question_answer1) A solenoid of length 0.6 m has a radius of \[1\text{ }cm\] and is made up of 600 turns. It carries a current of \[6\text{ }A\]. What is the magnitude of the magnetic field inside the solenoid?
A) \[7.54\times {{10}^{-3}}T~\]
B) \[10.84\times {{10}^{-3}}\,\,T\]
C) \[4.87\times {{10}^{-3}}\,\,T\]
D) \[2.36\times {{10}^{-2}}\,\,T\]
View Answer play_arrowquestion_answer2) The bus moving with a speed of \[42\text{ }km/h\]is brought to a stop by brakes after\[6\text{ }m\]. If the same bus is moving at a speed of \[90\text{ }km/h,\] then the minimum stopping distance is
A) \[15.48\text{ }m\]
B) \[18.64\text{ }m\]
C) \[22.13\text{ }m\]
D) \[27.55\text{ }m\]
View Answer play_arrowquestion_answer3) A \[15pF\] capacitor is connected to a \[60\text{ }V\] battery. How much electrostatic energy is stored?
A) \[2.77\times {{10}^{-8}}\,J\]
B) \[1.77\times {{10}^{-8}}\,J\]
C) \[2.35\times {{10}^{-8}}\,J\]
D) \[1.35\times {{10}^{-8}}\,J\]
View Answer play_arrowquestion_answer4) In a video signal for transmission of picture, what value of bandwidth is used " in communication system?
A) \[2.4\text{ }MHz\]
B) \[4.2\text{ }MHz\]
C) \[4.2\text{ }MHz\]
D) \[42\text{ }MHz\]
View Answer play_arrowquestion_answer5) A straight wire of mass 300 g and length \[2.5\text{ }m\]carries a current of \[3.5\text{ }A\]. It is suspended in mid-air by a uniform horizontal magnetic field B. What is the magnitude of the magnetic field?
A) \[0.654\text{ }T\]
B) \[0.336\text{ }T\]
C) \[1.576\text{ }T\]
D) \[0.939\text{ }T\]
View Answer play_arrowquestion_answer6) When longitudinal wave propagates, what happens in the region of compressions and rarefactions?
A) Density varies
B) Density remains constant
C) There is heat transfers
D) Boyle's law is obeyed
View Answer play_arrowquestion_answer7) If the temperature of the body is increased by \[10%,\] the percentage increase in the emitted indication will be
A) \[46%\]
B) \[40%\]
C) \[30%\]
D) \[80%\]
View Answer play_arrowquestion_answer8) A galaxy is moving away from an observe on the earth so that sodium light of wavelength \[5892\overset{\text{o}}{\mathop{\text{A}}}\,\] is observed at \[5896\overset{\text{o}}{\mathop{\text{A}}}\,\]. The speed of galaxy is
A) \[306\,\,km/s\]
B) \[204\text{ }km/s\]
C) \[185\,km/s\]
D) \[158\text{ }km/s\]
View Answer play_arrowquestion_answer9) The correct order of arrangement of electromagnetic waves according to their wavelength is
A) gamma rays < microwaves < AM radiowaves < FM radiowaves
B) microwaves < AM radiowaves < FM radiowaves < gamma rays
C) gamma rays < AM radiowaves < FM radiowaves < microwaves
D) gamma rays < microwaves < FM radiowaves < AM radiowaves
View Answer play_arrowquestion_answer10) A constant retarding force of \[80\text{ }N\]is applied to a body of mass \[50\text{ }kg\]which is moving initially with a speed of\[20\text{ }m/s\]. What would be the time required by the body to come to rest?
A) \[15\,\,s\]
B) \[14\,\,s\]
C) \[12.5\,\,s\]
D) \[1\,8\,\,s\]
View Answer play_arrowquestion_answer11) Light from a point source in air falls on a spherical glass surface (\[n=1.67\]and radius of curvature \[~=25\text{ }cm\]). The distance of the light source from the glass surface is \[95\text{ }cm\]. At what position, the image is formed?
A) \[75.45\text{ }cm\]
B) \[90.50\text{ }cm\]
C) \[105.25\text{ }cm\]
D) \[99.40\text{ }cm\]
View Answer play_arrowquestion_answer12) The length of the wire is increase by 2% by applying a load of\[2.5\text{ }kg-wt\]. What is the linear strain produced in the wire?
A) \[0.1\]
B) \[0.01\]
C) \[0.2\]
D) \[0.02\]
View Answer play_arrowquestion_answer13) The half life of an old rock element is 5800 years. In how many years its sample of \[25\text{ }g\]is reduced to \[6.25\text{ }g\].
A) \[2900\text{ }years\]
B) \[5800\text{ }years\]
C) \[11600\text{ }years\]
D) \[23200\text{ }years\]
View Answer play_arrowquestion_answer14) The earth takes \[24\text{ }h\]to rotate once about its axis. How much time does the sun take to shift by \[{{5}^{o}}\] when viewed from the earth?
A) \[20\text{ }min\]
B) \[15\text{ }min\]
C) \[10\text{ }min\]
D) \[5\text{ }min\]
View Answer play_arrowquestion_answer15) Which of the following is a dimension less quantity?
A) Magnetic flux density
B) Electric flux density
C) Lumen flux density
D) Optical density
View Answer play_arrowquestion_answer16) A crane lifts weight of \[75\text{ }kg\]to a height of \[15\text{ }m\] in\[15\text{ }s\]. The power of the crane is (assuming \[g=9.8\,m/{{s}^{2}}\])
A) \[635\,\,W\]
B) \[735\,\,W\]
C) \[835\,\,W\]
D) \[1135\,\,W\]
View Answer play_arrowquestion_answer17) The escape velocity from the surface of the earth is\[11.2\text{ }km{{s}^{-1}}\]. What is the escape velocity in a planet whose radius is three times that of the earth and on which the acceleration due to gravity is three times of that on the earth?
A) \[11.2\text{ }km{{s}^{-1}}\]
B) \[22.4\text{ }km{{s}^{-1}}\]
C) \[33.6\text{ }km{{s}^{-1}}\]
D) \[5.6\text{ }km{{s}^{-1}}\]
View Answer play_arrowquestion_answer18) What is the dimensional formula for Work?
A) \[[ML{{T}^{-2}}]\]
B) \[[M{{L}^{2}}{{T}^{-2}}]\]
C) \[[M{{L}^{3}}{{T}^{-2}}]\]
D) \[[M{{L}^{2}}{{T}^{-1}}]\]
View Answer play_arrowquestion_answer19) When the gas expands with temperature using the relation \[V=K{{T}^{2/3}}\] for the temperature change of \[40\text{ }K,\] the work done is
A) \[20.1\,\,R\]
B) \[30.2\,\,R\]
C) \[26.6\,\,R\]
D) \[35.6\,\,R\]
View Answer play_arrowquestion_answer20) The resonant frequency of a L-C-R circuit depends upon
A) L and R
B) C and R
C) L and C
D) L, C and R
View Answer play_arrowquestion_answer21) A wheel with 30 metallic spokes each of \[7.0\text{ }m\] long is rotated with a speed of \[120\text{ }rev/min,\] in a plane normal to the horizontal component of the earth's magnetic field Hg /at a place. If \[{{H}_{E}}=0.8G\]at the place what is the induced emf between the axis and the rim of the wheel? (Give \[1G={{10}^{-4}}\text{ }T\])
A) \[2.46\times {{10}^{-4}}V\]
B) \[6.28\times {{10}^{-4}}V\]
C) \[5.76\times {{10}^{-5}}V\]
D) \[4.92\times {{10}^{-4}}V\]
View Answer play_arrowquestion_answer22) In a circuit, 3 resistors of resistance \[1.2\Omega \]\[1.2\,\,\Omega ,\]\[2\,\,\Omega ,\] \[3\,\,\Omega ,\] are connected in parallel. The value of equivalent resistance is
A) less than \[1.2\,\Omega \]
B) greater than \[1.2\,\Omega \]
C) between \[1.2\,\Omega \] and \[2\,\Omega \]
D) between \[2\,\Omega \] and \[3\,\Omega \]
View Answer play_arrowquestion_answer23) The magnetic field is absent in which one of the following physical situation?
A) Surface of neutron star
B) Surface of the earth
C) Human nerve fiber
D) At some point on the axis of bar magnet
View Answer play_arrowquestion_answer24) What amount of energy is associated with mass of\[2.5\text{ }kg\]?
