question_answer1) The dimension of \[\frac{p}{a}\] in the equation\[p=\frac{b-{{t}^{2}}}{ax}\] where \[p\] is pressure, \[x\] is distance and \[t\] is time are
A) \[[ML{{T}^{-2}}]\]
B) \[[M{{T}^{-2}}]\]
C) \[[M{{L}^{3}}{{T}^{-2}}]\]
D) \[[L{{T}^{-3}}]\]
View Answer play_arrowquestion_answer2) A body moving with uniform acceleration describes \[12\,\,m\] in the third second of its motion and \[20\,\,m\] in the \[5th\] second. Find the velocity after \[10th\] second.
A) \[40\,\,m/s\]
B) \[42\,\,m/s\]
C) \[52\,\,m/s\]
D) \[4\,\,m/s\]
View Answer play_arrowquestion_answer3) A ball rolls of the top of a stair way with a horizontal velocity\[u\,\,m{{s}^{-1}}\]. If the steps are \[h\] metre high and \[b\] metre wide, the ball will hit the edge of the nth step, where \[n\] is
A) \[\frac{2hu}{g{{b}^{2}}}\]
B) \[\frac{2h{{u}^{2}}}{g{{b}^{2}}}\]
C) \[\frac{2h{{u}^{2}}}{gb}\]
D) \[\frac{h{{u}^{2}}}{g{{b}^{2}}}\]
View Answer play_arrowquestion_answer4) A man slides down a light rope whose breaking strength is \[\eta \] times his weight. What should be his maximum acceleration so that the rope just not breaks?
A) \[g(1-\eta )\]
B) \[\eta g\]
C) \[\frac{g}{1+\eta }\]
D) \[\frac{g}{1-\eta }\]
View Answer play_arrowquestion_answer5) The motor of an engine is rotating about its axis with an angular velocity of\[100\,\,rev/m\]. It comes to rest in\[15\,\,s\], after being switched off. Assuming constant angular deceleration. What are the numbers of revolutions made by it before coming to rest?
A) \[12.5\]
B) \[40\]
C) \[32.6\]
D) \[15.6\]
View Answer play_arrowquestion_answer6) By what percent the energy of a satellite has to be increased to shift it from an orbit of radius\[r\]to\[3r\]?
A) \[22.3%\]
B) \[33.3%\]
C) \[66.7%\]
D) \[100%\]
View Answer play_arrowquestion_answer7) To maintain a rotar at uniform angular speed of\[200\,\,rad/s\], an engine needs to transmit a torque of\[180\,\,Nm\]. What is the power required by engine? (Assume efficiency of engine to be \[80%)\]
A) \[36\,\,kW\]
B) \[18\,\,kW\]
C) \[45\,\,kW\]
D) \[54\,\,kW\]
View Answer play_arrowquestion_answer8) Two pendulum have time period \[T\] and \[\frac{5T}{4}\] they start \[SHM\] at the same time form the mean position. What will be the phase difference between them after the bigger pendulum completed one oscillation
A) \[{{45}^{o}}\]
B) \[{{90}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{30}^{o}}\]
View Answer play_arrowquestion_answer9) An open pipe of length \[33\,\,cm\] resonates with frequency of\[1000\,\,Hz\]. If the speed of sound is \[333\,\,m{{s}^{-1}}\], then this frequency is
A) fundamental frequency of the pipe
B) third harmonic of the pipe
C) second harmonic of the pipe
D) fourth harmonic of the pipe
View Answer play_arrowquestion_answer10) Water rises to a height h in a capillary at the surface of earth on the surface of the moon the height of water column in the same capillary will be
A) \[6h\]
B) \[h/6\]
C) \[h\]
D) \[zero\]
View Answer play_arrowquestion_answer11) The molar heat capacity in a process of a diatomic gas, if it does a work of \[Q/4\] when heat \[Q\] is supplied to it, is
A) \[\frac{2}{5}R\]
B) \[\frac{10}{3}R\]
C) \[\frac{5}{3}R\]
D) \[\frac{6}{5}R\]
View Answer play_arrowquestion_answer12) A black body has maximum energy at wavelength \[{{\lambda }_{m}}\] at temperature\[2000\,\,K\]. The corresponding wavelength at a temperature of \[3000\,\,K\] will be
A) \[\frac{3}{2}{{\lambda }_{m}}\]
B) \[\frac{2}{3}{{\lambda }_{m}}\]
C) \[\frac{4}{9}{{\lambda }_{m}}\]
D) \[\frac{9}{4}{{\lambda }_{m}}\]
View Answer play_arrowquestion_answer13) The potential field of an electric field \[\mathbf{E}=(y\mathbf{i}+x\mathbf{j})\] is
A) \[V=-(x+y)+\]constant
B) \[V=\]constant
C) \[V=-({{x}^{2}}+{{y}^{2}})+\]constant
D) \[V=-xy+\]constant
View Answer play_arrowquestion_answer14) The \[80\,\,\Omega \] galvanometer deflects full scale for a potentials of\[20\,\,mV\]. A voltmeter deflecting full scale of \[5\,\,V\] is to made using this galvanometer. We must connect
A) a resistance of \[19.92\,\,k\Omega \] parallel to the galvanometer
B) assistance of \[19.92\,\,k\Omega \] in series with the galvanometer
C) a resistance of \[20\,\,k\Omega \] parallel to the galvanometer
D) a resistance of \[20\,\,k\Omega \] in series with galvanometer
View Answer play_arrowquestion_answer15) A current of \[1\,\,A\] is passed through a straight wire of length\[20\,\,m\]. The magnetic field at a point air at a distance of \[3\,\,m\] from either end of wire and lying on the axis of wire will be
A) \[\frac{{{\mu }_{0}}}{2\pi }\]
B) \[\frac{{{\mu }_{0}}}{4\pi }\]
C) \[\frac{{{\mu }_{0}}}{8\pi }\]
D) \[zero\]
