestion_answer193) Rectilinear motion is performed in accordance with the formulae \[s=\frac{2}{9}\sin \frac{\pi t}{2}+{{s}_{0}}.\] Then the acceleration at the end of the 1st second (in\[cm/{{s}^{2}}\]) is
A) \[\frac{{{\pi }^{2}}}{18}\] done clear
B) \[\frac{{{\pi }^{2}}}{7}\] done clear
C) \[\frac{-{{\pi }^{2}}}{9}\] done clear
D) \[\frac{-{{\pi }^{2}}}{18}\] done clear
View Answer play_arrowquestion_answer194) A value on x in the interval \[(1,2)\] such that \[f'(x)=0,\] where \[f(x)={{x}^{3}}-3{{x}^{2}}+2x+10\] is
A) \[\frac{3+\sqrt{3}}{3}\] done clear
B) \[\frac{3+\sqrt{2}}{2}\] done clear
C) \[1+\sqrt{2}\] done clear
D) \[\sqrt{2}\] done clear
View Answer play_arrowquestion_answer195) Given that the force acting on a material point is inversely proportional to the velocity of the moving point. Then the kinetic energy of the point is a ...... function of time.
A) exponential done clear
B) linear done clear
C) second degree done clear
D) non-linear done clear
View Answer play_arrowquestion_answer196) If \[f(x)={{x}^{2}}-5x,A=\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \\ \end{matrix} \right],\] then \[f(A)\] is equal to
A) \[\left[ \begin{matrix} -7 & 0 \\ 0 & -7 \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} 0 & -7 \\ -7 & 0 \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} 0 & 7 \\ 7 & 0 \\ \end{matrix} \right]\] done clear
View Answer play_arrowquestion_answer197) If A is a square matrix. A' its transpose, then \[\frac{1}{2}(A-A')\]is
A) a symmetric matrix done clear
B) a skew symmetric matrix done clear
C) a unit matrix done clear
D) an elementary matrix done clear
View Answer play_arrowquestion_answer198) The number of solutions of the system of equations \[x-y+z=2\] \[2x+y-z=5\] \[4x+y+z=10\] is
A) \[\infty \] done clear
B) \[1\] done clear
C) \[2\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer199) The adjoin of the matrix\[\left[ \begin{matrix} \cos \,\theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right]\]is
A) \[\left[ \begin{matrix} \cos \,\theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} sin\,\theta & \cos \theta \\ \cos \theta & sin\theta \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} \cos \,\theta & sin\theta \\ -sin\theta & \cos \theta \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} -sin\,\theta & \cos \theta \\ \cos \theta & sin\theta \\ \end{matrix} \right]\] done clear
View Answer play_arrowquestion_answer200) If \[x\ne 0,\,\left| \begin{matrix} x+1 & 2x+1 & 3x+1 \\ 2x & 4x+3 & 6x+3 \\ 4x+4 & 6x+4 & 8x+4 \\ \end{matrix} \right|=0,\] then \[x+1\] is equal to
A) \[x\] done clear
B) \[0\] done clear
C) \[2x\] done clear
D) \[3x\] done clear
View Answer play_arrowquestion_answer201) \[\left| \begin{matrix} 1 & x & y+z \\ 1 & y & z+x \\ 1 & z & x+y \\ \end{matrix} \right|\] is equal to
A) \[0\] done clear
B) \[x\] done clear
C) \[y\] done clear
D) \[xyz\] done clear
View Answer play_arrowquestion_answer202) If P is any point with in a triangle ABC, then \[\overrightarrow{PA}+\overrightarrow{CP}\] is equal to
A) \[\overrightarrow{AC}+\overrightarrow{CB}\] done clear
B) \[\overrightarrow{BC}+\overrightarrow{BA}\] done clear
C) \[\overrightarrow{CB}+\overrightarrow{AB}\] done clear
D) \[\overrightarrow{CB}+\overrightarrow{BA}\] done clear
View Answer play_arrowquestion_answer203) If the vector \[3i-2\hat{j}-5\hat{k}\] is perpendicular to \[c\hat{k}-\hat{j}+6\hat{i},\] then c is equal to