A) \[6.27\times {{10}^{17}}\,\,J\]
B) \[4.27\times {{10}^{17}}J\]
C) \[0.27\times {{10}^{17}}\,J\]
D) \[2.27\times {{10}^{17}}\,J\]
View Answer play_arrowquestion_answer25) The ratio of radii of nuclei of two atoms of element of atomic mass numbers 27 and 64 is
A) \[3:4\]
B) \[4:3\]
C) \[9:16\]
D) \[16:9\]
View Answer play_arrowquestion_answer26) MSI integrated chip contains
A) less than 10 gates
B) 10 to 100 gates
C) 100 to 1000 gates
D) 1000 to 10000 gates
View Answer play_arrowquestion_answer27) What is the torque of a force \[3\hat{i}+7\hat{j}+4\hat{k}\] about the origin, if the force acts on a particle whose position vector is \[2\hat{i}+2\hat{j}+1\hat{k}\]?
A) \[\hat{i}-5\hat{j}+8\hat{k}\]
B) \[2\hat{i}+2\hat{j}+2\hat{k}\]
C) \[\hat{i}+\hat{j}+\hat{k}\]
D) \[3\hat{i}+2\hat{j}+3\hat{k}\]
View Answer play_arrowquestion_answer28) A message signal of frequency \[20\text{ }kHz\] and peak voltage of \[15\text{ }V\]is used to modulate a carrier wave of \[1000\text{ }kHz\]and peak voltage of\[30\text{ }V\]. The modulation index and upper side band are respectively
A) \[0.50\]and \[1020\text{ }kHz\]
B) \[0.66\]and \[1020\text{ }kHz\]
C) \[0.50\]and \[980\text{ }kHz\]
D) \[0.66\]and \[980\text{ }kHz\]
View Answer play_arrowquestion_answer29) Calculate, the efficiency of the engine, if Carnot cycle operates at \[{{T}_{1}}=550\,K\] and \[{{T}_{2}}=320\,K\] producing \[2.3\text{ }kJ\]of mechanical work per cycle?
A) \[0.418\]
B) \[0.622\]
C) \[0.823\]
D) \[0.902\]
View Answer play_arrowquestion_answer30) Which of the following device is the application of photoelectric effect?
A) Light emitting diode
B) Diode
C) Photocell
D) Transistor
View Answer play_arrowquestion_answer31) The waves used for Line-of-Sight (LOS) communication are
A) ground waves
B) space waves
C) sound waves
D) sky waves
View Answer play_arrowquestion_answer32) The inductance L of a solenoid depends upon its radius R as
A) \[L\propto R\]
B) \[L\propto 1/R\]
C) \[L\propto {{R}^{2}}\]
D) \[L\propto {{R}^{3}}\]
View Answer play_arrowquestion_answer33) How much revolution does the engine make during the time when a motor wheel with angular speed is increased from \[720\text{ }rpm\]to \[2820\text{ }rpm\]in \[1,4\,s\]?
A) \[354\]
B) \[490\]
C) \[413\]
D) \[620\]
View Answer play_arrowquestion_answer34) If the pressure at half of the lake is equal to 1/3 pressure at the bottom of the lake, what is the depth of the lake? (Assume \[g=10\text{ }m/{{s}^{2}}\]and \[1\text{ }atm=1\times {{10}^{5}};\] \[\rho \]p water\[={{10}^{3}}\])
A) \[9.6\text{ }m\]
B) \[7.5\text{ }m\]
C) \[4.4\text{ }m\]
D) \[3.2\text{ }m\]
E) Not Available
View Answer play_arrowquestion_answer35) The value of Rydberg constant is
A) \[1.997\times {{10}^{7}}\text{ }{{m}^{-1}}\]
B) \[1.097\times {{10}^{-7}}\text{ }m\]
C) \[1.097\times {{10}^{7}}{{m}^{-1}}\]
D) \[19.97\times {{10}^{7}}\,{{m}^{-1}}\]
View Answer play_arrowquestion_answer36) A car moving on a straight road covers \[1/3\] of the distance with \[25\text{ }km/h\] and rest with'\[75\text{ }km/h\]. The average speed is
A) \[25\text{ }km/h\]
B) 45 km/h
C) \[55\text{ }km/h\]
D) \[~75\text{ }km/h\]
View Answer play_arrowquestion_answer37) The distance at which average radius of the earth orbit subtends an angle of \[1\text{ }arc\]second is
A) parsec
B) astronomical unit
C) light year
D) unified atomic unit
View Answer play_arrowquestion_answer38) What happens to the acceleration due to gravity with the increase in altitude from the surface of the earth?
A) Increase
B) Decrease
C) First decrease and then increase
D) Remains same
View Answer play_arrowquestion_answer39) Lenz's law is a consequence of the law of conservation of.
A) charge
B) mass
C) momentum
D) energy
View Answer play_arrowquestion_answer40) The angle between the true geographic north and the north shown by a compass needle is called as
A) inclination
B) magnetic declination
C) angle of meridian
D) magnetic pole
View Answer play_arrowquestion_answer41) An air bubble of \[2\text{ }c{{m}^{3}}\]rises from the bottom of a lake of \[32\text{ }m\]at a temperature of \[{{9}^{o}}C\]. When the bubble reaches the surface of the lake from the bottom of the lake, what volume does it grows for which temperature is \[{{30}^{o}}C\](assume \[g=10m/{{s}^{2}}\]and density\[\rho ={{10}^{3}}\text{ }kg/{{m}^{3}}\])
A) \[5.937\text{ }c{{m}^{3}}\]
B) \[8.937\text{ }c{{m}^{3}}\]
C) \[~12.937\,\,c{{m}^{3}}\]
D) \[16.937\,\,c{{m}^{3}}\]
View Answer play_arrowquestion_answer42) Which quantity is transmitted with propagation of longitudinal waves through a medium?
A) Dispersion
B) Energy
C) Matter
D) Frequency
View Answer play_arrowquestion_answer43) A monochromatic light of frequency \[3\times {{10}^{14}}\,\,Hz\] is produced by a Laser, emits the power of \[3\times {{10}^{-3}}W\]. Find, how many number of photons are emitted per second
A) \[1.5\times {{10}^{16}}\]
B) \[2.5\times {{10}^{16}}\]
C) \[4.5\times {{10}^{16}}\]
D) \[8.5\times {{10}^{16}}\]
View Answer play_arrowquestion_answer44) A mountaineer standing on the edge of a cliff \[441\,\,m\]above the ground throws a stone horizontally with an initial speed of \[20\text{ }m/s\]. What is the speed with which the stone reaches the ground?
A) \[90\text{ }m/s\]
B) \[95.08\text{ }m/s\]
C) \[85\text{ }m/s\]
D) \[92\text{ }m/s\]
View Answer play_arrowquestion_answer45) A zener diode is used as
A) an amplifier
B) a rectifier
C) a voltage regulator
D) a light emitting device
View Answer play_arrowquestion_answer46) In which of the following does the intensity of sound vary with time?
A) Doppler effect
B) Beats
C) Transverse waves
D) Longitudinal waves
View Answer play_arrowquestion_answer47) A solid cylindrical of mass \[30\text{ }kg\]rotates about its axis with an angular speed of \[50\text{ }rad/s\]. What is the KE associated with the rotation of the cylinder,(if the radius of the cylinder is\[0.30\,\,m\]?
A) \[1500.5\text{ }J\]
B) \[1687.5\text{ }J\]
C) \[2000.7\text{ }J~\]
D) \[1350.0\text{ }J\]
View Answer play_arrowquestion_answer48) The circuits that make rippled AC to pure DC are known as
A) DC converters
B) junction diodes
C) bipolar transistors
D) filters
View Answer play_arrowquestion_answer49) A string of mass \[3\text{ }kg\]is under tension of\[400\text{ }N\] The length of the stretched string is \[25\text{ }cm\]. If the transverse jerk is stuck at one end of the string' how long does the disturbance take to reach the other end?
