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) \[\tan \,\,\theta \ge \,3{{\mu }_{s}}\]
B) \[\tan \,\,\theta >3{{\mu }_{s}}\]
C) \[\tan \,\,\theta \le 3{{\mu }_{s}}\]
D) \[\tan \,\,\theta <3{{\mu }_{s}}\]
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) \[2\,\,m\]
B) \[4\,\,m\]
C) \[5\,\,m\]
D) \[6\,\,m\]
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) \[g\]
B) \[\frac{g}{2}\]
C) \[\frac{g}{3}\]
D) \[\frac{g}{9}\]
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) \[5\times {{10}^{16}}/s\]
B) \[10\times {{10}^{16}}/s\]
C) \[15\times {{10}^{16}}/s\]
D) \[20\times {{10}^{-16}}/s\]
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) \[3.18\]
B) \[6.36\]
C) \[5.18\]
D) \[1.59\]
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
B) The speed is low at the wider end and high at the narrow end
C) The speed is same at both ends in a stream line flow
D) The liquid flows with uniform velocity in the tube
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) \[v\]
B) \[2v\]
C) \[4v\]
D) \[9v\]
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) \[\frac{2\,S}{R}\]
B) \[\frac{2\,R}{S}\]
C) \[\frac{2\,S}{{{R}^{2}}}\]
D) \[\frac{2{{R}^{2}}}{S}\]
View Answer play_arrowquestion_answer9) The average kinetic energy of a gas molecule is
A) proportional to pressure of gas
B) inversely proportional to volume of gas
C) inversely proportional to absolute temperature of gas
D) directly proportional to absolute temperature of gas
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) \[W=\mu {{C}_{P}}({{T}_{1}}-{{T}_{2}})\]
B) \[W=\mu {{C}_{V}}({{T}_{1}}-{{T}_{2}})\]
C) \[W=\mu {{C}_{P}}({{T}_{1}}+{{T}_{2}})\]
D) \[W=\mu {{C}_{V}}({{T}_{1}}+{{T}_{2}})\]
View Answer play_arrowquestion_answer11) For an ideal gas
A) \[{{C}_{P}}\] is less than \[{{C}_{V}}\]
B) \[{{C}_{P}}\] is equal to \[{{C}_{V}}\]
C) \[{{C}_{P}}\] is greater than \[{{C}_{V}}\]
D) \[{{C}_{P}}={{C}_{V}}=0\]
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) \[{{C}_{V}}=\frac{R}{2}\]
B) \[{{C}_{V}}=R\]
C) \[{{C}_{V}}=2R\]
D) \[{{C}_{V}}=3R\]
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)
B) \[{{\lambda }_{\max }}\] is proportional to square of absolute temperature \[({{T}^{2}})\]
C) \[{{\lambda }_{\max }}\] is inversely proportional to absolute temperature (T)
D) \[{{\lambda }_{\max }}\] is inversely proportional to square of absolute temperature \[({{T}^{2}})\] (\[{{\lambda }_{\max }}\] = wavelength whose energy density is greatest)
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) \[25\,f\]
B) \[5\,f\]
C) \[10\,f\]
D) \[f\]
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
B) a pipe open at both ends
C) closed at both ends
D) having holes like flute
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) \[2({{L}_{2}}+{{L}_{1}})\]
B) \[2({{L}_{2}}-{{L}_{1}})\]
C) \[2\left( {{L}_{2}}-\frac{{{L}_{1}}}{2} \right)\]
D) \[2\left( {{L}_{2}}+\frac{{{L}_{1}}}{2} \right)\]
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) \[\frac{1}{{{f}_{1}}+{{f}_{2}}}\]
B) \[\frac{2}{{{f}_{1}}-{{f}_{2}}}\]
C) \[\frac{2}{{{f}_{1}}+{{f}_{2}}}\]
D) \[\frac{1}{{{f}_{1}}-{{f}_{2}}}\]
View Answer play_arrowquestion_answer18) If a body is executing simple harmonic motion, then
A) at extreme positions, the total energy is zero
B) at equilibrium position, the total energy is in the form of potential energy
C) at equilibrium position, the total energy is in the form of kinetic energy
D) at extreme position, the total energy is infinite
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
B) direction from negative charge to positive charge
C) perpendicular to the line joining the two charges drawn at the centre and pointing upward direction
D) perpendicular to the line joining the two charges drawn at the centre and pointing downward direction
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) \[\vec{\tau }=\vec{P}\times \vec{E}\]
B) \[\vec{\tau }=\vec{P}.\vec{E}\]
C) \[\vec{\tau }=2(\vec{P}+\vec{E})\]
D) \[\vec{\tau }=(\vec{P}+\vec{E})\]
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) \[2\,\phi \]
B) \[\phi /2\]
C) \[\phi /4\]
D) \[\phi \]
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 \[\sigma \]
B) directly proportional to \[{{x}^{2}}\]
C) directly proportional to \[\sigma \]
D) inversely proportional to \[{{x}^{2}}\]
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) \[\frac{WQ}{X}\]
B) \[W\]
C) \[\frac{W}{Q}\]
D) \[WQ\]
View Answer play_arrowquestion_answer24) The capacitance C of a capacitor is
A) independent of the charge and potential of the capacitor
B) dependent on the charge and independent of potential
C) independent of the geometrical configuration of the capacitor
D) independent of the dielectric medium between the two conducting surfaces of the capacitor
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) \[\frac{4}{3}\mu F\]
B) \[\frac{24}{5}\mu F\]
C) \[9\,\mu F\]
D) \[5\,\mu F\]
View Answer play_arrowquestion_answer26) Metals have
A) zero resistivity
B) high resistivity
C) low resistivity
D) infinite resistivity
View Answer play_arrowquestion_answer27) The electric potential inside a conducting sphere
A) increases from centre to surface
B) decreases from centre to surface
C) remains constant from centre to surface
D) is zero at every point inside
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
B) \[\frac{eE}{m},\] in the direction of the field
C) \[\frac{em}{E},\] m the direction of the field
D) \[\frac{eE}{m},\] in the opposite direction of the field,
View Answer play_arrowquestion_answer29) Kirchhoff?s second law for the analysis of circuit is based on
A) conservation of charge
B) conservation of energy
C) conservation of both charge and energy
D) conservation of momentum of electron
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) \[0.4V\]
B) \[0.6V\]
C) \[1.2\text{ }V\]
D) \[1.5V\]
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
B) of current element \[d\,\vec{L}\]
C) perpendicular to both \[d\,\vec{L}\] and \[\vec{r}\]
D) perpendicular to \[\vec{L}\] only
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
B) the charge of the particle remains same
C) the magnetic force is parallel to velocity of the particle
D) the magnetic force is parallel to magnetic field
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
B) a low resistance r is connected in parallel with MCG
C) a low resistance r is connected in series With MCG
D) a high resistance R is connected in series with MCG
View Answer play_arrowquestion_answer34) Identify the correct statement from the following.
