question_answer1) Vector which is perpendicular to \[a\,\,\cos \,\theta \,\,\hat{i}+b\,\sin \,\theta \,\,\hat{j}\] is
A) \[b\,\sin \,\theta \,\hat{i}-a\,\cos \,\theta \,\hat{j}\] done clear
B) \[\frac{1}{a}\,\sin \,\theta \,\hat{i}-a\,\cos \,\theta \,\hat{j}\] done clear
C) \[5\hat{k}\] done clear
D) All of the above done clear
View Answer play_arrowquestion_answer2) Which of the following statements is true?
A) When the coordinate axes are translated the component of a vector in a plane changes done clear
B) When the coordinate axes are rotated through some angle components of the vector change but the vector's magnitude remains constant done clear
C) Sum of \[\vec{a}\]and \[\vec{b}\] is \[\vec{R}\]. If the magnitude of \[\vec{a}\]alone is increased angle between \[\vec{b}\] and \[\vec{R}\] decreases done clear
D) The cross product of \[3\,\,\hat{i}\] and \[4\,\,\hat{j}\] is 12 done clear
View Answer play_arrowquestion_answer3) From a balloon rising vertically upwards as \[5\text{ }m/s\]a stone is thrown up at 10 m/s relative to the balloon. Its velocity with respect to ground after \[2\text{ }s\]is (assume\[g=10\text{ }m/{{s}^{2}}\])
A) zero done clear
B) \[5\text{ }m/s\] done clear
C) \[10\text{ }m/s\] done clear
D) \[20\text{ }m/s\] done clear
View Answer play_arrowquestion_answer4) Two bodies are projected from ground with equal speed \[20\text{ }m/s\]from the same position in the same vertical plane to have equal range but at different angles above the horizontal. If one of the angle is 30? the sum of their maximum heights is (assume\[g=10\text{ }m/{{s}^{2}}\])
A) \[400\,\,m\] done clear
B) \[20\,\,m\] done clear
C) \[30\,\,m\] done clear
D) \[40\,\,m\] done clear
View Answer play_arrowquestion_answer5) Which of the following quantities measured from different inertial reference frames are same?
A) Force done clear
B) Velocity done clear
C) Displacement done clear
D) Kinetic energy done clear
View Answer play_arrowquestion_answer6) Two particles of equal mass are connected to a rope AB of negligible mass, such that one is at end A and the other dividing the length of the rope in the ratio \[1:2\] from B. The rope is rotated about end B in a horizontal plane. Ratio of the tensions in the smaller part to the other is (ignore effect of gravity)
A) \[4:3\] done clear
B) \[1:4\] done clear
C) \[1:2\] done clear
D) \[1:3\] done clear
View Answer play_arrowquestion_answer7) Angle of banking for a vehicle speed of \[10\text{ }m/s\] for a radius of curvature \[10\text{ }m\]is (assume\[g=10\text{ }m/{{s}^{2}}\])
A) \[{{30}^{o}}\] done clear
B) \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\] done clear
C) \[{{60}^{o}}\] done clear
D) \[{{45}^{o}}\] done clear
View Answer play_arrowquestion_answer8) A body of mass \[2\text{ }kg\]is projected at \[20\text{ }m/s\]at an angle \[{{60}^{o}}\] above the horizontal. Power due to the gravitational force at its highest point is
A) \[200\text{ }W\] done clear
B) \[100\sqrt{3\,}W\] done clear
C) \[50\,W\] done clear
D) zero done clear
View Answer play_arrowquestion_answer9) A block of mass \[2\text{ }kg\]rests on a horizontal surface. If a horizontal force of \[5\text{ }N\]is applied on the block the frictional force on, it is \[({{\mu }_{k}}=0.4,\,\,{{\mu }_{s}}=0.5)\]
A) \[5\,\,N\] done clear
B) \[10\,\,N\] done clear
C) \[8\,\,N\] done clear
D) zero done clear
View Answer play_arrowquestion_answer10) Three idential spheresof mass M each are placed at the comers of an equilateral triangle of side \[2m\]. Taking one of the comer as the origin, the position vector of the centre of mass is
A) \[\sqrt{3}\,\,(\hat{i}-\hat{j})\] done clear