A) \[0.047\,\,s\]
B) \[0.055\,\,s\]
C) \[0.034\text{ }s\]
D) \[0.065\text{ }s\]
View Answer play_arrowquestion_answer50) The total energy of an electron in 4th orbit of hydrogen atom is
A) \[-13.6\,\,eV\]
B) \[-3.4\,\,eV\]
C) \[-1.51\,\,eV\]
D) \[-0.85\,\,eV\]
View Answer play_arrowquestion_answer51) The graph between voltage and current across a conductor that follows Ohm's law is
A) straight line
B) parabolic
C) sine-curve
D) cos-curve
View Answer play_arrowquestion_answer52) An athlete throws the shot-put of mass \[4\text{ }kg\]with initial speed of \[2.2\text{ }m{{s}^{-1}}\] at \[{{41}^{o}}\] from a height of \[1.3\text{ }m\]from the ground. What is the KE of the shot-put when it reaches the ground? (Ignoring the air resistance and gravity \[g=9.8m/{{s}^{2}}\])
A) \[42.84\text{ }J\]
B) \[52.84\text{ }J\]
C) \[62.84\text{ }J\]
D) \[72.84\text{ }J\]
View Answer play_arrowquestion_answer53) Two bulbs operating on standard voltage \[110V\] have resistances in the ratio\[9:16\]. The ratio of brightness of light from them is
A) \[9:16\]
B) \[16:9\]
C) \[3:4\]
D) \[4:3\]
View Answer play_arrowquestion_answer54) The neutral point on potentiometer's scale for two cells of EMF \[2.1\] and E volts is observed at distances \[40\text{ }cm\]and \[56\text{ }cm\]respectively. The value of E is
A) \[2.10\,\,V\]
B) \[2.94\,\,V\]
C) \[1.50\,\,V\]
D) \[~1.20\,\,V\]
View Answer play_arrowquestion_answer55) Which one of the following equation is Torricelli law?
A) \[P=\rho gh\]
B) \[v=\sqrt{2hg}\]
C) \[\eta {{R}_{e}}=\rho vd\]
D) \[S\,(2dI)=Fd\]
View Answer play_arrowquestion_answer56) Which of the law representing Maxwell's third equation?
A) Gauss's law for electricity
B) Ampere-Maxwell law
C) Gauss's law of magnetism
D) Faraday's law
View Answer play_arrowquestion_answer57) A silver wire has a resistance of \[1.6\text{ }\Omega \]. At \[{{25.5}^{o}}C,\] and a resistance of \[2.5\text{ }\Omega \]. at \[{{100}^{o}}C,\] then temperature coefficient of resistivity of silver is
A) \[5.55\times {{10}^{-3}}\,{{\,}^{o}}C\]
B) \[7.55\times {{10}^{-3}}\,{{\,}^{o}}C\]
C) \[11.75\times {{10}^{-2}}\,{{\,}^{o}}C\]
D) \[15.5\times {{10}^{-3}}\,{{\,}^{o}}C\]
View Answer play_arrowquestion_answer58) When a particle returns to its initial point, its
A) displacement is zero
B) average velocity is zero
C) distance is zero
D) average speed is zero
View Answer play_arrowquestion_answer59) A body weight \[45\text{ }N\]on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half of the radius of the earth?
A) \[20\,\,N\]
B) \[45\,\,N\]
C) \[40\text{ }N\]
D) \[90\text{ }N\]
View Answer play_arrowquestion_answer60) The angle of a prism is \[{{42}^{o}}\] and refractive index of its material is\[3/2\]. Then, angle of minimum deviation for this prism is
A) \[{{63}^{o}}\]
B) \[{{42}^{o}}\]
C) \[{{28}^{o}}\]
D) \[{{21}^{o}}\]
View Answer play_arrowquestion_answer61) A conducting sphere of radius \[5\text{ }cm\]has an unknown charge. The electric field at \[10\text{ }cm\] from the centre of the sphere is \[1.8\times {{10}^{3}}\text{ }N/C\] and points radially inward. What is the net charge on the sphere?
A) \[1.8\,\,nC\]
B) \[2\,\,nC\]
C) \[1\,\,nC\]
D) \[1.5\,\,nC\]
View Answer play_arrowquestion_answer62) For transistors the value of \[\beta \] is 50 then, the value of a is
A) \[50/51\]
B) \[49/50\]
C) \[51/50\]
D) \[50/49\]
View Answer play_arrowquestion_answer63) An infinite line charge produces a field of \[18\times {{10}^{5}}\text{ }N/C\]at a distance of \[4\text{ }cm\]. What is the linear charge density?
A) \[18\,\mu \,C/m\]
B) \[5\,\mu \,C/m\]
C) \[4\,\mu \,C/m\]
D) \[10\,\mu \,C/m\]
View Answer play_arrowquestion_answer64) What is the fraction of molecular volume to the actual volume occupied by oxygen gas at STP? Given, the diameter of oxygen molecule is \[2\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\].
A) \[1.75\times {{10}^{-4}}\]
B) \[1.5\times {{10}^{-4}}\]
C) \[12\times {{10}^{-4}}\]
D) \[1.125\times {{10}^{-4}}\]
View Answer play_arrowquestion_answer65) A \[400\text{ }pF\]capacitor is charged by a' \[100\text{ }V\] supply. How much electrostatic energy is lost in the process of disconnecting from the supply and connecting another uncharged \[400\text{ }pF\] capacitor?
A) \[{{10}^{-5}}\,\,J\]
B) \[{{10}^{-6}}\,\,J\]
C) \[{{10}^{-7}}\,\,J\]
D) \[{{10}^{-4}}\,\,J\]
View Answer play_arrowquestion_answer66) The ratio of magnitude of electric displacement and electric field (E) is
A) charge density
B) permittivity
C) electric susceptibility
D) dielectric constant
View Answer play_arrowquestion_answer67) An object is gently placed on a long converges belt moving with \[11\text{ }m{{s}^{-1}}\]. If the coefficient of friction is \[0.4,\] then the block will slide in the belt up to a distance of
A) \[10.21\,\,m\]
B) \[15.43\,\,m\]
C) \[20.3\text{ }m\]
D) \[25.6\text{ }m\]
View Answer play_arrowquestion_answer68) A spring balance has a scale that reads from \[0\]to\[60\text{ }kg\]. The length of the scale is \[30\text{ }cm\]. A body suspended from this balance and when displaced and released, oscillates with a period of \[0.8\text{ }s,\] what is the weight of the body when oscillating?
A) \[350.67\text{ }N\]
B) \[540.\text{ }11\text{ }N\]
C) \[311.24\,\,N\]
D) \[300.5\text{ }N\]
View Answer play_arrowquestion_answer69) The magnetic needle has magnetic moment \[8.7\times {{10}^{-2}}\text{ }A-{{m}^{2}}\]and moment of inertia\[11.5\times {{10}^{-6}}\text{ }kg-{{m}^{2}}\]. It performs 10 complete oscillations in \[6.70\text{ }s,\] what is the magnitude of the magnetic field?
A) \[0.012\text{ }T\]
B) \[0.120\text{ }T\]
C) \[1.200\,\,T\]
D) \[2.10\,\,T\]
View Answer play_arrowquestion_answer70) The distance for which ray optics is good approximation for an aperture \[5\,\,mm\]and wavelength \[5000\overset{\text{o}}{\mathop{\text{A}}}\,\]is
A) \[18\,m\]
B) \[30\,\,m\]
C) \[38\,\,m\]
D) \[50\,\,m\]
View Answer play_arrowquestion_answer71) A compound microscope has a magnification of\[30\]. The focal length of the eye-piece is \[5\text{ }cm\] If the final image is formed at the least distance of distinct vision \[(25\,\,cm)\] the magnification produced by the objective is
A) \[10\]
B) \[7.5\]
C) \[5\]
D) \[15\]
View Answer play_arrowquestion_answer72) Which of the following relation is called mirror equation?
A) \[u/v+f/u=1f\]
B) \[1/v+1/u=1f\]
C) \[1/f+u=1/v\]
D) \[uf+vf=uv\]
View Answer play_arrowquestion_answer73) A stone of mass \[0.05\text{ }kg\] is thrown vertically upwards. What is the direction and magnitude of the net force on the stone during its upward motion?
A) \[0.49\text{ }N\]vertically downward direction
B) \[0.49\text{ }N\] vertically upwards direction
C) \[0.05\text{ }N\]vertically downwards direction
D) \[9.8\text{ }N\]vertically upwards direction
View Answer play_arrowquestion_answer74) Two different coils have self-inductance \[{{L}_{1}}=8\,\,mH,\]\[{{L}_{2}}=2\,\,mH,\] The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage and the energy stored in the first coil are \[{{i}_{1}},\,\,{{V}_{1}}\] and \[{{W}_{1}}\] respectively. Corresponding values for the second coil at the same instant are \[{{i}_{2}},\,{{V}_{2}}\] and \[{{W}_{2}}\] respectively. Then,
A) \[{{W}_{2}}/{{W}_{1}}=8\]
B) \[{{W}_{2}}/{{W}_{1}}=1/8\]
C) \[{{W}_{2}}/{{W}_{1}}=4\]
D) \[{{W}_{2}}/{{W}_{1}}=1/4\]
View Answer play_arrowquestion_answer75) A concave mirror of focal length 'f produces a real image n times the size of the object. The distance of the object from the mirror is
A) \[(n-1)f\]
B) \[(n+1)f\]
C) \[(n+1)f/n\]
D) \[(n-1)f/n\]
View Answer play_arrowquestion_answer76) Which of the following mentioned is a type of hydrocarbon?