View Answer play_arrowquestion_answer16) A short bar magnet placed with its axis at \[{{30}^{o}}\] with a uniform external magnetic field of \[0.16\,\,T\] experience a torque of magnitude\[0.032\,\,J\]. The magnetic moment of the bar magnet will be
A) \[0.23\,\,J{{T}^{-1}}\]
B) \[0.40\,\,J{{T}^{-1}}\]
C) \[0.80\,\,J{{T}^{-1}}\]
D) \[zero\]
View Answer play_arrowquestion_answer17) A coil has an area of \[0.05\,\,{{m}^{2}}\] and has \[800\] turns. After placing the coil in a magnetic field of strength \[4\times {{10}^{-5}}Wb{{m}^{-2}}\] perpendicular to the field, the coil is rotated through \[{{90}^{o}}\] in\[0.1\,\,s\]. The average emf induced is
A) \[zero\]
B) \[0.016\,\,V\]
C) \[0.01\,\,V\]
D) \[0.032\,\,V\]
View Answer play_arrowquestion_answer18) An alternating voltage (in volt) given by \[V=200\sqrt{2}\sin (100t)\] is connected to \[1\,\,\mu F\] capacitor through an \[AC\] ammeter. The reading of the ammeter will be
A) \[10\,\,mA\]
B) \[20\,\,mA\]
C) \[40\,\,mA\]
D) \[80\,\,mA\]
View Answer play_arrowquestion_answer19) Instantaneous displacement current of \[1.0\,\,A\] in the space between the parallel plates of \[1\,\,\mu F\] capacitor can be established by changing potential difference of
A) \[{{10}^{-6}}V/s\]
B) \[{{10}^{6}}V/s\]
C) \[{{10}^{-8}}V/s\]
D) \[{{10}^{8}}V/s\]
View Answer play_arrowquestion_answer20) The maximum magnification that can be obtained with a convex lens of focal length \[2.5\,\,cm\] is least distance of distinct vision is \[25\,\,cm\]
A) \[10\]
B) \[0.1\]
C) \[62.5\]
D) \[11\]
View Answer play_arrowquestion_answer21) The magnifying power of an astronomical telescope is \[8\] and the distance between the two lenses is\[54\,\,cm\]. The focal length of eye lens and objective lens will be respectively
A) 6 cm and 48 cm
B) 48 cm and 6 cm
C) 8 cm and 64 cm
D) 6 cm and 60 cm
View Answer play_arrowquestion_answer22) The path difference between two wave fronts emitted by coherent sources of wavelength \[5460\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\] is \[2.1\] micron. The phase difference between the wave fronts at that point is
A) \[7.692\,\,rad\]
B) \[7.692\,\,\pi \,\,rad\]
C) \[\frac{7.692}{\pi }rad\]
D) \[\frac{7.692}{3\pi }rad\]
View Answer play_arrowquestion_answer23) A photocell with a constant potential difference of \[V\] volt across it is illuminated by a point source from a distance of\[25\,\,cm\]. When the source is moved to a distance of\[1\,\,m\], the electrons emitted by the photocell
A) carry 1/4th their previous energy
B) are 1/6th as numerous as before
C) are 1/4th as numerous as before
D) carry 1/4th their previous momentum
View Answer play_arrowquestion_answer24) When an electron in hydrogen atom is excited from its 4th to 5th stationary orbit, the change in angular momentum of electron is (Planck's constant\[h=6.6\times {{10}^{-34}}Js)\]
A) \[4.16\times {{10}^{-34}}Js\]
B) \[3.32\times {{10}^{-34}}Js\]
C) \[1.05\times {{10}^{-34}}Js\]
D) \[2.08\times {{10}^{-34}}Js\]
View Answer play_arrowquestion_answer25) Let \[T\] be the mean life of a radioactive sample. \[75%\] of the active nuclei present in the sample initially will decay in time
A) \[2T\]
B) \[\frac{1}{2}(\ln 2)T\]
C) \[4T\]
D) \[2(\ln 2)T\]
View Answer play_arrowquestion_answer26) A potential barrier of 0.50 V exists across a \[p-n\] junction. If the depletion region is \[5.0\times {{10}^{-7}}m\] wide, the strength of electric field in this region is
A) \[1.0\times {{10}^{6}}V/m\]
B) \[1.0\times {{10}^{5}}V/m\]
C) \[2.0\times {{10}^{5}}V/m\]
D) \[2.0\times {{10}^{6}}V/m\]
View Answer play_arrowquestion_answer27) What is an \[AND\] gate?
A) It has not equivalence to switching circuit
B) It is equivalent to series switching circuit
C) It is equivalent to parallel switching circuit
D) It is a mixture of series and parallel switching
View Answer play_arrowquestion_answer28) A parachutist, drops first freely from an aero plane for \[10\,\,s\] and then parachute opens out. Now he descends with a net retardation of\[2.5\,\,m/{{s}^{2}}\]. If. he bails out of the plane at a height of \[2495\,\,m\] and \[g=10\,\,m/{{s}^{2}}\], his velocity on reaching the ground will be
A) \[5\,\,m/s\]
B) \[10\,\,m/s\]
C) \[15\,\,m/s\]
D) \[20\,\,m/s\]
View Answer play_arrowquestion_answer29) A particle is moving along a circular path with uniform speed. Through what angle does it angular velocity change when it completes half of the circular path?
A) \[{{0}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{180}^{o}}\]
D) \[{{360}^{o}}\]
View Answer play_arrowquestion_answer30) Tick out the wrong statement.
A) Transverse waves can be generated in solids.
B) A system having ice floating on water has the same volume even after the ice is melted.
C) Heat radiations have the velocity of light.
D) Phase will not change when sound or light waves are reflected back.