A) Cyclotron frequency is dependent on speed of the charged particle
B) Kinetic energy of charged particle in cyclotron does not dependent on its mass
C) Cyclotron frequency does not depend on speed of charged particle
D) Kinetic energy of charged particle in cyclotron is independent of its charge
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
B) the two currents are anti-parallel in direction
C) the magnetic lines of induction are parallel
D) the magnetic lines of induction are parallel to length of conductors
View Answer play_arrowquestion_answer36) The magnetic susceptibility of paramagnetic materials is
A) positive, but very high
B) negative, but small
C) negative but very high
D) positive, but small
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
B) the relative motion between the coil and magnet produces change in magnetic flux
C) only the magnet should be moved towards coil
D) only the coil should be moved towards magnet
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
B) the mutual inductance depends on the intrinsic magnetic property, like relative permeability of the material
C) the mutual inductance is independent of the magnetic property of the material
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
View Answer play_arrowquestion_answer39) The natural frequency \[({{\omega }_{0}})\] of oscillations in L-C circuit is given by
A) \[\frac{1}{2\pi }\frac{1}{\sqrt{LC}}\]
B) \[\frac{1}{2\pi }\,\sqrt{LC}\]
C) \[\frac{1}{\,\sqrt{LC}}\]
D) \[\sqrt{LC}\]
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) \[{{X}_{C}}+{{X}_{L}}=0\]
B) \[{{X}_{C}}=0\]
C) \[{{X}_{L}}=0\]
D) \[{{X}_{C}}-{{X}_{L}}=0\]
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 \[{{N}_{p}}\]
B) \[{{N}_{p}}\] is greater than \[{{N}_{s}}\]
C) \[{{N}_{s}}\] is equal to \[{{N}_{p}}\]
D) \[{{N}_{p}}=2{{N}_{s}}\]
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
B) when they have same frequency and a constant phase difference
C) when they have constant phase difference and different frequencies
D) when they have varying phase difference and different frequencies
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
B) can be changed only by changing the separation between the two slits
C) can be changed either by changing the wavelength or by changing the separation between two sources
D) is a universal constant and hence cannot be changed
View Answer play_arrowquestion_answer44) Colours in thin films are due to
A) diffraction phenomenon
B) scattering phenomenon
C) interference phenomenon
D) polarization phenomenon
View Answer play_arrowquestion_answer45) Brewster?s angle in terms of refractive index (n) of the medium
A) \[{{\tan }^{-1}}\,\sqrt{n}\]
B) \[{{\sin }^{-1}}\,n\]
C) \[{{\sin }^{-1}}\,\sqrt{n}\]
D) \[{{\tan }^{-1}}\,n\]
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
B) [A] and [B] are true
C) [A] and [C] are true
D) [B] and [C] are true
View Answer play_arrowquestion_answer47) The working of optical fibres is based on
A) dispersion of light
B) total internal reflection
C) polarization of light
D) interference of light
View Answer play_arrowquestion_answer48) First Bohr radius of an atom with \[Z=82\]is R. Radius of its third orbit is
A) \[9\,\,R\]
B) \[6\,\,R\]
C) \[3\,R\]
D) \[R\]
View Answer play_arrowquestion_answer49) The de-Broglie wavelength associated with a particle moving with momentum (p) and mass (m) is
A) \[\frac{h}{p}\]
B) \[\frac{h}{mp}\]
C) \[\frac{h}{{{p}^{2}}}\]
D) \[\frac{{{h}^{2}}}{{{p}^{2}}}\]
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 \[\frac{h}{2\pi }\]
B) integral multiple of h
C) integral multiple of \[\frac{h}{2\pi }\]
D) half integral multiple of h
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) \[\sqrt{v}=k{{Z}^{2}}\]
B) \[\sqrt{v}=\frac{h}{{{Z}^{2}}}\]
C) \[v=kZ\]
D) \[\sqrt{v}=kZ\]
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) \[\lambda {{N}^{2}}\]
B) \[\lambda N\]
C) \[\frac{\lambda }{N}\]
D) \[{{\lambda }^{2}}N\]
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) \[\frac{{{T}_{B}}}{{{T}_{A}}}\]
B) \[\frac{{{T}_{A}}}{{{T}_{B}}}\]
C) \[\frac{{{T}_{A}}+{{T}_{B}}}{{{T}_{A}}}\]
D) \[\frac{{{T}_{A}}-{{T}_{B}}}{{{T}_{A}}}\]
View Answer play_arrowquestion_answer54) For a nuclear to be in critical condition, the value of neutron multiplication factor (k) must be
A) \[k>1\]
B) \[k<1\]
C) \[k=1\]
D) \[k=0\]
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) \[{{n}_{E}}<<{{n}_{H}}\]
B) \[{{n}_{E}}>>{{n}_{H}}\]
C) \[{{n}_{E}}={{n}_{H}}\]
D) \[{{n}_{E}}={{n}_{H}}=0\]
View Answer play_arrowquestion_answer56) An intrinsic semiconductor at \[0\text{ }K\]temperature behaves like
A) conductor
B) p-type semiconductor
C) n-typesemiconductor
D) insulator
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
B) decreases and more current flows in the circuit
C) increases and more current flows in the circuit
D) decreases and no current flows in the circuit
View Answer play_arrowquestion_answer58) The main cause of zener breakdown is
A) the base semiconductor being germanium
B) production of electron-hole pairs due to thermal excitation
C) low doping
D) high doping
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) \[0.6\text{ }V/m\]
B) \[6\times {{10}^{4}}\,V/m\]
C) \[6\times {{10}^{5}}\,V/m\]
D) zero
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
B) Output Y will be 0 when the either of the inputs A or B is 1
C) Output Y will be 1 only when both the inputs A and Bare 1
D) Output Y will be 1 only when either of the inputs A and B are 1
View Answer play_arrowquestion_answer61) Dimensional formula for force is
A) \[[M{{L}^{2}}{{T}^{-2}}]\]
B) \[[ML{{T}^{-2}}]\]
C) \[[M{{L}^{-1}}{{T}^{-2}}]\]
D) \[[M{{L}^{2}}{{T}^{-2}}]\]
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) \[A\,\vec{A}\]
B) \[\vec{A}.\,\vec{A}\]