A) Saturated hydrocarbons
B) Unsaturated hydrocarbons
C) Aromatic hydrocarbons
D) All of the above
View Answer play_arrowquestion_answer77) The process of formation of polymers from respective monomers is called
A) polyacrylonitrile
B) copolymerisation
C) polymerization
D) None of the above
View Answer play_arrowquestion_answer78) Energy of one mole of photons of radiation whose frequency is \[5\times {{10}^{14}}\,Hz\]is
A) \[199.51\text{ }kJ\text{ }mo{{l}^{-1}}\]
B) \[~189.51\text{ }kJ\,mo{{l}^{-1}}\]
C) \[198.51\,kJ\,mo{{l}^{-1}}\]
D) \[188.51\,kJ\,mo{{l}^{-1}}\]
View Answer play_arrowquestion_answer79) The total number of orbitals associated with the principal quantum number \[n=3\]is
A) 9
B) 8
C) 5
D) 7
View Answer play_arrowquestion_answer80) Mass number of an atom is the sum of
A) number of protons + number of neutrons + number of electrons
B) number of protons + number of neutrons
C) number of protons + number of electrons
D) number of electrons + number of neutrons
View Answer play_arrowquestion_answer81) Which of the following is used in the manufacture of alloys?
A) Lithium
B) Hatides
C) Plaster of Paris
D) Beryllium
View Answer play_arrowquestion_answer82) Williamson's synthesis is used to prepare
A) acetone
B) PVC
C) ethers
D) bakelite
View Answer play_arrowquestion_answer83) Which acid is present in vinegar?
A) Formic acid
B) Acetic acid
C) Butyric acid
D) Tartaric acid
View Answer play_arrowquestion_answer84) What is the percentage of free space in body centered cubic unit cell?
A) 32%
B) 20%
C) 34%
D) 28%
View Answer play_arrowquestion_answer85) In the formation of\[\pi -\]bond, the atomic orbitals overlap in such a way that
A) their axes remain parallel to each other and perpendicular to the internuclear axis
B) their axes remain parallel to each other and parallel to the internuclear axis
C) their axes remain perpendicular to each other and parallel to the internuclear axis
D) their axes remain perpendicular to each other and perpendicular to the internuclear axis
View Answer play_arrowquestion_answer86) What elements are present in\[f-\]block series?
A) Lanthanoids
B) Actinoids
C) Lanthanoids and actinoids
D) Lipids
View Answer play_arrowquestion_answer87) What colour is imparted into the flame when lithium is burnt?
A) Golden yellow
B) Brick red
C) Crimson red
D) Grassy green
View Answer play_arrowquestion_answer88) Which among the following is a non-colligative property?
A) Elevation in boiling point
B) Osmotic pressure
C) Refractive index
D) Lowering of vapour pressure
View Answer play_arrowquestion_answer89) Ethylene can be converted into alcohol by treatment of
A) \[Aq.\text{ }KOH\]
B) \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]as catalyst
C) Moist silver oxide
D) \[~Zn/HCl\]
View Answer play_arrowquestion_answer90) Negatively charged particles are called
A) electrons
B) protons
C) neutrons
D) None of these
View Answer play_arrowquestion_answer91) Atoms with identical atomic number but different atomic mass number are known as
A) polymers
B) isobars
C) isotopes
D) isomers
View Answer play_arrowquestion_answer92) The colour of transition metal compound is due to
A) complete ns subshell
B) small size metal ions
C) incomplete \[(n-1)\,d\]subshell
D) absorption of light in UV region
View Answer play_arrowquestion_answer93) The mixture of reactants and products in the equilibrium state is called?
A) Chemical mixture
B) Equilibrium mixture
C) Chemical equilibrium
D) Dynamic equilibrium
View Answer play_arrowquestion_answer94) Among the following molecule which has the zero dipole moment?
A) \[B{{F}_{3}}\]
B) \[{{H}_{2}}O\]
C) \[N{{F}_{3}}\]
D) \[Cl{{O}_{2}}\]
View Answer play_arrowquestion_answer95) Who has synthesised the organic compound 'urea' for the first time?
A) Friedrich Wohler
B) Berzelius
C) Kolbe
D) Berthelot
View Answer play_arrowquestion_answer96) How much is the pH of human blood?
A) 5.2
B) 8.3
C) 6.3
D) 7.4
View Answer play_arrowquestion_answer97) A reagent which lowers the oxidation number of an element in a given substance in known as
A) oxidising agent
B) reduction
C) reducing agent
D) oxidation
View Answer play_arrowquestion_answer98) Sodium carbonate is manufactured by
A) Castner-Kellner
B) Solvay process
C) oxidation
D) transmission process
View Answer play_arrowquestion_answer99) EDTA can form complex with how many number of donor atoms?
A) One
B) Two
C) Six
D) Three
View Answer play_arrowquestion_answer100) Henry's law constant value for\[{{O}_{2}}\] in water is
A) 46.82
B) 43.86
C) 88.84
D) 76.48
View Answer play_arrowquestion_answer101) Polycondensation products of dicarboxylic acids and diols are
A) polyamides
B) neoprene
C) glyptal
D) polyesters
View Answer play_arrowquestion_answer102) The attractive force which holds various constituents together in different chemical species is called
A) valence bond
B) chemical bond
C) atomic bond
D) electrovalent bond
View Answer play_arrowquestion_answer103) What are lanthanides and actinides?
A) Inner transition element
B) Noble gas
C) Normal element
D) Transition element
View Answer play_arrowquestion_answer104) Compounds having the same molecular formula but different structures are classified as
A) functional group isomers
B) structural isomers
C) optical isomerism
D) Metamerism
View Answer play_arrowquestion_answer105) Gas constant is equal to the
A) product of two specific heat
B) difference of two specific heat
C) ratio of two specific heat
D) sum of two specific heat
View Answer play_arrowquestion_answer106) The colour in the coordination compounds can be readily explained in terms of
A) spectrochemistry
B) chelate effect
C) crystal field theory
D) None of the above
View Answer play_arrowquestion_answer107) Paramagnetism is exhibited due to which one of the following reason?
A) Presence of unpaired electrons
B) Presence of completely filled electronic subshell
C) By non-transition element
D) By elements with noble gas configuration
View Answer play_arrowquestion_answer108) Which one of the following acid does not have a carboxylic group?
A) Methanoic acid
B) Ethanoic acid
C) Propanoic acid
D) Picric acid
View Answer play_arrowquestion_answer109) How will you define the specific heat at constant volume?
A) The amount of heat required to raise the temperature of unit mass of gas through one degree at constant pressure
B) The amount of heat required to raise the temperature of 1 kg of water through one degree
C) The amount of heat required to raise the temperature of unit mass of gas through one degree at constant volume
D) All of the above
View Answer play_arrowquestion_answer110) The chief commercial use of amines as intermediates in the synthesis of
A) medicines
B) fibers
C) medicines and fibers
D) proteins
View Answer play_arrowquestion_answer111) Silver, gold, platinum, iron, copper and titanium are part of the
A) minerals
B) transition metals
C) salts
D) All of these
View Answer play_arrowquestion_answer112) Wood spirit is known as
A) Ethanol
B) Methanol
C) Propanol
D) None of these
View Answer play_arrowquestion_answer113) What is the value of 1/n in Freundlich adsorption isotherm2
A) Between 2 and 4 in all cases
B) Between 0 and 1 in all cases
C) 1 in case of chemisorptions
D) 1 in case of physical adsorption
View Answer play_arrowquestion_answer114) What is the product of reaction between calcium carbide and water?
A) Ethylene
B) Acetylene
C) Methane
D) Benzene
View Answer play_arrowquestion_answer115) The crystal lattice of electrovalent compound is composed of
A) oppositely charged ions
B) both molecules and ions
C) molecules
D) atoms
View Answer play_arrowquestion_answer116) Anti-Markownikoff addition of HBr is observed in
A) propene
B) but-2-ene
C) pent-2-ene
D) All of these
View Answer play_arrowquestion_answer117) What kind of isomerism is exhibited by the compounds\[C{{H}_{3}}C{{H}_{2}}CHO\]and \[C{{H}_{3}}COC{{H}_{3}}?\]
A) Geometrical isomerism
B) Functional isomers
C) Tautomers
D) Metamers
View Answer play_arrowquestion_answer118) Mass of a proton is
A) 0.00727 amu
B) 1.0087 amu
C) 0.00054 amu
D) 1.00727 amu
View Answer play_arrowquestion_answer119) The concentration of hydrogen ion in a sample of soft drink is \[3.8\times {{10}^{-3}}M.\] What is its pH?