View Answer play_arrowquestion_answer31) Two particles \[P\] and \[Q\] describe \[SHM\] of same amplitude\[a\], frequency \[v\] along the same Straight line. The maximum distance between the two particles is\[a\sqrt{2}\]. The initial phase difference between the particles is
A) \[zero\]
B) \[\pi /2\]
C) \[\pi /6\]
D) \[\pi /3\]
View Answer play_arrowquestion_answer32) The magnitude of electric intensity \[E\] is such that an electron placed in it would experience an electrical force equal to its weight. \[E\] is given by
A) \[mge\]
B) \[\frac{e}{mg}\]
C) \[\frac{mg}{e}\]
D) \[\frac{{{e}^{2}}g}{{{m}^{2}}}\]
View Answer play_arrowquestion_answer33) In the figure, charge and the potential difference across the 4uF capacitor will be nearly
A) \[600\mu C,\,\,150\,\,V\]
B) \[300\,\,\mu C,\,\,75\,\,V\]
C) \[800\,\,\mu C,\,\,200\,\,V\]
D) \[580\,\,\mu C,\,\,145\,\,V\]
View Answer play_arrowquestion_answer34) A dip circle lies initially in the magnetic meridian. If it is now rotated through angle \[\theta \] in the horizontal plane, then tangent of the angle of dip is changed in the ratio
A) \[1:\cos \theta \]
B) \[\cos \theta :1\]
C) \[1:\sin \theta \]
D) \[\sin \theta :1\]
View Answer play_arrowquestion_answer35) A \[5\,\,cm\] long solenoid having \[10\,\,\Omega \] resistance and \[5\,\,mH\] inductance is joined to a \[10\,\,V\] battery. At steady state, the current through the solenoid (in ampere) will be
A) \[5\]
B) \[2\]
C) \[1\]
D) \[zero\]
View Answer play_arrowquestion_answer36) A convex lens makes a real image \[4\,\,cm\] long on a screen. When the lens is shifted to a new position without disturbing the object, we again get a real image on the screen which is \[16\,\,cm\] tall. The length of the object must be
A) \[\frac{1}{4}cm\]
B) \[8\,\,cm\]
C) \[12\,\,cm\]
D) \[20\,\,cm\]
View Answer play_arrowquestion_answer37) For a particle of mass \[m\] enclosed in a one-dimensional box of length\[L\], the de-Broglie concept would lead to stationary waves, with nodes at the two ends. The energy values allowed for such a system (with \[n\] as integer) will be
A) \[\frac{{{h}^{2}}}{8m{{L}^{2}}}{{n}^{2}}\]
B) \[\frac{{{h}^{2}}}{4m{{L}^{2}}}{{n}^{2}}\]
C) \[\frac{h}{4mL}n\]
D) \[\frac{{{h}^{2}}}{4m{{L}^{2}}}{{n}^{2}}\]
View Answer play_arrowquestion_answer38) If no is the original mass of the substance of half-life period\[{{t}_{1/5}}=5\,\,yrs\], then the amount of substance left after 15 days is
A) \[\frac{{{N}_{0}}}{8}\]
B) \[\frac{{{N}_{0}}}{16}\]
C) \[\frac{{{N}_{0}}}{2}\]
D) \[\frac{{{N}_{0}}}{4}\]
View Answer play_arrowquestion_answer39) A doubled layered wall has layer\[A\], \[10\,\,cm\] thick and B, \[20\,\,cm\] thick. The thermal conductivity of \[A\] is thrice that of\[B\]. In the steady state, the temperature difference across the wall is\[{{35}^{o}}C\]. The temperature difference across the layer \[A\] is
A) \[{{28}^{o}}C\]
B) \[{{14}^{o}}C\]
C) \[{{7}^{o}}C\]
D) \[{{5}^{o}}C\]
View Answer play_arrowquestion_answer40) The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is
A) \[\sqrt{3}v\]
B) \[\sqrt{2}v\]
C) \[\sqrt{5}v\]
D) \[\sqrt{12}v\]
View Answer play_arrowquestion_answer41) Power supplied to a particle of mass \[2\,\,kg\] varies with time as\[P=\frac{3{{t}^{2}}}{2}W\]. Here \[t\] is in second. If velocity of particle at \[t=0\] is\[v=0\], the velocity of particle at time\[t=2\,\,s\] will be
A) \[1\,\,m/s\]
B) \[4\,\,m/s\]
C) \[2\,\,m/s\]
D) \[2\sqrt{2}\,\,m/s\]
View Answer play_arrowquestion_answer42) A particle is projected from the ground with an initial speed of \[v\] at an angle \[\theta \] with horizontally. The average velocity of the particle between its point of projection and highest point of trajectory is
A) \[\frac{v}{2}\sqrt{1+2{{\cos }^{2}}\theta }\]
B) \[\frac{v}{2}\sqrt{1+2{{\cos }^{2}}\theta }\]
C) \[\frac{v}{2}\sqrt{1+3{{\cos }^{2}}\theta }\]
D) \[v\cos \theta \]
View Answer play_arrowquestion_answer43) Given \[\sigma \] is the compressibility of water, \[p\] is the density of water and \[k\] is the bulk modulus of water. What is the energy density of water at the bottom of a lake \[h\] metre deep?
A) \[\frac{1}{2}\sigma {{(h\rho g)}^{2}}\]
B) \[\frac{1}{2}\sigma (h\rho g)\]
C) \[\frac{1}{2}\frac{h\rho g}{\sigma }\]
D) \[\frac{h\rho g}{\sigma }\]
View Answer play_arrowquestion_answer44) An ideal gas heat engine operates in a Carnot cycle between \[{{227}^{o}}C\] and\[{{127}^{o}}C\]. It absorbs \[6.0\times {{10}^{4}}\,\,cal\] at the higher temperature. The amount of heat converted into work is equal to
A) \[4.8\times {{10}^{4}}cal\]
B) \[3.5\times {{10}^{4}}cal\]
C) \[1.6\times {{10}^{4}}cal\]
D) \[1.2\times {{10}^{4}}cal\]
View Answer play_arrowquestion_answer45) The latent heat of vaporisation of water is\[2240\,\,J\]. If the work done in the process of vaporisation of \[1\,\,g\] is\[168\,\,J\], then increases in internal energy is
A) \[2408\,\,J\]
B) \[2240\,\,J\]
C) \[2072\,\,J\]
D) \[1904\,\,J\]
View Answer play_arrowquestion_answer46) A body dropped from the top of a tower covers a distance \[7x\] in the last second of its journey, where \[x\] is the distance; covered in first second. How much time does it take to reach the ground?
A) \[3\,\,s\]
B) \[4\,\,s\]
C) \[5\,\,s\]
D) \[6\,\,s\]
View Answer play_arrowquestion_answer47) A body just dropped from a tower explodes into two pieces of equal mass in mid-air. Which of the following is not possible?
A) Each part will follow parabolic path
B) Only one part will follow parabolic path
C) Both parts move along a vertical line
D) One part reaches the ground earlier than the other
View Answer play_arrowquestion_answer48) Moment of inertia of a uniform circular disc about a diameter is\[I\]. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be
A) \[5\,\,I\]
B) \[3\,\,I\]
C) \[6\,\,I\]
D) \[4\,\,I\]
View Answer play_arrowquestion_answer49) Two sources \[A\] and \[B\] are sounding notes of frequency\[680\,\,Hz\]. A listener moves from \[A\] to \[B\] with a constant velocity\[u\]. If the speed of sound\[340\,\,m/s\], what must be the value of \[u\] so that he hears \[10\] beats per second?