A) \[3\] done clear
B) \[4\] done clear
C) \[5\] done clear
D) \[6\] done clear
View Answer play_arrowquestion_answer204) The vector \[\vec{a}\times (\vec{b}\times \vec{c})\] is coplanar with the vectors
A) \[\vec{b},\,\vec{c}\] done clear
B) \[\vec{a},\,\vec{b}\] done clear
C) \[\vec{a},\,\vec{c}\] done clear
D) \[\vec{a},\,\,\vec{b}\,,\vec{c}\] done clear
View Answer play_arrowquestion_answer205) If \[\vec{a},\,\,\vec{b}\,\] are any two vectors, then \[(2\vec{a}+3\vec{b})\times (5\vec{a}+7\vec{b})+\vec{a}\times \vec{b}\] is equal to
A) \[\vec{0}\] done clear
B) \[0\] done clear
C) \[\vec{a}\times \vec{b}\] done clear
D) \[\vec{b}\times \vec{a}\] done clear
View Answer play_arrowquestion_answer206) A unit vector perpendicular to \[\hat{i}-\hat{j}+\hat{k}\]and \[\hat{i}+\hat{j}-\hat{k}\] is
A) \[\frac{\hat{k}+\hat{i}}{\sqrt{2}}\] done clear
B) \[\frac{\hat{j}+\hat{k}}{\sqrt{2}}\] done clear
C) \[\frac{\hat{i}-\hat{k}}{\sqrt{3}}\] done clear
D) \[\frac{\hat{j}-\hat{k}}{\sqrt{2}}\] done clear
View Answer play_arrowquestion_answer207) If \[\vec{a}\times \vec{b}=\vec{c}\times \vec{d}\]and \[\vec{a}\times \vec{c}=\vec{b}\times \vec{d},\] then \[\vec{a}-\vec{d}\] is parallel to
A) \[\vec{b}+\vec{c}\] done clear
B) \[\vec{b}-2\vec{c}\] done clear
C) \[\vec{b}+2\vec{c}\] done clear
D) \[\vec{b}-\vec{c}\] done clear
View Answer play_arrowquestion_answer208) \[3a{{\int_{0}^{1}{\left( \frac{ax-1}{a-1} \right)}}^{2}}\,\,dx\]is equal to
A) \[a-1+{{(a-1)}^{-2}}\] done clear
B) \[a+{{a}^{-2}}\] done clear
C) \[a-{{a}^{-2}}\] done clear
D) \[{{a}^{2}}+\frac{1}{{{a}^{2}}}\] done clear
View Answer play_arrowquestion_answer209) \[\int_{-\pi /2}^{\pi /2}{\frac{dx}{1+\cos x}}\] is equal to
A) \[0\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer210) \[\int{\sin \,\,\sqrt{x}}\,\,dx\] is equal to
A) \[\sin \sqrt{x}-\sqrt{x}\,\cos \,\sqrt{x}\] done clear
B) \[2(\sin \,\sqrt{x}-\sqrt{x}\,\cos \,\sqrt{x})+c\] done clear
C) \[\cos \,\sqrt{x}-\sqrt{x}\,\sin \,\sqrt{x}+c\] done clear
D) \[2(\cos \sqrt{x}-\sqrt{x}\,\sin \sqrt{x})+c\] done clear
View Answer play_arrowquestion_answer211) \[\int{\frac{\sqrt{x}}{x+1}\,dx}\] is equal to
A) \[2(\sqrt{x}+{{\tan }^{-1}}\sqrt{x})+c\] done clear
B) \[2(\sqrt{x}+{{\cot }^{-1}}\sqrt{x})+c\] done clear
C) \[2(\sqrt{x}-{{\cot }^{-1}}-\sqrt{x})+c\] done clear
D) \[2(\sqrt{x}-ta{{n}^{-1}}\sqrt{x})+c\] done clear
View Answer play_arrowquestion_answer212) The area (in square unit) bounded by the curves \[y={{x}^{3}}\]and \[y=x\] is
A) \[1/2\text{ }sq\text{ }unit\] done clear
B) \[1/4\text{ }sq\text{ }unit\] done clear
C) \[1/8\text{ }sq\text{ }unit\] done clear
D) \[1/16\text{ }sq\text{ }unit\] done clear
View Answer play_arrowquestion_answer213) The area (in square unit) bounded by the curves \[4y={{x}^{2}}\]and \[2y=6-{{x}^{2}}\]is
A) \[8\] done clear
B) \[6\] done clear
C) \[4\] done clear
D) \[10\] done clear
View Answer play_arrowquestion_answer214) The general solution of the differential equation \[\frac{dy}{dx}=\frac{(1+{{y}^{2}})}{xy(1+{{x}^{2}})}\] is
A) \[(1+{{x}^{2}})(1+{{y}^{2}})=c\] done clear
B) \[(1+{{x}^{2}})(1+{{y}^{2}})=c{{x}^{2}}\] done clear
C) \[(1-{{x}^{2}})(1-{{y}^{2}})=c\] done clear
D) \[(1+{{x}^{2}})(1+{{y}^{2}})=c{{y}^{2}}\] done clear