A) \[3.84\]
B) \[2.42\]
C) \[4.44\]
D) \[1.42\]
View Answer play_arrowquestion_answer120) Which factor has no influence on the rate of reaction?
A) Molecularity
B) Temperature
C) Concentration of reactant
D) Nature of reactant
View Answer play_arrowquestion_answer121) What kinds of bonds are present in ethene molecule?
A) 1 pi and 5 sigma bonds
B) 1 pi and 3 sigma bonds
C) 1 sigma and 1 pi bonds
D) 3 sigma and 3 pi bonds
View Answer play_arrowquestion_answer122) r. The smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation is known as
A) quantum
B) photon
C) spectrum
D) photoelectron
View Answer play_arrowquestion_answer123) Food preservatives prevent spoilage of food due to microbial growth. The most commonly used preservatives are
A) table salt, sugar
B) vegetable oils and sodium benzoate
C) \[{{C}_{6}}{{H}_{5}}COONa\]
D) All of the above
View Answer play_arrowquestion_answer124) Based on which method amines are prepared?
A) Reduction of nitro compounds
B) Ammonolysis of alkyl halides
C) Reduction of nitrites and amides
D) All of the above
View Answer play_arrowquestion_answer125) All substances that conduct electricity in aqueous solutions are called?
A) Electrolytes
B) Acids
C) Buffers
D) Catalyst
View Answer play_arrowquestion_answer126) In which year, IUPAC draft recommends that anionic ligands will end with-ido so that chloro would become chloride
A) 1994
B) 1984
C) 2000
D) 2004
View Answer play_arrowquestion_answer127) Use of chemicals for therapeutic effect is called
A) medicines
B) chemotherapy
C) drug-target interaction
D) phototherapy
View Answer play_arrowquestion_answer128) What is the type of hybridisation found in methane?
A) \[s{{p}^{3}}\]
B) \[s{{p}^{2}}\]
C) \[sp\]
D) None of these
View Answer play_arrowquestion_answer129) Addition of oxygen to an element or a compound is termed as
A) oxidation
B) reduction
C) ionisation
D) redox reaction
View Answer play_arrowquestion_answer130) Molality of 2.5 g of ethanoic acid \[(C{{H}_{3}}COOH)\] in 75 g of benzene is
A) \[~0.565\text{ }mol\text{ }k{{g}^{-1}}\]
B) \[~0.656\text{ }mol\text{ }k{{g}^{-1}}\]
C) \[~0.556\text{ }mol\text{ }k{{g}^{-1}}\]
D) \[0.665\text{ }mol\text{ }k{{g}^{-1}}\]
View Answer play_arrowquestion_answer131) It has been found that for a chemical reaction with rise in temperature by\[{{10}^{o}},\]the rate constant is
A) nearly doubled
B) nearly tripled
C) increases 5 times
D) increases 4 times
View Answer play_arrowquestion_answer132) Carbonyl compounds are constituents of
A) fabrics, drugs
B) fabrics, plastics
C) flavourings, plastics
D) All of these
View Answer play_arrowquestion_answer133) What is IUPAC name of \[iso-\]propylamine?
A) Propan-2-amine
B) Ethanamine
C) 2-aminotoluene
D) Propan-1 -amine
View Answer play_arrowquestion_answer134) lonization energy and electron affinity are defined at
A) enthalpy
B) spontaneity
C) equilibrium
D) absolute zero
View Answer play_arrowquestion_answer135) When acetaldehyde is heated with dilute sodium hydroxide solution, the product is
A) ethanol and sodium acetate
B) paraldehyde
C) aldol
D) brown resin
View Answer play_arrowquestion_answer136) Monovalent sodium and potassium ions, divalent magnesium and calcium ions are found in
A) lipids
B) biological fluids
C) fats
D) enzymes
View Answer play_arrowquestion_answer137) The removal of an electron from an atom results in the formation of
A) anion
B) anode
C) cation
D) cathode
View Answer play_arrowquestion_answer138) Which compound is responsible for perfumery?
A) Ketones
B) Ethers
C) Alcohols
D) Esters
View Answer play_arrowquestion_answer139) Which is the metal present in the coordination compound chlorophyll?
A) Ca
B) Mg
C) K
D) Na
View Answer play_arrowquestion_answer140) 45 g of ethylene glycol \[({{C}_{2}}{{H}_{6}}{{O}_{2}})\] is mixed with 600 g of water, what is the depression of freezing point?
A) 7.9 K
B) 2.5 K
C) 6.6 K
D) 2.2 K
View Answer play_arrowquestion_answer141) In \[\text{B}{{\text{r}}_{\text{3}}}{{\text{O}}_{\text{8}}}\]compound, oxidation number of bromine is
A) 16/13
B) 26/3
C) 24/3
D) 16/3
View Answer play_arrowquestion_answer142) How many octahedral void(s) are present per atom in a cubic close - packed structure?
A) 3
B) 4
C) 1
D) 2
View Answer play_arrowquestion_answer143) Lithium shows diagonal relationship with
A) sodium
B) magnesium
C) calcium
D) aluminium
View Answer play_arrowquestion_answer144) Why d-block element form complexes?
A) Due to large size and high nuclear charge
B) Due to small size and low nuclear charge
C) Due to small size and high nuclear charge
D) None of the above
View Answer play_arrowquestion_answer145) What is conductance?
A) Inverse of resistance
B) Proportional of resistance
C) Equal of resistivity
D) Equal of resistance
View Answer play_arrowquestion_answer146) Which is the correct statement about solid?
A) Very high compressibility
B) Maximum intermolecular distance
C) Definite mass but no definite volume
D) Maximum intermolecular force of attraction
View Answer play_arrowquestion_answer147) The enthalpy change accompanying a reaction is called
A) reaction enthalpy
B) standard enthalpy
C) thermochemical equation
D) enthalpy of atomization
View Answer play_arrowquestion_answer148) According to IUPAC system, what is the correct name of the compound\[[Cr{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{3}}]C{{l}_{3}}\]
A) triamminetriaquachromium \[(III)\] chloride
B) triamminetriaquachromiumchloride \[(III)\]
C) tetraammoniumtriaquachromium \[(III)\] chloride
D) None of the above
View Answer play_arrowquestion_answer149) The relative ease of dehydration of alcohols follows following order
A) tertiary > secondary > primary
B) primary > secondary > tertiary
C) secondary > tertiary > primary
D) tertiary > primary > secondary
View Answer play_arrowquestion_answer150) What is the unit of zero order reaction?
A) \[mol\,L\,{{s}^{-1}}\]
B) \[{{S}^{-1}}\]
C) \[L\,mo{{l}^{-1}}{{s}^{-1}}\]
D) None of the above
View Answer play_arrowquestion_answer151) Find the value of \[\cos \,\,(29\pi /3)?\]
A) \[1\]
B) \[0\]
C) \[\frac{\sqrt{3}}{2}\]
D) \[1/2\]
View Answer play_arrowquestion_answer152) Find the derivative of \[\sqrt{2}x+2\sqrt{x}-\frac{1}{x}\]?
A) \[\sqrt{2}+1/\sqrt{x}(1-1/2x)\]
B) \[\sqrt{2}-1/\sqrt{x}(1+1/2x)\]
C) \[\sqrt{2}-1/\sqrt{x}(1-1/2x)\]
D) \[\sqrt{2}+1/\sqrt{x}(1+1/2x)\]
View Answer play_arrowquestion_answer153) Solve \[\frac{dy}{dx}+\frac{y}{x}={{x}^{3}}\]
A) \[y=\frac{{{x}^{4}}}{5}+Cx\]
B) \[y=\frac{{{x}^{3}}}{3}+Cx\]
C) \[y=\frac{{{x}^{3}}}{3}+C\]
D) \[y=\frac{{{x}^{4}}}{4}+x\]
E) None of these
View Answer play_arrowquestion_answer154) Given two vectors are \[\hat{i}-\hat{j}\] and \[\hat{i}+2\hat{j},\] the unit vector is coplanar with the two vectors and perpendicular to the first. Find the vector?