C) \[\vec{A}\times \,\vec{A}\]
D) \[\frac{|\vec{A}|}{A}\]
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) \[7\,N\]
B) \[1\,N\]
C) \[5\,N\]
D) zero
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) \[{{45}^{o}}\]
B) \[{{90}^{o}}\]
C) \[{{180}^{o}}\]
D) \[{{360}^{o}}\]
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) \[D<s\]
B) \[D>s\]
C) \[D=s\]
D) \[D\le s\]
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) \[R=\frac{{{u}^{2}}\,\sin \,\,2\theta }{g}\]
B) \[R=\frac{{{u}^{2}}\,{{\sin }^{2}}\theta }{2g}\]
C) \[R=\frac{{{u}^{2}}}{g}\]
D) \[R={{u}^{2}}\,\,\sin \,\,\theta \]
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) \[4\,a\]
B) \[2\,a\]
C) \[\frac{a}{4}\]
D) \[\frac{a}{2}\]
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) \[\tan \,\theta =\frac{Rg}{{{v}^{2}}}\]
B) \[\tan \,\theta ={{v}^{2}}\,Rg\]
C) \[\tan \,\theta =\frac{{{v}^{2}}\,g}{R}\]
D) \[\tan \,\theta =\frac{{{v}^{2}}}{Rg}\]
View Answer play_arrowquestion_answer69) A body starts from rest and moves with uniform acceleration. Which of the following graphs represent its motion?
A)
B)
C)
D)
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) \[vNm\]
B) \[\frac{mv}{N}\]
C) \[mv{{N}^{2}}\]
D) \[\frac{m{{v}^{2}}}{N}\]
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) \[5\]
B) \[5.2\]
C) \[2.5\]
D) \[25\]
View Answer play_arrowquestion_answer72) The area under the displacement-force curve gives
A) distance travelled
B) total force
C) momentum
D) work done
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
B) The centre of mass of the body remains unchanged
C) The centre of mass of the body moves uniformly in a circular path
D) Individual particles and centre of mass the body undergo an accelerated motion
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
B) half of the rotational kinetic energy
C) rotational kinetic energy
D) twice the rotational kinetic energy
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) \[10\]
B) \[8\]
C) \[6\]
D) \[4\]
View Answer play_arrowquestion_answer76) The phenomenon observed when a beam of light is passed through a colloidal solution, is
A) cataphoresis
B) delectrophoresis
C) coagulation
D) Tyndall effect
View Answer play_arrowquestion_answer77) In case of condensation of polymers
A) high molecular weight polymers are formed all at once
B) lower molecular weight polymers are formed all at once
C) molecular weight of polymer rises throughout the reaction
D) have no Specific relation to their molecular weight
View Answer play_arrowquestion_answer78) The element with the lowest ionization potential is
A) Na
B) K
C) Rb
D) Cs
View Answer play_arrowquestion_answer79) Differentiating electron in inner transition elements enters the ......... orbital.
A) s
B) p
C) d
D) \[f\]
View Answer play_arrowquestion_answer80) Which one of the following is a non-polar molecule?
A) \[CC{{l}_{4}}\]
B) \[CHC{{l}_{3}}\]
C) \[C{{H}_{2}}C{{l}_{2}}\]
D) \[C{{H}_{3}}Cl\]
View Answer play_arrowquestion_answer81) The nature of the bond in diamond is
A) ionic
B) covalent
C) metallic
D) coordinate covalent
View Answer play_arrowquestion_answer82) According to VSEPR theory the repulsion between different pair (lone or bond) of electrons obey the order
A) \[lp-bp-lp-lp>bp-bp\]
B) \[lp-bp>bp-bp>lp-lp\]
C) \[lp-lp>lp-bp>lp-bp\]
D) \[bp-bp>lp-lp>lp-bp\]
View Answer play_arrowquestion_answer83) From the molecular orbital theory, one can show that the bond order in \[{{F}_{2}}\]molecule as
A) 2
B) 1
C) 3
D) 4
View Answer play_arrowquestion_answer84) Which of the following metal oxides is most basic?
A) \[ZnO\]
B) \[~A{{l}_{2}}{{O}_{3}}\]
C) \[A{{s}_{2}}{{O}_{3}}\]
D) \[{{K}_{2}}O\]
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) \[~FeS{{O}_{4}}\]
B) \[~Mn{{O}_{2}}\]
C) \[FeS\]
D) \[FeS{{O}_{3}}\]
View Answer play_arrowquestion_answer86) The order of electron affinity of halogens is
A) \[F>Cl>Br>I\]
B) \[Cl>F>Br>I\]
C) \[Cl>F>I>Br\]
D) \[Br>Cl>F>I\]
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
B) + 1 and + 4
C) + 5 and +3
D) - 1 and + 1
View Answer play_arrowquestion_answer88) The highest oxidation state exhibited by transition metals is
A) + 7
B) + 8
C) + 6
D) + 5
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
B) They show variable oxidation states
C) All their ions are colourless
D) Their ions contain partially filled d-electrons
View Answer play_arrowquestion_answer90) The catalyst used in the manufacture of ammonia is
A) \[{{V}_{2}}{{O}_{5}}\]
B) \[Pt\]
C) \[Fe\]
D) \[Ni{{(CO)}_{4}}\]
View Answer play_arrowquestion_answer91) The most stable oxidation state of lanthanides is
A) + 2
B) + 4
C) 0
D) + 3
View Answer play_arrowquestion_answer92) The number of ions formed when hexamine copper (II) sulphate is dissolved in water is
A) 1
B) 2
C) 4
D) 6
View Answer play_arrowquestion_answer93) The number of unpaired electrons in the square planar \[{{[Pt{{(CN)}_{4}}]}^{2-}}\]ion is
A) 2
B) 1
C) 0
D) 3
View Answer play_arrowquestion_answer94) In metal carbonyl (organometallic) complexes, the M-C bond is
A) ionic
B) covalent with ionic character
C) covalent
D) coordinate covalent
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
B) optical
C) ionisation
D) linkage
View Answer play_arrowquestion_answer96) The metallurgical process in which a metal is obtained in a fused state is called
A) smelting
B) roasting
C) calcination
D) froth floatation
View Answer play_arrowquestion_answer97) Metallic silver may be obtained from \[\text{AgCl}\]by
A) heating it in the current of \[{{\text{H}}_{\text{2}}}\]
B) fusing it with sand
C) treating with carbon monoxide
D) fusing it with \[\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]
View Answer play_arrowquestion_answer98) Which one of the following metals is extracted by a carbon reduction process?