B) \[\frac{i}{\sqrt{3}}+\hat{j}\] done clear
C) \[\frac{\hat{i}+\hat{j}}{3}\] done clear
D) \[\hat{i}+\frac{{\hat{j}}}{\sqrt{3}}\] done clear
View Answer play_arrowquestion_answer11) A shell initially at rest explodes into two pieces of equal mass, the two pieces will
A) move with different velocities in different Directions done clear
B) move with the same velocity in opposite directions done clear
C) move with the same velocity in the same direction done clear
D) be at rest done clear
View Answer play_arrowquestion_answer12) Impulse is
A) a scalar done clear
B) equal to change in the momentum of a body done clear
C) equal to rate of change of momentum of a body done clear
D) a force done clear
View Answer play_arrowquestion_answer13) In a head on elastic collision of a very heavy body moving at V with a light body at rest, velocity of heavy body after collision is
A) \[V\] done clear
B) \[2\,V\] done clear
C) zero done clear
D) \[\frac{V}{2}\] done clear
View Answer play_arrowquestion_answer14) A T Joint is formed by two identical rods A and B each of mass m and length L in the XY plane as shown. Its moment of inertia about axis coinciding with A is
A) \[\frac{2\,m{{L}^{2}}}{3}\] done clear
B) \[\frac{\,m{{L}^{2}}}{12}\] done clear
C) \[\frac{\,m{{L}^{2}}}{6}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer15) A disc of moment of inertia \[5\text{ }kg-{{m}^{2}}\]is acted upon by a constant torque of\[40\text{ }Nm\]. Starting from rest the time taken by it to acquire an angular velocity of 24 rad/s is
A) \[3\text{ }s\] done clear
B) \[\text{4 }s\] done clear
C) \[2.5\,\,s\] done clear
D) \[120\,\,s\] done clear
View Answer play_arrowquestion_answer16) If the angular momentum of a rotating body about a fixed axis is increased by\[10%\]. Its kinetic energy will be increased by
A) \[10%\] done clear
B) \[20%\] done clear
C) \[21%\] done clear
D) \[5%\] done clear
View Answer play_arrowquestion_answer17) If the earth were to spin faster, acceleration due to gravity at the poles
A) increases done clear
B) decreases done clear
C) remains the same done clear
D) depends on how fast it spins done clear
View Answer play_arrowquestion_answer18) The time period of an artificial satellite in a circular orbit is independent of
A) the mass of the satellite done clear
B) radius of the orbit done clear
C) mass of the earth and radius of the earth done clear
D) None of the above done clear
View Answer play_arrowquestion_answer19) Angle of contact of a liquid with a solid depends on
A) solid only done clear
B) liquid only done clear
C) both on solid and liquid done clear
D) orientation of the solid surface in liquid done clear
View Answer play_arrowquestion_answer20) If longitudinal strain for a wire is \[0.03\] and its Poisson's ratio is \[0.5,\] then its lateral strain is
A) \[0.003\] done clear
B) \[0.0075\] done clear
C) \[0.015\] done clear
D) \[0.4\] done clear
View Answer play_arrowquestion_answer21) When the temperature increases, the viscosity of
A) gas decreases and liquid increases done clear
B) gas increases and liquid decreases done clear
C) gas and liquid increases done clear
D) gas and liquid decreases done clear
View Answer play_arrowquestion_answer22) Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is p at a point where flow speed is v, the pressure at another point where the flow of speed is \[2\text{ }v,\]is (take density of water as p)
A) \[p-\frac{3\,\rho {{v}^{2}}}{2}\] done clear
B) \[p-\frac{\,\rho {{v}^{2}}}{2}\] done clear
C) \[p-\frac{3\,\rho {{v}^{2}}}{4}\] done clear
D) \[p-\rho {{v}^{2}}\] done clear
View Answer play_arrowquestion_answer23) Which of the following statements is true?