A) \[+\frac{1}{\sqrt{2}}\,(i+k)\]
B) \[+\frac{1}{\sqrt{5}}\,(2i+j)\]
C) \[+\frac{1}{\sqrt{2}}\,(i+j)\]
D) \[+\frac{1}{\sqrt{2}}\,(2i+3j)\]
View Answer play_arrowquestion_answer155) Solve the linear programming problem: max \[Z=x+2y\]subject to constraints: \[x-y\le 10,\]\[2x+3y\le 20.\],
A) \[max\text{ }Z=10~\]
B) \[max\text{ }Z=30\]
C) \[max\text{ }2=40\]
D) \[max\text{ }Z=50\]
E) None of these
View Answer play_arrowquestion_answer156) Find the intersection of the spheres \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13\] and \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+3y+4z=8\]
A) \[x-y-z=1\]
B) \[x-2y-z=1\]
C) \[x-y-2z=1\]
D) \[2x-y-z=1\]
View Answer play_arrowquestion_answer157) Convert \[(i+1)/(\cos \,\pi /4)-i\,\sin (\pi /4)\] in polar form?
A) \[\cos \,(\pi /4)+i\,sin\,(\pi /4)\]
B) \[\cos \,(\pi /2)+i\,\sin \,(\pi /2)\]
C) \[\sqrt{2}\,(\cos \,(\pi /4)+i\,\sin (\pi /4))\]
D) \[\sqrt{2}\,(\cos \,(\pi /2)\,+\,i\,\sin (\pi /2))\]
View Answer play_arrowquestion_answer158) Solve \[{{\sin }^{-1}}\,2x+{{\cos }^{-1}}\,2x+2\,{{\tan }^{-1}}\,x=\pi \]
A) \[1\]
B) \[0\]
C) \[-1\]
D) \[1/\sqrt{2}\]
View Answer play_arrowquestion_answer159) For what values of x, the numbers \[-1,\,x,-3/4\] are in GP?
A) \[3/2\]
B) \[\sqrt{3}/4\]
C) \[\sqrt{3}/2\]
D) \[3/\sqrt{2}\]
View Answer play_arrowquestion_answer160) \[{{(1+i)}^{3}}+{{(1-i)}^{3}}\]
A) \[1\]
B) \[-2\]
C) \[0\]
D) \[-4\]
View Answer play_arrowquestion_answer161) Find the length of the diagonal of the parallelepiped formed by planes drawn through the points \[(2,3,5)\] and \[(5,9,7),\] parallel to the co-ordinate planes?
A) \[\sqrt{38}\] units
B) \[7\]nits
C) \[\sqrt{155}\] units
D) \[13\]units
View Answer play_arrowquestion_answer162) If \[g(x)=({{x}^{2}}+2x+3)\,f(x),\,\,f(0)=5\] and \[{{\lim }_{x\to 0}}\,\frac{f(x)-5)}{x}=4,\]then \[f'(0)\] equal to
A) \[22\]
B) \[18\]
C) \[20\]
D) \[25\]
E) None of these
View Answer play_arrowquestion_answer163) Find \[\int{\frac{1}{\sqrt{7-{{x}^{2}}}}\,dx}\]
A) \[\frac{1}{2\sqrt{7}}\,\log \,\left| \frac{\sqrt{7+x}}{\sqrt{7-x}} \right|+C\]
B) \[{{\sin }^{-1}}\,\left( \frac{x}{\sqrt{7}} \right)+C\]
C) \[\log |x+\sqrt{{{x}^{2}}-7}|+C\]
D) \[\frac{1}{2\sqrt{7}}\log \,\left| \frac{x-\sqrt{7}}{x+\sqrt{7}} \right|+C\]
View Answer play_arrowquestion_answer164) Find the range of the function \[f:[0,\,1]\to R,\,\,f(x)={{x}^{3}}-{{x}^{2}}+4x+2{{\sin }^{-1}}x\]?
A) \[[-(\pi +2),\,0]\]
B) \[[0,4+\pi ]\]
C) \[[2,3]\]
D) \[(0,\,2+\pi ]\]
View Answer play_arrowquestion_answer165) Solve the inequality \[3x+2>-16,\,2x-3\le 11\]
A) \[(-6,7)\]
B) \[[-6,7)\]
C) \[(-6,7]\]
D) [-6, 7]
View Answer play_arrowquestion_answer166) Events A, B and C are mutually exclusive events such that \[P(A)=(3x+1)/3,\] \[P(B)=(x-1)/4,\] \[P(C)=(1-2x)/2,\] Find the set of possible value of x in the interval.
A) \[[-1/3,\,\,1/2]\]
B) \[[1/3,\,2/3]\]
C) \[[1/3,\,13/3]\]
D) \[[0,1]\]
E) None of these
View Answer play_arrowquestion_answer167) If \[{{\cos }^{-1}}(2-{{x}^{2}})/(1+{{x}^{2}})+{{\tan }^{-1}}x=\pi /2,\], then x is equal to?
A) \[0\]
B) \[1\]
C) \[\frac{1}{\sqrt{3}}\]
D) \[\sqrt{3}\]
View Answer play_arrowquestion_answer168) There are 7 horses in a race, Mr. X selected 2 horses at random and bet on them. The probability that Mr. X selected the winning horse, is
A) \[1/7\]
B) \[4/7\]
C) \[3/7\]
D) \[2/7\]
View Answer play_arrowquestion_answer169) If \[{{x}^{y}}={{e}^{(x-y)}},\] then find \[dy/dx\]
A) \[\log x/{{(1+\log x)}^{2}}\]
B) \[(\log x)\,/\,(1+\log x)\]
C) \[(1-\log x)\,/\,(1+\log x)\]
D) \[(\log x)\,/\,{{(1-\log x)}^{2}}\]
View Answer play_arrowquestion_answer170) The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, find the value of \[P(X=1)\].
A) \[1/4\]
B) \[1/16\]
C) \[1/8\]
D) \[1/32\]
View Answer play_arrowquestion_answer171) Find the domain of the function \[f(x)=({{x}^{2}}+1)/({{x}^{2}}-3x+3)?\]
A) \[R-\{1,\,\,2\}\]
B) \[R-\{1,\,\,4\}\]
C) \[R\]
D) \[R-\{\,1\,\}\]
View Answer play_arrowquestion_answer172) Let \[A\,\,(2,\,\,-3)\]and \[B\,\,(-2,\,\,1)\] be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line
A) \[3x-2y=3\]
B) \[2x+3y=9\]
C) \[2x-3y=7\]
D) \[3x-2y=5\]
View Answer play_arrowquestion_answer173) Find \[^{n}{{C}_{21}}\] if \[^{n}{{C}_{10}}{{=}^{n}}{{C}_{11}}.\]
A) \[1\]
B) \[0\]
C) \[11\]
D) \[10\]
View Answer play_arrowquestion_answer174) 9th term in \[n(n-4)/({{n}^{2}}+1)\] is
A) \[55/82\]
B) \[40/82\]
C) \[45/82\]
D) \[36/82\]
View Answer play_arrowquestion_answer175) Find the area of the triangle with vertices \[(2,3),\]\[(0,\,\,1)\]and \[(1,\,\,2)\].
A) \[{\scriptstyle{}^{1}/{}_{2}}\]sq. unit
B) \[1\] sq. unit
C) \[2\] sq. units
D) \[2\,\,{\scriptstyle{}^{1}/{}_{2}}\]sq. units
E) None of these
View Answer play_arrowquestion_answer176) Solve the system of linear equations \[x+y=1,\]\[x-2y=4\].
A) \[x=2,y=-5\]
B) \[x=1,y=2\]
C) \[x=2,\,y=-1\]
D) \[x=-1,y=2\]
View Answer play_arrowquestion_answer177) Find \[\frac{dy}{dx},\] if \[y={{\sin }^{2}}x+{{\cos }^{4}}x\]
A) \[\frac{-\sin \,4x}{4}\]
B) \[\frac{-\sin \,2x}{2}\]
C) \[\frac{\sin \,4x}{4}\]
D) \[\frac{-\sin \,4x}{2}\]
View Answer play_arrowquestion_answer178) A manufacturer has \[500\text{ }L\]of a \[10%\]solution of acid, find the range of 40% acid to be added to it y such that the acid content in the resultant mixture will be more than \[15%\] but less than \[20%\] .