A) Copper
B) Iron
C) Aluminium
D) Magnesium
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
B) 3-chlorobutanaldehyde
C) 3-chlorobutanal
D) 2-chlorobutanol
View Answer play_arrowquestion_answer100) Di-chloroacetic acid is a stronger acid than acetic acid. This is due to occurrence of
A) mesomeric effect
B) hyperconjugation
C) inductive effect
D) steric effect
View Answer play_arrowquestion_answer101) Dehydration of alcohol is an example of which type of reaction?
A) Substitution
B) Elimination
C) Addition
D) Rearrangement
View Answer play_arrowquestion_answer102) Number of monochloro derivatives obtained when neo-pentane is chlorinated, is
A) one
B) two
C) three
D) four
View Answer play_arrowquestion_answer103) Which of the following alkenes gives only acetaldehyde on ozonolysis?
A) Ethene
B) Propene
C) 1-butene
D) 2-butene
View Answer play_arrowquestion_answer104) 1-butyne on hydration gives
A) butan-1, 2-diol
B) butan-1-ol
C) butan-2-ol
D) butan-2-one
View Answer play_arrowquestion_answer105) Least stable conformer of cyclohexane is
A) chair
B) boat
C) twist boat
D) planar hexagon
View Answer play_arrowquestion_answer106) Which one of the following monoenes does not exhibit geometric isomerism?
A) \[{{C}_{4}}{{H}_{8}}\]
B) \[{{C}_{3}}{{H}_{6}}\]
C) \[{{C}_{5}}{{H}_{10}}\]
D) \[{{C}_{8}}{{H}_{16}}\]
View Answer play_arrowquestion_answer107) Which one of the following chlorohydrocarbons readily undergoes solvolysis?
A) \[C{{H}_{2}}=CHCl\]
B)
C)
D)
View Answer play_arrowquestion_answer108) Conversion of chlorobenzene to phenol involves
A) electrophilic substitution
B) nucleophilic substitution
C) free radical substituion
D) electrophilic addition
View Answer play_arrowquestion_answer109) is
A) an ester
B) an anhydride
C) acetal
D) hemiacetal
View Answer play_arrowquestion_answer110) Which one of the following does not give iodoform?
A)
B) \[C{{H}_{3}}OH\]
C) \[C{{H}_{3}}C{{H}_{2}}OH\]
D) \[C{{H}_{3}}-\underset{OH}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{3}}\]
View Answer play_arrowquestion_answer111) The products obtained when anisole is heated in a sealed tube with HI are
A)
B)
C)
D) \[C{{H}_{3}}OH+C{{H}_{3}}I\]
View Answer play_arrowquestion_answer112) Which of the following diacid readily gives anhydride on heating?
A) Fumaric
B) Maleic acid
C) Malic acid
D) Terephthalic acid
View Answer play_arrowquestion_answer113) Hydroxamic acid test is employed to detect
A) ketones
B) aldehydes
C) esters
D) amides
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
B) two\[-COOH\] groups
C) phenolic group
D) three \[-COOH\]groups
View Answer play_arrowquestion_answer115) Benzamide can be converted into benzonitrile with
A) \[{{H}_{3}}{{O}^{+}}\]
B) \[O{{H}^{-}}/{{H}_{2}}O\]
C) KCN
D) \[{{P}_{2}}{{O}_{5}}\]
View Answer play_arrowquestion_answer116) The most basic compound in the following is
A) \[N{{H}_{3}}\]
B) \[~C{{H}_{3}}N{{H}_{2}}\]
C) \[HN{{(C{{H}_{3}})}_{2}}\]
D) \[N{{(C{{H}_{3}})}_{3}}\]
View Answer play_arrowquestion_answer117) The compound with foul odour among the following is-
A)
B)
C)
D)
View Answer play_arrowquestion_answer118) Nitration of nitrobenzene at \[125{}^\circ C\] with mixed acids gives
A) meto-dinitrobenzene
B) ortho-dinitrobenzene
C) para-dinitrobenzene
D) 1, 3, 5-trinitro benzene
View Answer play_arrowquestion_answer119) The \[\alpha -\]amino acid which does not give purple colour in the ninhydrin test is
A) proline
B) glycine
C) lysine
D) aspartic acid
View Answer play_arrowquestion_answer120) The anomeric carbon in \[\text{D}\,\text{(+)}\]glucose is
A) \[C-1\]carbon
B) \[C-2\]carbon
C) \[C-5\]carbon
D) \[C-6\] carbon
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
B) 1:1
C) 1:2
D) 2:1
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
B) 2:1
C) 1:2
D) 1:1
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
B) Niels Bohr
C) de-Broglie
D) Heisenberg
View Answer play_arrowquestion_answer124) Which one of the following is the set of correct quantum numbers of an electron in 3d orbital?
A) \[~n=3,l=0,m=0,s=-\text{ }1/2\]
B) \[~n=2,l=3,m=0,s=+1/2\]
C) \[~n=3,l=1,m=0,s=-1/2\]
D) \[~n=3,l=2,m=1,s=+\,1/2\]
View Answer play_arrowquestion_answer125) Electron density in the YZ plane of \[3{{d}_{{{x}^{2}}-{{y}^{2}}}}\] orbital is
A) zero
B) 0.50
C) 0.75
D) 0.90
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
B) 0.726 mg
C) 0.126 mg
D) 0.236 mg
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
B) 8
C) 6
D) 2
View Answer play_arrowquestion_answer128) What happens to the yield on application of high pressure in the Habefs synthesis of ammonia?