A) \[2.0\,\,m/s\]
B) \[2.5\,\,m/s\]
C) \[3.0\,\,m/s\]
D) \[3.5\,\,m/s\]
View Answer play_arrowquestion_answer50) A current of \[1\,\,A\] flows in a circular area of wire which subtends an angle of \[\left( \frac{3\pi }{4} \right)rad\] at its centre, whose radius is\[R\]. The magnetic induction \[B\] at the centre is
A) \[\frac{{{\mu }_{0}}I}{R}\]
B) \[\frac{{{\mu }_{0}}I}{2R}\]
C) \[\frac{2{{\mu }_{0}}I}{R}\]
D) \[\frac{3{{\mu }_{0}}I}{8R}\]
View Answer play_arrowquestion_answer51) Which of the following compounds corresponds to van't Hoff factor \[(i)\] to be equal to \[2\] for dilute solution?
A) \[{{K}_{2}}S{{O}_{4}}\]
B) \[NaHS{{O}_{4}}\]
C) \[Sugar\]
D) \[MgS{{O}_{4}}\]
View Answer play_arrowquestion_answer52) \[0.1\,\,M\,\,NaCI\] and \[0.1\,\,M\,\,C{{H}_{3}}COOH\] are kept in separate containers. If their osmotic pressures are \[{{p}_{1}}\] and \[{{p}_{2}}\] respectively then what is the correct statement?
A) \[{{p}_{1}}>{{p}_{2}}\]
B) \[{{p}_{1}}={{p}_{2}}\]
C) \[{{p}_{1}}<{{p}_{2}}\]
D) \[{{p}_{1}}={{p}_{2}}=0\,\,atm\]
View Answer play_arrowquestion_answer53) Primary, secondary and tertiary alcohols may be distinguished by
A) Fehling solution
B) Victor-Meyer test
C) Hofmann test
D) Beilstein test
View Answer play_arrowquestion_answer54) Which of the following will respond to Cannizaro's reaction?
A) \[2,\,\,2-\]dimethylpropanal
B) Acetaldehyde
C) Propionaldehyde
D) Cinnamaldehyde
View Answer play_arrowquestion_answer55) Which one of the following will increase the voltage of the cell? \[Sn(s)+2A{{g}^{+}}(aq)\xrightarrow{{}}S{{n}^{2+}}+(aq)+2Ag(s)\]
A) Increase in the size of silver rod
B) Increasing the size of plate
C) Increase in the concentration of \[A{{g}^{+}}\] ions
D) Increase in the concentration of \[S{{n}^{2+}}\] ions
View Answer play_arrowquestion_answer56) Which among the following can be purified by steam distillation?
A) Phenol
B) Aniline
C) Benzoic acid
D) \[p-\]nitrophenol
View Answer play_arrowquestion_answer57) For a chemical reaction\[A+BC\], the thermodynamic equilibrium constant \[{{K}_{p}}\] is
A) in\[at{{m}^{-2}}\]
B) in\[at{{m}^{-3}}\]
C) in\[at{{m}^{-1}}\]
D) dimensionless
View Answer play_arrowquestion_answer58) If the equivalent, weight of a trivalent metal is \[32.7\], the molecular weight of its chloride is
A) \[68.2\]
B) \[103.7\]
C) \[204.6\]
D) \[32.7\]
View Answer play_arrowquestion_answer59) Conjugate base of hydrazoic acid is
A) \[HN_{3}^{-}\]
B) \[N_{2}^{-}\]
C) \[N_{3}^{-}\]
D) \[{{N}^{3-}}\]
View Answer play_arrowquestion_answer60) The geometrical arrangement and shape of\[I_{3}^{-}\] are respectively
A) trigonal bipyramidal geometry, linear shape
B) hexagonal geometry, T-shape
C) triangular planar geometry, triangular shape
D) tetrahedral geometry, pyramidal shape
View Answer play_arrowquestion_answer61) Sodium reacts with water more vigorously than \[Li\] because it has
A) higher atomic mass
B) more electropositive character
C) metallic nature
D) more electronegative character
View Answer play_arrowquestion_answer62) When sodium is treated with sufficient oxygen/air, the product obtained is
A) \[N{{a}_{2}}O\]
B) \[N{{a}_{2}}{{O}_{2}}\]
C) \[Na{{O}_{2}}\]
D) \[NaO\]
View Answer play_arrowquestion_answer63) Gallium arsenide is purified by
A) froth floatation process
B) van-Arkel method
C) zone refining method
D) electrolytic method
View Answer play_arrowquestion_answer64) Which ion has the lowest radius from the following ions?
A) \[N{{a}^{+}}\]
B) \[M{{g}^{2+}}\]
C) \[A{{l}^{3+}}\]
D) \[S{{i}^{4+}}\]
View Answer play_arrowquestion_answer65) The extraction of which of the following metals involves bessemerisation?
A) Iron
B) Copper
C) Aluminium
D) Silver
View Answer play_arrowquestion_answer66) Terylene is made by polymerisation of terephthalic acid with
A) ethylene glycol
B) phenol
C) ethanol
D) catechol
View Answer play_arrowquestion_answer67) Treatment of ammonia with excess of ethyl iodide will yield
A) diethylamine
B) ethylamine
C) triethylamine
D) tetraethylammonium iodide
View Answer play_arrowquestion_answer68) In the combustion of \[2.0\,\,g\] \[\text{of}\] methane, \[25\,\,kcal\] heat is liberated. Heat of combustion of methane would be
A) \[150\,\,kcal\]
B) \[200\,\,kcal\]
C) \[250\,\,kcal\]
D) \[350\,\,kcal\]
View Answer play_arrowquestion_answer69) Arsenic sulphide is a negative sol. The reagent with least precipitating power is
A) \[AlC{{l}_{3}}\]
B) \[NaCl\]
C) \[Ca{{F}_{2}}\]
D) glucose
View Answer play_arrowquestion_answer70) Which of the following salt when dissolved in water gets hydrolysed?
A) \[NaCl\]
B) \[N{{H}_{4}}Cl\]
C) \[KCl\]
D) \[N{{a}_{2}}S{{O}_{4}}\]
View Answer play_arrowquestion_answer71) \[20\,\,mL\] of a \[HCl\] solution exactly neutralises \[40\,\,mL\] of \[0.005\,\,N\,\,NaOH\] solution. The\[pH\] of\[HCl\]. solution is
A) \[2.5\]
B) \[2.0\]
C) \[1.5\]
D) \[1\]
View Answer play_arrowquestion_answer72) Which of the following is used for inducing sleep?
A) Paracetamol
B) Chloroquine
C) Bithional
D) Barbituric acid derivatives
View Answer play_arrowquestion_answer73) Which of the following acids has the smallest dissociation constant?