A) Internal energy of a gas depends only on the state of the gas done clear
B) In an isothermal process change in internal energy is maximum done clear
C) Area under pressure, volume graph equals heat supplied in any process done clear
D) Work done is state dependent but not path dependent done clear
View Answer play_arrowquestion_answer24) A gas \[\left( \gamma =\frac{5}{3} \right),\] expands isobaric ally. The percentage, of heat supplied that increases thermal energy and that involved in doing work for expansion is
A) \[40:60\] done clear
B) \[60:40\] done clear
C) \[50:50\] done clear
D) \[25:30\] done clear
View Answer play_arrowquestion_answer25) A perfect black body is one whose emissive power is
A) maximum done clear
B) zero done clear
C) unity done clear
D) minimum done clear
View Answer play_arrowquestion_answer26) A black body at a temperature T radiates energy at E. If the temperature falls to \[\frac{T}{2},\] the radiated energy will be
A) \[\frac{E}{4}\] done clear
B) \[\frac{E}{2}\] done clear
C) \[2E\] done clear
D) \[\frac{E}{16}\] done clear
View Answer play_arrowquestion_answer27) If the units of mass, length and time are doubled unit of angular momentum will be .
A) doubled done clear
B) tripled done clear
C) quadrupled done clear
D) 8 times the original value done clear
View Answer play_arrowquestion_answer28) Which of the following graphs shows variation of potential energy (U) with position x?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer29) Choose the correct statement
A) Time period of a simple pendulum depends on amplitude done clear
B) Time shown by a spring watch varies with acceleration due to gravity done clear
C) In a simple pendulum time period varies linearly with the length of the pendulum done clear
D) The graph between length of the pendulum and time period is a parabola done clear
View Answer play_arrowquestion_answer30) Time period of a spring mass system is T. If this spring is cut into two parts whose lengths are in the ratio \[1:3\] and the same mass is attached to the longer part, the new time period will be
A) \[\sqrt{\frac{3}{2}}T\] done clear
B) \[\frac{T}{\sqrt{3}}\] done clear
C) \[\frac{\sqrt{3}T}{2}\] done clear
D) \[\sqrt{3}T\] done clear
View Answer play_arrowquestion_answer31) Equation of progressive wave is \[y=A\,\sin \left( 10\,\pi x+11\pi t+\frac{\pi }{3} \right)\]
A) its wavelength is \[2\text{ }units\] done clear
B) it is travelling in the positive x-direction done clear
C) wave velocity is \[1.5\text{ }units\] done clear
D) time period of SHM is 1 s done clear
View Answer play_arrowquestion_answer32) The phenomenon of sound propagation in air is
A) isothermal process done clear
B) isobaric process done clear
C) adiabatic process done clear
D) None of the above done clear
View Answer play_arrowquestion_answer33) The second overtone of an open pipe is in resonance with the first overtone of a closed pipe of length \[2\,m\]. Length of the open pipe is
A) \[4\,m\] done clear
B) \[2\,m\] done clear
C) \[8\,m\] done clear
D) \[1\,m\] done clear
View Answer play_arrowquestion_answer34) Choose the correct statement
A) Beats are due to destructive interference done clear
B) Maximum beat frequency audible to a human being is 20 done clear
C) Beats are as a result of Doppler?s effect done clear
D) Beats are due to superposition of two waves of nearly equal frequencies done clear
View Answer play_arrowquestion_answer35) A motor car is approaching towards a crossing with a velocity of\[72\text{ }km/h\]. The frequency of sound of its horn as heard by a policeman standing on the crossing is\[260\text{ }Hz\]. The frequency of horn is
A) \[200\text{ }Hz\] done clear
B) \[244\text{ }Hz\] done clear
C) \[150\text{ }Hz\] done clear
D) \[80\text{ }Hz\] done clear
View Answer play_arrowquestion_answer36) Forces exerted by a uniform electric field on an electron having mass \[{{m}_{e}}\] and proton of mass \[{{m}_{p}}\]are represented as \[{{F}_{e}}\] and \[{{F}_{p}}\] respectively are related as
A) \[{{F}_{p}}={{F}_{e}}\] done clear
B) \[\frac{{{F}_{e}}}{{{F}_{p}}}=\frac{{{m}_{e}}}{{{m}_{p}}}\] done clear