A) Increases
B) Decreases
C) Unaffected
D) Reaction stops
View Answer play_arrowquestion_answer129) In the reaction\[{{H}_{2}}(g)+C{{l}_{2}}(g)\rightleftharpoons 2HCl(g)\]
A) \[{{K}_{p}}\ne {{K}_{c}}\]
B) \[{{K}_{p}}={{K}_{c}}\]
C) \[{{K}_{p}}>{{K}_{c}}\]
D) \[{{K}_{p}}<{{K}_{c}}\]
View Answer play_arrowquestion_answer130) pH of an aqueous solution containing \[{{10}^{-8}}mol/L\]of \[HCl\]is
A) 8
B) 10
C) 6.96
D) 12
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
B) NiS and CoS
C) CoS and NiS
D) PbS and NiS
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
B) 2
C) 3
D) 4
View Answer play_arrowquestion_answer133) The units of the rate of a second order reaction are
A) \[\text{tim}{{\text{e}}^{-1}}\]
B) \[\text{mol}\,{{\text{L}}^{-1}}\,\text{tim}{{\text{e}}^{-1}}\]
C) \[\text{L}\,\text{mol}{{\,}^{-1}}\,\text{tim}{{\text{e}}^{-1}}\]
D) \[{{\text{L}}^{2}}\,\text{mol}{{\,}^{-2}}\,\text{tim}{{\text{e}}^{-1}}\]
View Answer play_arrowquestion_answer134) Activation energy of a reaction
A) is independent of temperature
B) increases with temperature
C) gets doubled for every 10 degree rise in temperature
D) decreases with temperature
View Answer play_arrowquestion_answer135) Which one of the following concentration units is independent of temperature?
A) Normality
B) Molarity
C) Molality
D) ppm
View Answer play_arrowquestion_answer136) Maximum lowering of vapour pressure is observed in the case of
A) 0.1 M glucose
B) \[0.1\text{ }M\text{ }BaC{{l}_{2}}\]
C) \[\text{ }\!\!~\!\!\text{ 0}\text{.1 M MgS}{{\text{O}}_{\text{4}}}\]
D) \[\text{ }\!\!~\!\!\text{ 0}\text{.1 NaCl}\]
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
B) 10,000
C) \[\text{2}\text{.4}\times \text{1}{{\text{0}}^{5}}\]
D) \[\text{2}\times \text{1}{{\text{0}}^{12}}\]
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
B) offers an intense colour
C) associates or dissociates
D) offers no colour
View Answer play_arrowquestion_answer139) We believe in the laws of thermodynamics because they are
A) theoretical
B) derived based on mathematical analysis
C) empirical and nobody disproved
D) mere statements
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
B) 8.0
C) 0.0
D) 0.293
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) \[-\text{ }17900\text{ cal}\]
B) \[\text{ }\!\!~\!\!\text{ 17900 cal}\]
C) \[\text{17308 cal}\]
D) \[~-\text{ }17308\text{ cal}\]
View Answer play_arrowquestion_answer142) Which one of the following is spontaneous at all temperatures?
A) \[{{H}_{2}}(g)\xrightarrow{{}}2{{H}_{\text{atom}}}\] \[\Delta {{H}^{o}}=436\,kJ,\Delta {{S}^{o}}=90.7\,\text{eu}\]
B) \[\frac{1}{2}{{N}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}NO(g);\] \[\Delta {{H}^{o}}=90.3\,kJ,\Delta {{S}^{o}}=3.0\,\text{eu}\]
C) \[2N{{O}_{2}}(g)\xrightarrow{{}}{{N}_{2}}{{O}_{4}}(g)\] \[\Delta {{H}^{o}}=-56.0\,kJ\,\Delta {{S}^{o}}=-17.7\text{eu}\]
D) \[{{H}_{2}}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l)+\frac{1}{2}{{O}_{2}}(g)\] \[\Delta {{H}^{o}}=-98.3\,kJ\Delta {{S}^{o}}=80.0\,\text{eu}\]
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
B) 5
C) 4
D) 2
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
B) 0
C) 2.5
D) 3.5
View Answer play_arrowquestion_answer145) Galvanic cell is a device in which
A) chemical energy is converted into electrical energy
B) electrical energy is converted into chemical energy
C) chemical energy is seen in the form of heat
D) thermal energy from an outside source is used to drive the cell reaction
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) \[\Delta G=nFE\]
B) \[\Delta G=nF/E\]
C) \[\Delta G=-nFE\]
D) \[\Delta G=E/nF\]
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 \[\text{mo}{{\text{l}}^{-1}}\]
B) \[\text{L}\,\,\text{atm}\,\text{mo}{{\text{l}}^{2}}\]and \[\text{mol L}\]
C) \[{{\text{L}}^{2}}\,\,\text{atm}\,\text{mo}{{\text{l}}^{-2}}\]and \[\text{mo}{{\text{l}}^{-1}}\text{ L}\]
D) \[{{\text{L}}^{-2}}\,\,\text{at}{{\text{m}}^{-1}}\,\text{mo}{{\text{l}}^{-1}}\]and \[\text{L}\,\text{mo}{{\text{l}}^{-2}}\]
View Answer play_arrowquestion_answer148) Identify the pair of gases that have equal rates of diffusion
A) CO, NO
B) Np.CO
C) \[{{N}_{2}}O,C{{O}_{2}}\]
D) \[~C{{O}_{2}},N{{O}_{2}}\]
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
B) greater than 0.73
C) less than 0.41
D) equal to 1.0
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
B) decrease in pressure increases the extent of adsorption
C) gases which are easily liquefiable are adsorbed more in quantity
D) gas which has a behaviour similar to an inert gas is adsorbed more
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) \[0.4\]
B) \[0.25\]
C) \[0.45\]
D) \[0.43\]