A) \[C{{H}_{3}}CHFCOOH\]
B) \[FC{{H}_{2}}C{{H}_{2}}COOH\]
C) \[BrC{{H}_{2}}C{{H}_{2}}COOH\]
D) \[C{{H}_{3}}CBrCOOH\]
View Answer play_arrowquestion_answer74) Hydrolysis of benzonitrile by dilute \[HCl\] yields
A) aniline
B) benzoic acid
C) berizamide
D) benzaldehyde
View Answer play_arrowquestion_answer75) Anti-Markownikoff's addition of \[HBr\] is not observed in
A) propene
B) 1-butene
C) but-2-ene
D) pent-2-ene
View Answer play_arrowquestion_answer76) Kjeldahl's method can be used for estimation of nitrogen in
A) \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}\]
B) pyridine
C) \[{{C}_{6}}{{H}_{5}}-N=N-{{C}_{6}}{{H}_{5}}\]
D) \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]
View Answer play_arrowquestion_answer77) How many electrons in \[19\,\,K\] have\[n=3;\,\,l=0?\]
A) \[1\]
B) \[2\]
C) \[4\]
D) \[3\]
View Answer play_arrowquestion_answer78) Metallic bond is
A) similar to ionic bond
B) similar to covalent bond
C) neither similar to ionic nor covalent bond
D) formed by the movement of positively charged spheres in a sea of electrons
View Answer play_arrowquestion_answer79) Which of the following is not a Lewis base?
A) \[C{{N}^{-}}\]
B) \[ROH\]
C) \[N{{H}_{3}}\]
D) \[AlC{{l}_{3}}\]
View Answer play_arrowquestion_answer80) Hydrogen can have oxidation number/s of
A) \[-1\]only
B) \[+1\]only
C) \[0\]only
D) \[-1,\,\,0,\,\,+1\]
View Answer play_arrowquestion_answer81) \[250\,\,mL\] of a sodium carbonate solution contains \[2.65\,\,g\] of\[N{{a}_{2}}C{{O}_{3}}\]. If \[10\,\,mL\] of this solution is diluted to\[1\,\,L\], what is the concentration of the resultant solution? (Mol. wt. of\[N{{a}_{2}}C{{O}_{3}}=106)\]
A) \[0.1\,\,M\]
B) \[0.001\,\,M\]
C) \[0.01\,\,M\]
D) \[{{10}^{-4}}M\]
View Answer play_arrowquestion_answer82) At constant temperature, in a given mass of an ideal gas
A) the ratio of pressure and volume always remains constant
B) volume always remains constant
C) pressure always remains Constant
D) the product of pressure and volume always remains constant
View Answer play_arrowquestion_answer83) The rate of the reaction intermediates can be determined by the study of
A) catalyst effects
B) concentration of the reactants
C) temperature effects
D) solvent effects
View Answer play_arrowquestion_answer84) Order of reaction is decided by
A) temperature
B) mechanism of reaction
C) molecularity
D) pressure
View Answer play_arrowquestion_answer85) Which of the following conditions will always lead to a non-spontaneous change?
A) \[+ve\Delta H\] and\[+ve\Delta S\]
B) \[-ve\Delta H\]and\[-ve\Delta S\]
C) \[+ve\Delta H\] and\[-ve\Delta S\]
D) \[-ve\Delta H\]and\[+ve\Delta S\]
View Answer play_arrowquestion_answer86) The passage of current liberates \[{{H}_{2}}\] at cathode and \[C{{l}_{2}}\] at anode. The solution is
A) copper chloride in water
B) \[NaCl\] in water
C) ferric chloride in water
D) \[AuC{{l}_{3}}\] in water
View Answer play_arrowquestion_answer87) Compounds with \[{{C}_{4}}{{H}_{11}}N\] as molecular formula can exhibit
A) position isomerism
B) metamerism
C) functional isomerism
D) All the three
View Answer play_arrowquestion_answer88) Which of the following species is nucleophile?
A) \[\overset{+}{\mathop{N}}\,{{O}_{2}}\]
B) \[:C{{X}_{2}}\]
C) \[:\overset{\bullet \,\,\,\bullet }{\mathop{NH_{2}^{-}}}\,\]
D) \[\bullet C{{H}_{3}}\]
View Answer play_arrowquestion_answer89) Which of the following carbocation is most stable?
A) \[C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]
B) \[C{{H}_{2}}=\overset{+}{\mathop{C}}\,H\]
C) \[CH\equiv {{C}^{+}}\]
D) \[{{C}_{6}}H_{5}^{+}\]
View Answer play_arrowquestion_answer90) Brown colour in \[HN{{O}_{3}}\] can be removed by
A) adding \[Mg\] powder
B) boiling the acid
C) passing \[N{{H}_{3}}\] through acid
D) passing air through warm acid
View Answer play_arrowquestion_answer91) What products are expected from the disproportionation reaction of hypochlorous acid?
A) \[HCl{{O}_{3}}\]and\[C{{l}_{2}}O\]
B) \[HCl{{O}_{2}}\]and\[HCl{{O}_{4}}\]
C) \[HCl\]and\[C{{l}_{2}}O\]
D) \[HCl\]and\[HCl{{O}_{3}}\]
View Answer play_arrowquestion_answer92) Which of the following is not a wax?
A) Myricyl palmitate
B) Tripalmitin
C) Myricyl cerotate
D) Cetyl palmitate
View Answer play_arrowquestion_answer93) Which of the following ions forms most stable complex compound?
A) \[F{{e}^{3+}}\]
B) \[M{{n}^{2+}}\]
C) \[N{{i}^{2+}}\]
D) \[C{{u}^{2+}}\]
View Answer play_arrowquestion_answer94) Silver plating is carried out from which of the following?
A) \[AgN{{O}_{3}}\]
B) \[AgCl\]
C) \[K[Ag{{(CN)}_{2}}]\]
D) All of these
View Answer play_arrowquestion_answer95) Which one of the following is an example of non-typical transition elements?
A) \[Li,\,\,K,\,\,Na\]
B) \[Be,\,\,Al,\,\,Pb\]
C) \[Zn,\,\,Cd,\,\,Hg\]
D) \[Ba,\,\,Ga,\,\,Sr\]
View Answer play_arrowquestion_answer96) In the reaction,\[{{C}_{6}}{{H}_{6}}\xrightarrow[AlC{{l}_{3}}]{C{{H}_{3}}Cl}A\xrightarrow{KMn{{O}_{4}}}B\], \[B\]is
A) benzoic acid
B) benzoyl chloride
C) benzaldehyde
D) chlorobenzene
View Answer play_arrowquestion_answer97) The reaction,\[{{C}_{6}}{{H}_{5}}OH\xrightarrow[Pyridine]{C{{H}_{3}}COCl}{{C}_{6}}{{H}_{5}}COC{{H}_{3}}\]is called
A) Reimer-Tiemann reaction
B) Schotten-Baumann reaction
C) acetylation
D) benzoylation
View Answer play_arrowquestion_answer98) Which of the following enzymes is not useful in the digestion of proteins?