View Answer play_arrowquestion_answer215) A particle moves along a straight line with the law of motion given by \[{{s}^{2}}=a{{t}^{2}}+2bt+c\]. Then the acceleration varies are
A) \[1/{{s}^{3}}\] done clear
B) \[1/s\] done clear
C) \[~1/{{s}^{4}}\] done clear
D) \[1/{{s}^{2}}\] done clear
View Answer play_arrowquestion_answer216) A point is moving with uniform acceleration in the eleventh and fifteenth seconds from the commencement it moves through 720 and 960 cm respectively. Its initial velocity and the acceleration with which it moves are
A) \[60\text{ }m/s,\text{ }40\text{ }m/{{s}^{2}}\] done clear
B) \[70\text{ }m/s,\text{ }30\text{ }m/{{s}^{2}}\] done clear
C) \[90\text{ }m/s,\text{ }60\text{ }m/{{s}^{2}}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer217) A particle of mass m is projected from a fixed point 0 into the air with velocity u in a direction making an angle a with the horizontal. Then the motion of the particle describes a parabola with the latusrectum is
A) \[\frac{2}{g}{{(horizontal\text{ }velocity)}^{2}}\] done clear
B) \[\frac{2}{g}(vertical\text{ }velocity)\] done clear
C) \[\frac{2}{{{g}^{2}}}{{(horizontal\text{ }velocity)}^{2}}\] done clear
D) \[\frac{2}{{{g}^{2}}}{{(vertical\text{ }velocity)}^{2}}\] done clear
View Answer play_arrowquestion_answer218) The vector equation of the line passing through the points \[(3,2,1)\] and \[(-2,1,3)\] is
A) \[\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}-\hat{j}+2\hat{k})\] done clear
B) \[\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}+\hat{j}+\hat{k})\] done clear
C) \[\vec{r}=-2\hat{i}+\hat{j}+3\hat{k}+\lambda (5\hat{i}+\hat{j}+2\hat{k})\] done clear
D) \[\vec{r}=-2\hat{i}+\hat{j}+\hat{k}+\lambda (5\hat{i}+\hat{j}+2\hat{k})\] done clear
View Answer play_arrowquestion_answer219) The line \[\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\] meets the plane \[2x+3y-z=-4\]in the point
A) \[(1,2,3)\] done clear
B) \[(-1,-1,-1)\] done clear
C) \[(2,1,3)\] done clear
D) \[(1,1,1)\] done clear
View Answer play_arrowquestion_answer220) The shortest distance between the lines \[1+x=2y=-12z\]and \[x=y+2=6z-6\]is
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer221) The foot of the perpendicular from \[(2,4,-1)\]to the line \[x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)\]
A) \[(-4,1,-3)\] done clear
B) \[(4,-1,-3)\] done clear
C) \[(-4,-1,3)\] done clear
D) \[(-4,-1,-3)\] done clear
View Answer play_arrowquestion_answer222) The radius of the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=x+2y+3z\]is
A) \[\frac{\sqrt{14}}{2}\] done clear
B) \[\sqrt{7}\] done clear
C) \[\frac{7}{2}\] done clear
D) \[\frac{\sqrt{7}}{2}\] done clear
View Answer play_arrowquestion_answer223) The distance between the planes \[2x-2y+z+3=0\]and \[4x-4y+2z+5=0\] is
A) \[3\] done clear
B) \[6\] done clear
C) \[\frac{1}{6}\] done clear
D) \[\frac{1}{3}\] done clear
View Answer play_arrowquestion_answer224) If B is a Boolean algebra and \[a,\,\,b\,\,\in \,B,\] then \[a.(a+b)\]is equal to
A) \[a\] done clear
B) \[b\] done clear
C) \[1\] done clear
D) \[a'\] done clear
View Answer play_arrowquestion_answer225) Let \[{{E}_{1}},{{E}_{2}}\] be two mutually exclusive events of an experiment with \[P(not\,{{E}_{2}})=0.6=P({{E}_{1}}\cup {{E}_{2}}).\]Then \[P({{E}_{1}})\] is equal to
A) \[0.1\] done clear
B) \[0.3\] done clear
C) \[0.4\] done clear
D) \[0.2\] done clear
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