A) More than \[250\text{ }L\]and less than \[~300\]
B) More than \[300\text{ }L\] and less than \[400\]
C) More than \[100\text{ }L\] and less than \[250\]
D) More than \[250\text{ }L\]and less than \[350\]
View Answer play_arrowquestion_answer179) If the eccentricity of an ellipse with its centre at the origin is \[1/2\] and one of its directrices is\[x=4,\]then find the equation of the ellipse
A) \[3{{x}^{2}}+4{{y}^{2}}=1\]
B) \[4{{x}^{2}}+3{{y}^{2}}=12\]
C) \[3{{x}^{2}}+4{{y}^{2}}=12\]
D) \[4{{x}^{2}}+3{{y}^{2}}=12\]
View Answer play_arrowquestion_answer180) Integrate \[\frac{{{\sec }^{2}}\,({{\sin }^{-1}}x)}{\sqrt{1-{{x}^{2}}}}\]
A) \[\sin \,({{\tan }^{-1}}x)+C\]
B) \[\tan \,({{\sec }^{-1}}x)+C\]
C) \[\tan \,({{\sin }^{-1}}x)+C\]
D) \[-\tan \,(co{{s}^{-1}}x)+C\]
View Answer play_arrowquestion_answer181) A circle with centre \[(0,\,\,3)\] is passing through the foci of the ellipse \[{{x}^{2}}/16+{{y}^{2}}/9=1.\] Find the radius of the circle.
A) \[7/2\] units
B) \[3\] units
C) \[4\] units
D) \[\sqrt{12}\] units
View Answer play_arrowquestion_answer182) Which term of the series \[\sqrt{2},2/3,\,2\sqrt{2}/9,....\]is \[16/2187\]?
A) 10th term
B) 8th term
C) 9th term
D) 11th term
View Answer play_arrowquestion_answer183) Integrate \[\frac{1}{{{x}^{3}}\,({{x}^{2}}-1)}\]
A) \[\frac{1}{3}\log \left| \frac{{{x}^{3}}}{{{x}^{3}}-1} \right|+C\]
B) \[\frac{1}{3}\log \left| \frac{1-{{x}^{3}}}{{{x}^{3}}} \right|+C\]
C) \[\log \left| \frac{{{x}^{3}}}{{{x}^{3}}-1} \right|+C\]
D) \[\frac{1}{3}\log \left| \frac{{{x}^{3}}-1}{{{x}^{3}}} \right|+C\]
E) None of these
View Answer play_arrowquestion_answer184) Evaluate \[\underset{x\to 3}{\mathop{\lim }}\,\frac{3-x}{\sqrt{4+x}-\sqrt{1+2x}}\]
A) \[0\]
B) \[7\sqrt{2}\]
C) \[4\sqrt{7}\]
D) \[2\sqrt{7}\]
View Answer play_arrowquestion_answer185) \[\int{{{\sec }^{3}}\,\,x\,\,dx}\]
A) \[1/2[\sec x\tan x-\log |\sec x+\tan x|]+C\]
B) \[1/2[\sec x\tan x+\log |\sec x-\tan x|]+C\]
C) \[1/2[\sec x\tan x-\log |\sec x-\tan x|]+C\]
D) \[1/2[\sec x\tan x+\log |\sec x+\tan x|]+C\]
View Answer play_arrowquestion_answer186) The sum of first three terms of a GP is 7/9 and their product is\[~-8/27\]. Find the common ratio of the series
A) \[r=-2/3\] or \[-3/2\]
B) \[r=-2/3\] or \[3/2\]
C) \[r=2/3\] or \[-3/2\]
D) \[r=2/3\] or \[3/2\]
View Answer play_arrowquestion_answer187) Differentiate \[\sin \,\,(\sin \,\,2x).\]
A) \[2\,\cos \,2x.\,\cos \,2x\]
B) \[2\,\cos \,2x.\,\cos \,(\sin \,2x)\]
C) \[2\,\cos \,2x.\sin 2x\]
D) \[\cos \,2x.\cos \,(\sin 2x)\]
View Answer play_arrowquestion_answer188) In a moderately a symmetrical distribution, the mean and median are 36 and 34 respectively, find out, the value of empirical mode.
A) \[30\]
B) \[32\]
C) \[42\]
D) \[22\]
View Answer play_arrowquestion_answer189) If \[\sin y=x\sin (a+y),\] then find \[dy/dx\].
A) \[{{\sin }^{2}}\,(a+y)/\sin a\]
B) \[\sin a/{{\sin }^{2}}\,(a+y)\]
C) \[\sin a/{{\sin }^{2}}\,(a-y)\]
D) \[{{\sin }^{2}}(a-y)\sin a\]
View Answer play_arrowquestion_answer190) Solve the inequality \[2x-5\le (4x-7)/3?\]
A) \[x\in (-\infty ,\,4)\]
B) \[x\in (-\infty ,\,4]\]
C) \[x\in (-\infty ,\,8]\]
D) \[x\in (-\infty ,\,-4]\]
View Answer play_arrowquestion_answer191) If u , v and w are three non-coplanar vectors, then \[(u+v-w).\,[(u-v)\times (v-w)]\]equals to
A) \[u.\,\,w\times u\]
B) \[u.\,\,v\times w\]
C) \[0\]
D) \[3\,u.\,\,v\times w\]
View Answer play_arrowquestion_answer192) If \[y=x{{e}^{2y}},\]then find \[dy/dx\].
A) \[y/(x(1-2x))\]
B) \[x/(y\,(1-2x))\]
C) \[x/(y(1-2y))\]
D) \[y/(x(1-2y))\]
View Answer play_arrowquestion_answer193) A line makes the same angle 6 with each of the x and z-axis. If it makes the angle \[\beta \] with y-axis such that \[{{\sin }^{2}}\beta =3\,{{\sin }^{2}}\theta ,\] then \[{{\cos }^{2}}\,\theta \] equals
A) \[3/5\]
B) \[1/5\]
C) \[2/5\]
D) \[2/3\]
View Answer play_arrowquestion_answer194) The two curves \[{{x}^{3}}-3x{{y}^{2}}+2=0\] and \[3{{x}^{2}}y-{{y}^{2}}-2=0\]
A) touch each other
B) cut a an angle \[\pi /4\]
C) cut at an angle \[\pi /3\]
D) cut at an angle \[\pi /2\]
View Answer play_arrowquestion_answer195) . Solve for \[x,\,\,{{\tan }^{-1}}(1/x)=\pi +{{\tan }^{-1}}x,\,\,0<x<1\]
A) not defined
B) \[\sqrt{3}\]
C) \[\pm \,1\]
D) \[0\]
E) None of these
View Answer play_arrowquestion_answer196) Solve the equation \[{{x}^{2}}-\sqrt{3}x+1=0\]
A) \[x=(-\sqrt{3}\,\,\pm \,\,2i)/2\]
B) \[x=(-\sqrt{3}\,\,\pm \,i)/2\]
C) \[x=(-\sqrt{3}\,\,\pm \,i)\]
D) \[x=(\sqrt{3}\,\,\pm \,i)/2\]
View Answer play_arrowquestion_answer197) Differentiate \[{{x}^{-3}}\,(2+7x)\]
A) \[\frac{-1}{{{x}^{4}}}\,(3+7x)\]
B) \[\frac{-2}{{{x}^{3}}}\,(2+7x)\]
C) \[\frac{2}{{{x}^{4}}}\,(2+7x)\]
D) \[\frac{-2}{{{x}^{4}}}\,(3+7x)\]
View Answer play_arrowquestion_answer198) The probability that A speaks the truth is \[3\text{ }/5\] and probability that B speaks the truth is\[3\text{ }/4\] Find the probability that they contradict each other when; asked to speak a fact.
A) \[3/20\]
B) \[4/5\]
C) \[9/20\]
D) \[7/20\]
View Answer play_arrowquestion_answer199) Find the multiplicative-inverse of \[5-6i\]
A) \[-(5/61)+(6/61)i\]
B) \[(5/61)+(6/61)i\]
C) \[(5/61)-(6/61)i\]
D) \[-(5/61)+(6/61)i\]
View Answer play_arrowquestion_answer200) Find the sum to n terms of the series whose nth term is \[{{n}^{2}}-2\text{ }n\].