View Answer play_arrowquestion_answer152) \[\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{m}}-1}{{{x}^{n}}-1}\]is equal to
A) \[\frac{n}{m}\]
B) \[\frac{m}{n}\]
C) \[\frac{2m}{n}\]
D) \[\frac{2n}{m}\]
View Answer play_arrowquestion_answer153) \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{{{e}^{5x}}-{{e}^{4x}}}{x}\]is equal to
A) \[1\]
B) \[2\]
C) \[4\]
D) \[5\]
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) \[4\]
B) \[3\]
C) \[2\]
D) \[1\]
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) \[8\]
B) \[9\]
C) \[10\]
D) \[11\]
View Answer play_arrowquestion_answer156) The function \[f:R\to R\] given by \[f(x)={{x}^{3}}-1\] is
A) a one-one function
B) an onto function
C) a bijection
D) neither one-one nor onto
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) \[1\]
B) \[\omega \]
C) \[{{\omega }^{2}}\]
D) \[0\]
View Answer play_arrowquestion_answer158) The square roots of \[-7-24\sqrt{-1}\] are
A) \[\pm (4+3\sqrt{-1})\]
B) \[\pm (3+4\sqrt{-1})\]
C) \[\pm (3-4\sqrt{-1})\]
D) \[\pm (4-3\sqrt{-1})\]
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) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
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) \[\frac{{{a}^{2}}-2b}{{{b}^{2}}}\]
B) \[\frac{{{b}^{2}}-2a}{{{b}^{2}}}\]
C) \[\frac{{{a}^{2}}+2b}{{{b}^{2}}}\]
D) \[\frac{{{b}^{2}}+2a}{{{b}^{2}}}\]
View Answer play_arrowquestion_answer161) If \[|a|<1,\] then \[1+2a+3{{a}^{2}}+4{{a}^{3}}+.....\] is equal to
A) \[\frac{1}{1-a}\]
B) \[\frac{1}{1+a}\]
C) \[\frac{1}{1+{{a}^{2}}}\]
D) \[\frac{1}{{{(1-a)}^{2}}}\]
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) \[p-q+10\]
B) \[p+q+11\]
C) \[p+q-9\]
D) \[p+q-10\]
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) \[\frac{{{2}^{n+1}}-1}{n+1}\]
B) \[\frac{{{2}^{n}}-1}{n}\]
C) \[\frac{{{2}^{n-1}}-1}{n-1}\]
D) \[\frac{{{2}^{n+1}}-1}{n+2}\]
View Answer play_arrowquestion_answer164) The coefficient of \[{{x}^{r}}\] in the expansion of \[{{(1-x)}^{-2}}\]is
A) \[r\]
B) \[r+1\]
C) \[r+3\]
D) \[r-1\]
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) \[2454\]
B) \[2452\]
C) \[2450\]
D) \[1806\]
View Answer play_arrowquestion_answer166) \[\frac{1}{3!}+\frac{2}{5!}+\frac{3}{7!}+...\] is equal to
A) \[\frac{{{e}^{-1}}}{2}\]
B) \[e\]
C) \[\frac{e}{4}\]
D) \[\frac{e}{6}\]
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) \[{{\log }_{e}}\,(x-y)\]
B) \[{{\log }_{e}}\,(x+y)\]
C) \[{{\log }_{e}}\,\left( \frac{x}{y} \right)\]
D) \[{{\log }_{e}}\,\,xy\]
View Answer play_arrowquestion_answer168) The standard deviation of the first n natural numbers is
A) \[\frac{\sqrt{{{n}^{2}}+1}}{12}\]
B) \[\frac{{{n}^{2}}-1}{12}\]
C) \[\sqrt{\frac{{{n}^{2}}-1}{12}}\]
D) \[\frac{{{n}^{2}}+1}{12}\]
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) \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1\]
B) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1\]
C) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1+{{e}^{2}})}=1\]
D) \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}(1+{{e}^{2}})}=1\]
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) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,{{\cos }^{2}}\alpha -{{b}^{2}}\,{{\sin }^{2}}\alpha }}\]
B) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,{{\cos }^{2}}\alpha +{{b}^{2}}\,{{\sin }^{2}}\alpha }}\]
C) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,si{{n}^{2}}\alpha -{{b}^{2}}\,{{\cos }^{2}}\alpha }}\]
D) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,si{{n}^{2}}\alpha +{{b}^{2}}\,{{\cos }^{2}}\alpha }}\]
View Answer play_arrowquestion_answer171) The distance between the parallel lines \[y=x+a,\,\,y=x+b\]is
A) \[\frac{|b-a|}{\sqrt{2}}\]
B) \[|a-b|\]
C) \[|a+b|\]
D) \[\frac{|a+b|}{\sqrt{2}}\]
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) \[x+2y=1\]
B) \[x+2y=2\]
C) \[x+2y=4\]
D) \[x+2y=3\]
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) \[\sqrt{10}\]
B) \[10\]
C) \[5\sqrt{2}\]
D) \[5\]
View Answer play_arrowquestion_answer174) One of the directrices of the ellipse \[8{{x}^{2}}+6{{y}^{2}}-16x+12y+13=0\]is
A) \[3y-3=\sqrt{6}\]
B) \[3y+3=\sqrt{6}\]
C) \[y+1=\sqrt{3}\]
D) \[y-1=-\sqrt{3}\]
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) \[8\,a\,\sqrt{3}\]
B) \[4\,a\,\sqrt{3}\]
C) \[2\,a\,\sqrt{3}\]
D) \[a\,\sqrt{3}\]
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) \[{{({{x}^{2}}+{{y}^{2}})}^{3}}\]
B) \[{{({{x}^{2}}-{{y}^{2}})}^{3}}\]
C) \[{{({{x}^{2}}-{{y}^{2}})}^{2}}\]
D) \[{{({{x}^{2}}+{{y}^{2}})}^{2}}\]
View Answer play_arrowquestion_answer177) \[\tan {{25}^{o}}+\tan {{20}^{o}}+\tan {{25}^{o}}\,\tan {{20}^{o}}\] is equal to
A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