A) Chymotripsin
B) Pepsin
C) Tripsin
D) Lipase
View Answer play_arrowquestion_answer99) Which are isomers?
A) Ethyl alcohol and dimethyl ether
B) Acetone and acetaldehyde
C) Propionic acid and propanone
D) Methyl alcohol and dimethyl ether
View Answer play_arrowquestion_answer100) The dative bond is present in
A) \[N{{H}_{3}}\]
B) \[S{{O}_{3}}\]
C) \[PC{{l}_{5}}\]
D) \[B{{F}_{3}}\]
View Answer play_arrowquestion_answer101) The sum of \[i-2-3i+4...\] up to \[100\] terms, where\[i=\sqrt{-1}\]is
A) \[50(1-i)\]
B) \[25i\]
C) \[25(1+i)\]
D) \[100(1-i)\]
View Answer play_arrowquestion_answer102) In a college examination, a candidate is required to answer \[6\] out of \[10\] questions which are divided into sections each containing \[5\] questions. Further the candidate is not permitted to attempt more than \[4\] questions from either of the section. The number of ways in which he can make up a choice of \[6\] questions, is
A) \[200\]
B) \[150\]
C) \[100\]
D) \[50\]
View Answer play_arrowquestion_answer103) For the equations\[x+2y+3z=1\],\[2x+y+3z=2\], \[5x+5y+9z=4\]
A) there is only one solution
B) there exists infinitely many solution
C) there is no solution
D) None of the above
View Answer play_arrowquestion_answer104) If\[a\ne p,\,\,b\ne q,\,\,c\ne r\]and\[\left| \begin{matrix} p & b & c \\ a & q & c \\ a & b & r \\ \end{matrix} \right|=0\]. Then, the value of\[\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}\]is
A) \[0\]
B) \[1\]
C) \[-1\]
D) \[2\]
View Answer play_arrowquestion_answer105) If\[\tan (\pi cos\theta )=cot(\pi sin\theta )\], then the value\[(s)\] of\[\cos \left( \theta -\frac{\pi }{4} \right)\]is/are
A) \[\frac{1}{2}\]
B) \[\frac{1}{\sqrt{2}}\]
C) \[\pm \frac{1}{2\sqrt{2}}\]
D) None of these
View Answer play_arrowquestion_answer106) Form the top of a light house \[60\,\,m\] high with its base at the sea level, the angle of depression of a boat is\[{{15}^{o}}\]. The distance of the boat form the foot of the light house is
A) \[\left( \frac{\sqrt{3}-1}{\sqrt{3}+1} \right)60\,\,m\]
B) \[\left( \frac{\sqrt{3}+1}{\sqrt{3}-1} \right)60\,\,m\]
C) \[\left( \frac{\sqrt{3}+1}{\sqrt{3}-1} \right)m\]
D) None of these
View Answer play_arrowquestion_answer107) Three lines \[px+qy+r=0,\,\,qx+ry+p=0\] and \[rx+py+q=0\] are concurrent, if
A) \[p+q+r=0\]
B) \[{{p}^{2}}+{{q}^{2}}+{{r}^{2}}=pq+qr+rp\]
C) \[{{p}^{3}}+{{q}^{3}}+{{r}^{3}}=3pqr\]
D) None of the above
View Answer play_arrowquestion_answer108) Find the angle between the lines represented by the equation\[{{x}^{2}}-2pxy+{{y}^{2}}=0\]
A) \[{{\cos }^{-1}}(p)\]
B) \[{{\sec }^{-1}}(p)\]
C) \[{{\sec }^{-1}}(-p)\]
D) \[{{\sec }^{-1}}(\pm p)\]
View Answer play_arrowquestion_answer109) The length of the chord of the parabola \[{{x}^{2}}=4ay\] passing through the vertex and having slope \[\tan \alpha \] is
A) \[4a\cos \text{ec}\alpha \cdot \cot \alpha \]
B) \[4a\tan \alpha \cdot \sec \alpha \]
C) \[4a\cos \alpha \cdot \cot \alpha \]
D) \[4a\sin \alpha \cdot \tan \alpha \]
View Answer play_arrowquestion_answer110) If any tangent to the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] intercepts equal lengths I on the axes, then equals to
A) \[{{a}^{2}}+{{b}^{2}}\]
B) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
C) \[{{({{a}^{2}}+{{b}^{2}})}^{2}}\]
D) None of these
View Answer play_arrowquestion_answer111) If the normal at \[\left( ct,\,\,\frac{c}{t} \right)\] on the curve\[xy={{c}^{2}}\] meets the curve again in\[V\] , then
A) \[t'=\frac{-1}{{{t}^{3}}}\]
B) \[t'=\frac{-1}{t}\]
C) \[t'=\frac{1}{{{t}^{2}}}\]
D) \[t{{'}^{2}}=\frac{-1}{{{t}^{2}}}\]
View Answer play_arrowquestion_answer112) The line \[\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}\] intersects the curve\[xy=c,\,\,z=0\], if \[c\] equals to
A) \[\pm 1\]
B) b)\[\pm \frac{1}{3}\]
C) \[\pm \sqrt{5}\]
D) None of these
View Answer play_arrowquestion_answer113) If\[f(x)=\frac{1-x}{1+x}\], the domain of\[{{f}^{-1}}(x)\]is
A) \[R\]
B) \[R-\{-1\}\]
C) \[(-\infty ,\,\,-1)\]
D) \[(-1,\,\,\infty )\]
View Answer play_arrowquestion_answer114) If\[f'(2)=2\],\[f''(2)=1\], then\[\underset{x\to 2}{\mathop{\lim }}\,\frac{2{{x}^{2}}-4f'(x)}{x-2}\] is
A) \[4\]
B) \[0\]
C) \[2\]
D) \[\infty \]
View Answer play_arrowquestion_answer115) A function is denned as follows\[f(x)=\left\{ \begin{matrix} {{x}^{m}}\sin \left( \frac{1}{x} \right), & x\ne 0 \\ 0, & x=0 \\ \end{matrix} \right\}\]what condition should be imposed on m, so that \[f(x)\] may be continuous\[x=0?\]
A) \[m>0\]
B) \[m<0\]
C) \[m=0\]
D) any value of\[m\]
View Answer play_arrowquestion_answer116) The value of\[\lim {{(\cos x+a\sin bx)}^{1/x}}\]is
A) \[1\]
B) \[ab\]
C) \[{{e}^{ab}}\]
D) \[{{e}^{b/a}}\]
View Answer play_arrowquestion_answer117) \[\int{{{e}^{x}}}\left( \frac{x-1}{{{(x+1)}^{3}}} \right)dx\]
A) \[\frac{{{e}^{x}}}{x+1}+C\]
B) \[\frac{{{e}^{x}}}{{{(x+1)}^{2}}}+C\]
C) \[\frac{-{{e}^{x}}}{(x+1)}+C\]
D) \[\frac{-{{e}^{x}}}{{{(x+1)}^{2}}}+C\]
View Answer play_arrowquestion_answer118) For which of the following values of\[m\], is the area of the region bounded by the curve \[y=x-{{x}^{2}}\] and the line \[y=mx\] equals\[9/2\].