A) \[2n\,(n-1)\]
B) \[2n(n+1)\]
C) \[2{{n}^{2}}(n+1)\]
D) \[2{{n}^{2}}(n-1)\]
E) None of these
View Answer play_arrowquestion_answer201) A plane which passes through the point \[(3,\,2,\,0)\]and the line \[(x-4)/1=(y-7)/5=(z-4)/4\] is
A) \[x+y+z=1\]
B) \[x+2y-z=1\]
C) \[x-y+z=1\]
D) \[2x-y+z=5\]
View Answer play_arrowquestion_answer202) Find the value of \[\sin \,(2\,{{\tan }^{-1}}x),\,|x|\le 1\]
A) \[1/x\]
B) \[x\]
C) \[1/{{x}^{2}}\]
D) \[2x/(1+{{x}^{2}})\]
View Answer play_arrowquestion_answer203) In a group of students, 40 students choose Physics, 30 students choose Chemistry and 15 students choose both. Each of the students choose either Physics or Chemistry. How many students are there in the group?
A) \[60\]
B) \[70\]
C) \[75\]
D) \[55\]
View Answer play_arrowquestion_answer204) Discuss the continuity of the function \[f(x)=\sin 2x-1\]at the point \[x=0,\]and\[x=\pi \].
A) Continuous at \[x=0,\,\pi \]
B) Discontinuous at \[x=0\]but continuous at \[x=\pi \]
C) Continuous at \[x=0\] but discontinuous at \[x=\pi \]
D) Discontinuous at \[x=0,\,\pi \]
View Answer play_arrowquestion_answer205) The value of \[2{{\cot }^{2}}\,(\pi /6)+\,4\,{{\tan }^{2}}(\pi /6)\]\[-3\,\text{cosec }\pi \text{/6}\] is
A) \[2\]
B) \[4\]
C) \[4/3\]
D) \[3/4\]
View Answer play_arrowquestion_answer206) If \[A=\left[ \begin{matrix} 2 & -1 \\ 1 & 2 \\ \end{matrix} \right],\]then \[{{A}^{2}}+2A-3I=?\]
A) \[\left[ \begin{matrix} 4 & -6 \\ 6 & 4 \\ \end{matrix} \right]\]
B) \[0\]
C) \[\left[ \begin{matrix} -6 & 2 \\ -2 & 6 \\ \end{matrix} \right]\]
D) \[5l\]
View Answer play_arrowquestion_answer207) The sum of first 8 terms of the geometric series \[2+6+18+54+.....\]is
A) \[6506\]
B) \[5650\]
C) \[6650\]
D) \[6560\]
View Answer play_arrowquestion_answer208) Let \[A\{1,2,3,4,5\}.\]Find the domain in the relation from A to A by \[R=\{(x,y):y=2x-1\}.\]
A) \[\{1,2,3\}\]
B) \[\{1,2\}\]
C) \[\{1,3,5\}\]
D) \[\{2,4\}\]
View Answer play_arrowquestion_answer209) Find \[\cos \,(x/2),\] if \[\tan \,x=5/12,\,x\] in quadrant III
A) \[5/\sqrt{13}\]
B) \[5/\sqrt{26}\]
C) \[5/13\]
D) \[5/26\]
E) None of these
View Answer play_arrowquestion_answer210) \[\int{{{\sin }^{-1}}\,\,\cos \,\,3x\,\,dx}\]is
A) \[\frac{3\pi }{2}x-\frac{{{x}^{2}}}{2}+C\]
B) \[\frac{\pi }{2}x-\frac{{{x}^{2}}}{2}+C\]
C) \[\frac{3\pi }{2}x+\frac{{{x}^{2}}}{2}+C\]
D) \[\frac{\pi }{2}x+\frac{{{x}^{3}}}{3}+C\]
E) None of these
View Answer play_arrowquestion_answer211) If a, b, c are three vectors such that \[a\text{ }\times \text{b}=c\] and\[b\text{ }\times c=a\],then
A) \[a\ne b\ne c\]
B) \[a=b=c\]
C) \[a\ne b\text{ }\ne \text{ }c\ne 1\]
D) a, b, c are orthogonal in pairs
View Answer play_arrowquestion_answer212) Determine n, if \[^{2n}{{C}_{2}}{{:}^{n}}{{C}_{2}}:\,\,\,\,=\,\,9:2\]
A) \[5\]
B) \[4\]
C) \[3\]
D) \[2\]
View Answer play_arrowquestion_answer213) \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{{{\sin }^{-1}}\,(x-2)}{{{x}^{2}}-4}\]is equal to
A) \[0\]
B) \[2\]
C) \[1/2\]
D) \[1\]
View Answer play_arrowquestion_answer214) If \[a\ne 0\]and the line \[2bx+3cy+4d=0\] passes through the points of intersection of the parabolas\[{{y}^{2}}=4ax\]and \[{{x}^{2}}=4ay,\]then
A) \[{{d}^{2}}+{{(2b-3c)}^{2}}=0\]
B) \[{{d}^{2}}+{{(3b-2c)}^{2}}=0\]
C) \[{{d}^{2}}+{{(2b+3c)}^{2}}=0\]
D) \[{{d}^{2}}+{{(3b-2c)}^{2}}=0\]
View Answer play_arrowquestion_answer215) If \[f(x)={{x}^{3}}-1,\] then find \[[f(3)+f(2)]/11\]
A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
View Answer play_arrowquestion_answer216) The intercept- on the line \[y=x\]by the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\]is AB. Find the equation of the circle on AB as a diameter?
A) \[{{x}^{2}}+{{y}^{2}}+x+y=0\]
B) \[{{x}^{2}}+{{y}^{2}}-x-y=0\]
C) \[{{x}^{2}}+{{y}^{2}}+x-y=0\]
D) \[{{x}^{2}}+{{y}^{2}}-x+y=0\]
View Answer play_arrowquestion_answer217) Compute the product \[\left[ \begin{matrix} -1 & 3 & 0 \\ 2 & 1 & 4 \\ \end{matrix} \right]\times \left[ \begin{matrix} 1 & 3 \\ 0 & 2 \\ -2 & -1 \\ \end{matrix} \right]\]
A) \[\left[ \begin{matrix} 1 & 3 \\ 6 & -4 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} -1 & -3 \\ 6 & 4 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -1 & 3 \\ -6 & 4 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} -1 & 3 \\ -6 & -4 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer218) Find the values of x, y and z from the following equations \[\left[ \begin{matrix} 4 & x-z \\ 2+y & xz \\ \end{matrix} \right]=\left[ \begin{matrix} 4 & 3 \\ -1 & 10 \\ \end{matrix} \right]\]
A) \[x=-5,\text{ }y=3,\text{ }z=2\]
B) \[x=5,y=-3,z=2\]
C) \[x=5,y=3,\text{ }z=-2\]
D) \[x=5,y=-3,z=-2\]
View Answer play_arrowquestion_answer219) Let \[A=\{1,\,\,2\,\{a,\,\,b\},\,\,3,\,\,4\},\] which among the following statements is incorrect?
A) \[\{a,\,b\}\subset A\]
B) \[\{a,\,b\}\in A\]
C) \[\{\{a,\,b\}\}\subset A\]
D) \[\phi \,\,\in \,\,A\]
View Answer play_arrowquestion_answer220) The probability of India winning a test match against South Africa is \[1/2\]assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is
A) \[1/8\]
B) \[1/2\]
C) \[1/4\]
D) \[2/3\]
View Answer play_arrowquestion_answer221) In an experiment with 15 observations on x the following results are available \[\Sigma {{x}^{2}}=2830,\] \[\Sigma x=170.\] One observation that was 20, was found to be wrong and was replaced by correct value 30. Find the correct variance.
A) \[78'\]
B) \[186\]
C) \[158\]
D) \[18\]
View Answer play_arrowquestion_answer222) If a circle passes through the point \[(a,b)\] and cuts the circle \[{{x}^{2}}+{{y}^{2}}=4\]orthogonally, then the locus of its centre is
A) \[2ax+2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
B) \[2ax+2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
C) \[2ax-2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
D) 2ax \[2ax-2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
View Answer play_arrowquestion_answer223) Find the radius of the circle in which the sphere \[{{x}^{2}}+\text{ }{{y}^{2}}+\text{ }{{z}^{2}}+2x-2y-4z=19\]is cut by the plane\[x+2y+2z+7=0\].
A) \[2\]
B) \[3\]
C) \[1\]
D) \[4\]
View Answer play_arrowquestion_answer224) Let \[A=\{1,2,3,4\}\] and R be the relation on A defined by \[\{(a,b);\,\,a,\,b\,\in A,\,\,a\times b\] is an even number}, then find the range of R.
A) \[\{1,2,3,4\}\]
B) \[\{2,\,\,4\}\]
C) \[\{2,\,\,3,\,\,4\}\]
D) \[\{1,\,\,2,\,\,4\}\]
View Answer play_arrow
You need to login to perform this action.
You will be redirected in
3 sec