View Answer play_arrowquestion_answer178) If \[\cos x=3\cos y,\] then \[2\tan \frac{y-x}{2}\] is equal to
A) \[\cot \left( \frac{y-x}{2} \right)\]
B) \[\cot \left( \frac{x+y}{4} \right)\]
C) \[\cot \left( \frac{y-x}{4} \right)\]
D) \[\cot \left( \frac{y-x}{4} \right)\]
View Answer play_arrowquestion_answer179) In any \[\Delta \,ABC\] under usual notation, \[a(b\,\cos \,C-c\,\cos B)\] is equal to
A) \[{{b}^{2}}-{{c}^{2}}\]
B) \[{{c}^{2}}-{{b}^{2}}\]
C) \[\frac{{{b}^{2}}-{{c}^{2}}}{2}\]
D) \[\frac{{{c}^{2}}-{{b}^{2}}}{2}\]
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) \[1/3\]
B) \[1/9\]
C) \[1/27\]
D) \[~1/18\]
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) \[2n\pi \pm \frac{\pi }{4},n\in Z\]
B) \[2n\pi \pm \frac{\pi }{3},n\in Z\]
C) \[2n\pi \pm \frac{\pi }{6},n\in Z\]
D) \[2n\pi \pm \frac{\pi }{2},n\in Z\]
View Answer play_arrowquestion_answer182) \[{{\tan }^{-1}}\,\frac{x}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\]is equal to
A) \[2{{\sin }^{-1}}\frac{x}{a}\]
B) \[{{\sin }^{-1}}\frac{2x}{a}\]
C) \[{{\sin }^{-1}}\frac{x}{a}\]
D) \[{{\cos }^{-1}}\frac{x}{a}\]
View Answer play_arrowquestion_answer183) The solution of \[{{\tan }^{-1}}\,2\theta +{{\tan }^{-1}}3\theta =\frac{\pi }{4}\] is
A) \[\frac{1}{\sqrt{3}}\]
B) \[\frac{1}{3}\]
C) \[\frac{1}{6}\]
D) \[\frac{1}{\sqrt{6}}\]
View Answer play_arrowquestion_answer184) The number of solutions of \[\sin x=\sin 2x\]between \[\frac{-\pi }{2}\] and \[\frac{\pi }{2}\] is
A) \[3\]
B) \[2\]
C) \[1\]
D) \[0\]
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) \[\frac{t(2-{{t}^{3}})}{(1-2{{t}^{3}})}\]
B) \[\frac{t(2+{{t}^{3}})}{(1-2{{t}^{3}})}\]
C) \[\frac{t(2-{{t}^{3}})}{(1+2{{t}^{3}})}\]
D) \[\frac{t(2+{{t}^{3}})}{(1+2{{t}^{3}})}\]
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) \[\frac{1}{\sqrt{1-{{x}^{2}}}}\]
B) \[\frac{2}{\sqrt{1-{{x}^{2}}}}\]
C) \[\frac{1}{\sqrt{1+{{x}^{2}}}}\]
D) \[\frac{2}{\sqrt{1+{{x}^{2}}}}\]
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) \[(2,2)\]
B) \[(3,3)\]
C) \[(4,4)\]
D) \[(0,0)\]
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) \[3x+27y=79\]
B) \[27\text{ }x-3y=79\]
C) \[27x+3y=79\]
D) \[3x-27y=79\]
View Answer play_arrowquestion_answer189) The function \[f(x)=2{{x}^{3}}+3{{x}^{2}}-12x+1\] decreases in the interval
A) \[(2,3)\]
B) \[(1,2)\]
C) \[(-2,1)\]
D) \[(-3,-2)\]
View Answer play_arrowquestion_answer190) The function \[f(x)={{x}^{2}}{{e}^{-x}}\] increases in the interval
A) \[(0,2)\]
B) \[(2,3)\]
C) \[(3,4)\]
D) \[(4,5)\]
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) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
View Answer play_arrowquestion_answer192) If \[{{x}^{y}}={{y}^{x}},\] then \[\frac{dy}{dx}\] is equal to
A) \[\frac{{{y}^{2}}-xy\,\log \,y}{{{x}^{2}}-xy\,\log \,x}\]
B) \[\frac{{{y}^{2}}+xy\,\log \,y}{{{x}^{2}}+xy\,\log \,x}\]
C) \[\frac{{{y}^{2}}-xy\,\log \,x}{{{x}^{2}}-xy\,\log \,y}\]
D) \[\frac{{{y}^{2}}+xy\,\log \,y}{{{x}^{2}}-xy\,\log \,x}\]
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) \[\frac{{{\pi }^{2}}}{18}\]
B) \[\frac{{{\pi }^{2}}}{7}\]
C) \[\frac{-{{\pi }^{2}}}{9}\]
D) \[\frac{-{{\pi }^{2}}}{18}\]
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) \[\frac{3+\sqrt{3}}{3}\]
B) \[\frac{3+\sqrt{2}}{2}\]
C) \[1+\sqrt{2}\]
D) \[\sqrt{2}\]
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
B) linear
C) second degree
D) non-linear
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) \[\left[ \begin{matrix} -7 & 0 \\ 0 & -7 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 0 & -7 \\ -7 & 0 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 0 & 7 \\ 7 & 0 \\ \end{matrix} \right]\]
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
B) a skew symmetric matrix
C) a unit matrix
D) an elementary matrix
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) \[\infty \]
B) \[1\]
C) \[2\]
D) \[0\]
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) \[\left[ \begin{matrix} \cos \,\theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} sin\,\theta & \cos \theta \\ \cos \theta & sin\theta \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} \cos \,\theta & sin\theta \\ -sin\theta & \cos \theta \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} -sin\,\theta & \cos \theta \\ \cos \theta & sin\theta \\ \end{matrix} \right]\]
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) \[x\]
B) \[0\]
C) \[2x\]
D) \[3x\]
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) \[0\]
B) \[x\]
C) \[y\]
D) \[xyz\]
View Answer play_arrowquestion_answer202) If P is any point with in a triangle ABC, then \[\overrightarrow{PA}+\overrightarrow{CP}\] is equal to
A) \[\overrightarrow{AC}+\overrightarrow{CB}\]