A) \[-4\]
B) \[3\]
C) \[2\]
D) \[4\]
View Answer play_arrowquestion_answer119) Three numbers are chosen from \[1\] to\[30\]. Find the probability that they are not consecutive.
A) \[\frac{16}{81}\]
B) \[\frac{144}{145}\]
C) \[\frac{80}{145}\]
D) \[\frac{65}{81}\]
View Answer play_arrowquestion_answer120) If\[\frac{1+4p}{p},\,\,\frac{1-p}{2},\,\,\frac{1-2p}{2}\]are probabilities of three mutually exclusive events, then
A) \[\frac{1}{3}\le p\le \frac{1}{2}\]
B) \[\frac{1}{2}\le p\le \frac{2}{3}\]
C) \[\frac{1}{6}\le p\le \frac{1}{2}\]
D) None of these
View Answer play_arrowquestion_answer121) A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in nth second to the distance covered in a n second is
A) \[\frac{2}{n}-\frac{1}{{{n}^{2}}}\]
B) \[\frac{1}{{{n}^{2}}}-\frac{1}{n}\]
C) \[\frac{2}{{{n}^{2}}}-\frac{1}{n}\]
D) \[\frac{2}{n}+\frac{1}{{{n}^{2}}}\]
View Answer play_arrowquestion_answer122) The equation \[{{x}^{3}}-3x+4=0\] has only one real root. What is its first approximate value as obtained by the method of false position in\[(-3,\,\,-2)\]?
A) \[-2.125\]
B) \[2.125\]
C) \[-2.812\]
D) \[2.812\]
View Answer play_arrowquestion_answer123) If\[z+{{z}^{-1}}=1\], then \[{{z}^{100}}+{{z}^{-100}}\] is equal to
A) \[i\]
B) \[-i\]
C) \[1\]
D) \[-1\]
View Answer play_arrowquestion_answer124) If \[a,\,\,b,\,\,c\] are in\[G\,\,P\], then the equations \[a{{x}^{2}}+2bx+c=0\] and \[d{{x}^{2}}+2ex+f=0\] have a common root, if\[\frac{d}{a},\,\,\frac{e}{b},\,\,\frac{f}{c}\]are in
A) \[AP\]
B) \[GP\]
C) \[HP\]
D) None of these
View Answer play_arrowquestion_answer125) If the roots of the equation\[\frac{1}{x+a}+\frac{1}{x+b}=\frac{1}{c}\] are equal in magnitude but opposite in sign, then their product is
A) \[\frac{1}{2}({{a}^{2}}+{{b}^{2}})\]
B) \[-\frac{1}{2}({{a}^{2}}+{{b}^{2}})\]
C) \[\frac{1}{2}ab\]
D) \[-\frac{1}{2}ab\]
View Answer play_arrowquestion_answer126) The coefficient of \[y\] in expansion of\[{{\left( {{y}^{2}}+\frac{c}{y} \right)}^{2}}\] is
A) \[29c\]
B) \[10c\]
C) \[10{{c}^{3}}\]
D) \[20{{c}^{2}}\]
View Answer play_arrowquestion_answer127) In the expansion of\[{{(1+x)}^{50}}\], the sum of the coefficients of odd powers of \[x\] is
A) \[0\]
B) \[{{2}^{49}}\]
C) \[{{2}^{50}}\]
D) \[{{2}^{51}}\]
View Answer play_arrowquestion_answer128) If\[\cos A=\tan B,\,\,\,\cos B=\tan C,\,\,\,\cos C=\tan A\], then \[\sin A\] is equal to
A) \[\sin {{18}^{o}}\]
B) \[2\sin {{18}^{o}}\]
C) \[2\cos {{18}^{o}}\]
D) \[2\cos {{36}^{o}}\]
View Answer play_arrowquestion_answer129) If in a\[\Delta ABC\],\[\frac{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos c}{c}=\frac{a}{bc}+\frac{b}{ca}\] then the value of the \[\angle A\] is
A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrowquestion_answer130) If\[\tan (x+y)=33\]and\[x={{\tan }^{-1}}3\], then\[y\]will be
A) \[0.3\]
B) \[{{\tan }^{-1}}(1.3)\]
C) \[{{\tan }^{-1}}(0.3)\]
D) \[{{\tan }^{-1}}\left( \frac{1}{18} \right)\]
View Answer play_arrowquestion_answer131) If the algebraic sum of the perpendicular distances from the points \[(2,\,\,0),\,\,\,(0,\,\,2)\] and \[(1,\,\,1)\] to a variable straight line be zero, then the line passes through the point
A) \[(-1,\,\,1)\]
B) \[(1,\,\,1)\]
C) \[(1,\,\,-1)\]
D) \[(-1,\,\,-1)\]
View Answer play_arrowquestion_answer132) If the circles\[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{c}^{2}}\]and\[{{(x-b)}^{2}}+{{(y-a)}^{2}}={{c}^{2}}\]touch each other, then
A) \[a=b\pm 2c\]
B) \[a=b\pm \sqrt{2}c\]
C) \[a=b\pm c\]
D) None of these
View Answer play_arrowquestion_answer133) The number of common tangents of the circles \[{{x}^{2}}+{{y}^{2}}-2x-1=0\]and\[{{x}^{2}}+{{y}^{2}}-2y-7=0\] is
A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
View Answer play_arrowquestion_answer134) If\[S=\sum\limits_{n=2}^{\infty }{^{n}{{C}_{2}}}\frac{{{3}^{n-2}}}{n!}\], then\[2s\]equals to
A) \[{{e}^{3/2}}\]
B) \[{{e}^{3}}\]
C) \[{{e}^{-3/2}}\]
D) \[{{e}^{-3}}\]
View Answer play_arrowquestion_answer135) The sum of the series \[\frac{1}{2}{{x}^{2}}+\frac{2}{3}{{x}^{3}}+\frac{3}{4}{{x}^{4}}+\frac{4}{5}{{x}^{5}}+...\]is