B) \[\overrightarrow{BC}+\overrightarrow{BA}\]
C) \[\overrightarrow{CB}+\overrightarrow{AB}\]
D) \[\overrightarrow{CB}+\overrightarrow{BA}\]
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) \[3\]
B) \[4\]
C) \[5\]
D) \[6\]
View Answer play_arrowquestion_answer204) The vector \[\vec{a}\times (\vec{b}\times \vec{c})\] is coplanar with the vectors
A) \[\vec{b},\,\vec{c}\]
B) \[\vec{a},\,\vec{b}\]
C) \[\vec{a},\,\vec{c}\]
D) \[\vec{a},\,\,\vec{b}\,,\vec{c}\]
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) \[\vec{0}\]
B) \[0\]
C) \[\vec{a}\times \vec{b}\]
D) \[\vec{b}\times \vec{a}\]
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) \[\frac{\hat{k}+\hat{i}}{\sqrt{2}}\]
B) \[\frac{\hat{j}+\hat{k}}{\sqrt{2}}\]
C) \[\frac{\hat{i}-\hat{k}}{\sqrt{3}}\]
D) \[\frac{\hat{j}-\hat{k}}{\sqrt{2}}\]
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) \[\vec{b}+\vec{c}\]
B) \[\vec{b}-2\vec{c}\]
C) \[\vec{b}+2\vec{c}\]
D) \[\vec{b}-\vec{c}\]
View Answer play_arrowquestion_answer208) \[3a{{\int_{0}^{1}{\left( \frac{ax-1}{a-1} \right)}}^{2}}\,\,dx\]is equal to
A) \[a-1+{{(a-1)}^{-2}}\]
B) \[a+{{a}^{-2}}\]
C) \[a-{{a}^{-2}}\]
D) \[{{a}^{2}}+\frac{1}{{{a}^{2}}}\]
View Answer play_arrowquestion_answer209) \[\int_{-\pi /2}^{\pi /2}{\frac{dx}{1+\cos x}}\] is equal to
A) \[0\]
B) \[1\]
C) \[2\]
D) \[3\]
View Answer play_arrowquestion_answer210) \[\int{\sin \,\,\sqrt{x}}\,\,dx\] is equal to
A) \[\sin \sqrt{x}-\sqrt{x}\,\cos \,\sqrt{x}\]
B) \[2(\sin \,\sqrt{x}-\sqrt{x}\,\cos \,\sqrt{x})+c\]
C) \[\cos \,\sqrt{x}-\sqrt{x}\,\sin \,\sqrt{x}+c\]
D) \[2(\cos \sqrt{x}-\sqrt{x}\,\sin \sqrt{x})+c\]
View Answer play_arrowquestion_answer211) \[\int{\frac{\sqrt{x}}{x+1}\,dx}\] is equal to
A) \[2(\sqrt{x}+{{\tan }^{-1}}\sqrt{x})+c\]
B) \[2(\sqrt{x}+{{\cot }^{-1}}\sqrt{x})+c\]
C) \[2(\sqrt{x}-{{\cot }^{-1}}-\sqrt{x})+c\]
D) \[2(\sqrt{x}-ta{{n}^{-1}}\sqrt{x})+c\]
View Answer play_arrowquestion_answer212) The area (in square unit) bounded by the curves \[y={{x}^{3}}\]and \[y=x\] is
A) \[1/2\text{ }sq\text{ }unit\]
B) \[1/4\text{ }sq\text{ }unit\]
C) \[1/8\text{ }sq\text{ }unit\]
D) \[1/16\text{ }sq\text{ }unit\]
View Answer play_arrowquestion_answer213) The area (in square unit) bounded by the curves \[4y={{x}^{2}}\]and \[2y=6-{{x}^{2}}\]is
A) \[8\]
B) \[6\]
C) \[4\]
D) \[10\]
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) \[(1+{{x}^{2}})(1+{{y}^{2}})=c\]
B) \[(1+{{x}^{2}})(1+{{y}^{2}})=c{{x}^{2}}\]
C) \[(1-{{x}^{2}})(1-{{y}^{2}})=c\]
D) \[(1+{{x}^{2}})(1+{{y}^{2}})=c{{y}^{2}}\]
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) \[1/{{s}^{3}}\]
B) \[1/s\]
C) \[~1/{{s}^{4}}\]
D) \[1/{{s}^{2}}\]
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) \[60\text{ }m/s,\text{ }40\text{ }m/{{s}^{2}}\]
B) \[70\text{ }m/s,\text{ }30\text{ }m/{{s}^{2}}\]
C) \[90\text{ }m/s,\text{ }60\text{ }m/{{s}^{2}}\]
D) None of the above
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) \[\frac{2}{g}{{(horizontal\text{ }velocity)}^{2}}\]
B) \[\frac{2}{g}(vertical\text{ }velocity)\]
C) \[\frac{2}{{{g}^{2}}}{{(horizontal\text{ }velocity)}^{2}}\]
D) \[\frac{2}{{{g}^{2}}}{{(vertical\text{ }velocity)}^{2}}\]
View Answer play_arrowquestion_answer218) The vector equation of the line passing through the points \[(3,2,1)\] and \[(-2,1,3)\] is
A) \[\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}-\hat{j}+2\hat{k})\]
B) \[\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}+\hat{j}+\hat{k})\]
C) \[\vec{r}=-2\hat{i}+\hat{j}+3\hat{k}+\lambda (5\hat{i}+\hat{j}+2\hat{k})\]
D) \[\vec{r}=-2\hat{i}+\hat{j}+\hat{k}+\lambda (5\hat{i}+\hat{j}+2\hat{k})\]
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) \[(1,2,3)\]
B) \[(-1,-1,-1)\]
C) \[(2,1,3)\]
D) \[(1,1,1)\]
View Answer play_arrowquestion_answer220) The shortest distance between the lines \[1+x=2y=-12z\]and \[x=y+2=6z-6\]is
A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
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) \[(-4,1,-3)\]
B) \[(4,-1,-3)\]
C) \[(-4,-1,3)\]
D) \[(-4,-1,-3)\]
View Answer play_arrowquestion_answer222) The radius of the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=x+2y+3z\]is
A) \[\frac{\sqrt{14}}{2}\]
B) \[\sqrt{7}\]
C) \[\frac{7}{2}\]
D) \[\frac{\sqrt{7}}{2}\]
View Answer play_arrowquestion_answer223) The distance between the planes \[2x-2y+z+3=0\]and \[4x-4y+2z+5=0\] is
A) \[3\]
B) \[6\]
C) \[\frac{1}{6}\]
D) \[\frac{1}{3}\]
View Answer play_arrowquestion_answer224) If B is a Boolean algebra and \[a,\,\,b\,\,\in \,B,\] then \[a.(a+b)\]is equal to
A) \[a\]
B) \[b\]
C) \[1\]
D) \[a'\]
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) \[0.1\]
B) \[0.3\]
C) \[0.4\]
D) \[0.2\]
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