A) \[\frac{x}{1+x}+\log (1+x)\]
B) \[\frac{x}{1-x}+\log (1-x)\]
C) \[-\frac{x}{1+x}+\log (1+x)\]
D) None of these
View Answer play_arrowquestion_answer136) For any vector \[\mathbf{a},\,\,|\mathbf{a}\times \mathbf{i}{{|}^{2}}+|\mathbf{a}\times \mathbf{j}{{|}^{2}}+|\mathbf{a}+\mathbf{k}{{|}^{2}}\] is equal to
A) \[|\mathbf{a}{{|}^{2}}\]
B) \[2|\mathbf{a}{{|}^{2}}\]
C) \[3|\mathbf{a}{{|}^{2}}\]
D) None of these
View Answer play_arrowquestion_answer137) If the unit vectors \[a\] and \[b\] are inclined at an angle \[2\theta \] such that \[|a-b|\,\,<1\] and\[0\le \theta \le \pi \], then \[\theta \] lies in the interval
A) \[\left[ 0,\,\,\frac{\pi }{6} \right)\]
B) \[\left[ \frac{5\pi }{6},\,\,\pi \right]\]
C) \[\left[ \frac{\pi }{6},\,\,\frac{\pi }{2} \right]\]
D) \[\left[ \frac{\pi }{2},\,\,\frac{5\pi }{6} \right]\]
View Answer play_arrowquestion_answer138) The vectors\[\mathbf{a}=x\mathbf{i}+(x+1)\mathbf{j}+(x+2)\mathbf{k}\],\[\mathbf{b}=(x+3)\mathbf{i}+(x+4)\mathbf{j}+(x+5)\mathbf{k}\] and\[\mathbf{c}=(x+6)\mathbf{i}+(x+7)\mathbf{j}+(x+8)\mathbf{k}\]are coplanar for
A) all values of\[x\]
B) only\[x=1\]
C) only\[x=0\]
D) None of these
View Answer play_arrowquestion_answer139) If\[y={{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}+\sqrt{1-{{x}^{2}}}}{\sqrt{1+{{x}^{2}}}-\sqrt{1-{{x}^{2}}}} \right)\], then\[\frac{dy}{dx}\] equals to
A) \[\frac{1}{\sqrt{1-{{x}^{4}}}}\]
B) \[\frac{-1}{\sqrt{1-{{x}^{4}}}}\]
C) \[\frac{x}{\sqrt{1-{{x}^{4}}}}\]
D) \[\frac{-x}{\sqrt{1-{{x}^{4}}}}\]
View Answer play_arrowquestion_answer140) If the parametric equation of a curve given by\[x={{e}^{t}}\cos t,\,\,y={{e}^{t}}\sin t\], then the tangent to the curve at the point \[=\frac{\pi }{4}\] makes with axis of \[x\], the angle is
A) \[0\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{2}\]
View Answer play_arrowquestion_answer141) The function \[f(x)=\frac{x}{\log x}\] increases on the interval
A) \[(0,\,\,\infty )\]
B) \[(0,\,\,e)\]
C) \[(e,\,\,\infty )\]
D) None of these
View Answer play_arrowquestion_answer142) If\[f(x)={{\tan }^{-1}}\left\{ \frac{\log \left( \frac{e}{{{x}^{2}}} \right)}{\log (e{{x}^{2}})} \right\}+{{\tan }^{-1}}\left( \frac{1+2\log x}{1-2\log x} \right)\], then\[\frac{dy}{dx}\]is
A) \[{{\tan }^{-1}}(\log x)\]
B) \[0\]
C) \[\frac{1}{2}\]
D) None of these
View Answer play_arrowquestion_answer143) If\[{{I}_{m}}=\int_{1}^{x}{{{(\log x)}^{m}}dx}\]satisfies the relation \[{{I}_{m}}=K-l{{I}_{m-1}}\],then
A) \[K=e\]
B) \[l=m\]
C) \[K=\frac{1}{e}\]
D) None of these
View Answer play_arrowquestion_answer144) Let\[I=\int_{0}^{1}{\frac{{{e}^{x}}}{x+1}dx}\], then the value of the integral \[\int_{0}^{1}{\frac{x{{e}^{{{x}^{2}}}}}{{{x}^{2}}+1}dx}\]is
A) \[{{I}^{2}}\]
B) \[\frac{1}{2}I\]
C) \[2I\]
D) \[\frac{1}{2}{{I}^{2}}\]
View Answer play_arrowquestion_answer145) \[\int_{0}^{1}{|\sin 2\pi x|dx}\]is equal to
A) \[0\]
B) \[-\frac{1}{\pi }\]
C) \[\frac{1}{\pi }\]
D) \[\frac{2}{\pi }\]
View Answer play_arrowquestion_answer146) The differential equation of all conies whose centre is lie at the origin is of order
A) \[2\]
B) \[3\]
C) \[4\]
D) None of these
View Answer play_arrowquestion_answer147) The curve satisfying \[y\,dx-xdx+\log \,\,x\,dx=0\] for \[x>0\] and passing through\[(1,\,\,-1)\]is
A) \[y=-1-\log x\]
B) \[y+\log x=0\]
C) \[y={{e}^{x}}-1\]
D) None of the above
View Answer play_arrowquestion_answer148) The differential equation of\[y=cx+2{{c}^{2}}\]is
A) \[y=x{{y}_{1}}+2y_{1}^{2}\]
B) \[y=x{{y}_{1}}-2y_{1}^{2}\]
C) \[y+x{{y}_{1}}=2y_{1}^{2}\]
D) None of these
View Answer play_arrowquestion_answer149) Variance is independent to charge of
A) origin only
B) scale only
C) origin and scale both
D) None of the above
View Answer play_arrowquestion_answer150) The contrapositive of the statement\[(\tilde{\ }p\Rightarrow \tilde{\ }q)\] is
A) \[p\Rightarrow q\]
B) \[q\Rightarrow p\]
C) \[\tilde{\ }q\Rightarrow \tilde{\ }p\]
D) \[\tilde{\ }p\Rightarrow q\]
View Answer play_arrow
You need to login to perform this action.
You will be redirected in
3 sec