C) \[\frac{{{F}_{e}}}{{{F}_{p}}}=\frac{{{m}_{p}}}{{{m}_{e}}}\] done clear
D) \[\frac{{{F}_{e}}}{{{F}_{p}}}=\frac{m_{e}^{2}}{m_{p}^{2}}\] done clear
View Answer play_arrowquestion_answer37) Electric field strength due to a dipole at a point on the axial line of dipole is
A) from positive charge to negative charge done clear
B) from negative charge to positive charge done clear
C) along the equatorial line done clear
D) at an angle to axial line done clear
View Answer play_arrowquestion_answer38) Potential and field strength at a certain distance from a point charge are \[600\text{ }V\]and\[200\text{ }N/C\]. Distance of the point from the charge is
A) \[2\,m\] done clear
B) \[4\,m\] done clear
C) \[8\,m\] done clear
D) \[3\,m\] done clear
View Answer play_arrowquestion_answer39) Two identical spheres with charges \[4q,-2q\] kept some distance apart exert a force F on each other. If they are made to touch each other and replaced at their old positions, the force between them will be
A) \[\frac{1}{9}F\] done clear
B) \[\frac{1}{8}F\] done clear
C) \[\frac{9}{8}F\] done clear
D) \[\frac{8}{9}F\] done clear
View Answer play_arrowquestion_answer40) Two capacitors each of capacity \[2\mu F\] are connected in parallel. If they are connected to \[100\text{ }V\]battery, then energy stored in them is
A) \[0.02\text{ }J\] done clear
B) \[0.04\text{ }J\] done clear
C) \[0.01\text{ }J\] done clear
D) \[200\text{ }J\] done clear
View Answer play_arrowquestion_answer41) Which factor is immaterial for the wire used in electric fuse?
A) Length done clear
B) Radius done clear
C) Material done clear
D) Current done clear
View Answer play_arrowquestion_answer42) A battery of emf \[2\text{ }V\]and internal resistance \[0.1\Omega \] is being charged by a current of \[~5\text{ }A\]. The potential difference between the terminals of the battery is
A) \[2.5\text{ }V\] done clear
B) \[1.5\text{ }V\] done clear
C) \[0.5V\] done clear
D) \[1\,\,V\] done clear
View Answer play_arrowquestion_answer43) An electric bulb is rated at \[220\text{ }V,\] \[200\text{ }W;\] Power consumed by it when operated at \[110\text{ }V\]is
A) \[25\text{ }W\] done clear
B) \[50\text{ }W\] done clear
C) \[75\text{ }W\] done clear
D) \[90\text{ }W\] done clear
View Answer play_arrowquestion_answer44) two cells having emf \[4\text{ }V,\] \[2\text{ }V\]and internal resistances \[1\,\Omega ,\] \[1\,\,\Omega \] are connected as shown in figure below. Current through \[6\,\,\Omega \] resistance is
A) \[\frac{1}{3}A\] done clear
B) \[\frac{2}{3}A\] done clear
C) \[1\,\,A\] done clear
D) \[\frac{2}{9}\,\,A\] done clear
View Answer play_arrowquestion_answer45) For a given thermocouple neutral temperature
A) is a constant done clear
B) depends on cold junction temperature done clear
C) depends on inversion temperature done clear
D) double that of cold junction temperature done clear
View Answer play_arrowquestion_answer46) A charged particle enters a uniform magnetic field with a certain speed at right angles to it. In the magnetic field a change could occur in its
A) kinetic energy done clear
B) angular momentum done clear
C) linear momentum done clear
D) speed done clear
View Answer play_arrowquestion_answer47) A coil having 500 turns of square shape each of side \[10\text{ }cm\]is placed normal to a magnetic field which is increasing at \[1\text{ }T/s\]. The induced emf is
A) \[0.1\text{ }V\] done clear
B) \[0.5\,\,V\] done clear
C) \[1\,\,V\] done clear
D) \[-5\,\,V\] done clear
View Answer play_arrowquestion_answer48) A galvanometer has a resistance \[50\,\,\Omega \]. A resistance of \[5\,\,\Omega \] is connected parallel to it. Fraction of the total current flowing through galvanometer is
A) \[\frac{1}{10}\] done clear
B) \[\frac{1}{11}\] done clear
C) \[\frac{1}{50}\] done clear
D) \[\frac{2}{15}\] done clear
View Answer play_arrowquestion_answer49) A wire oriented in the east-west direction carries a current eastward. Direction of the magnetic field at a point to the south of the wire is
A) vertically down done clear
B) vertically up done clear
C) north-east done clear
D) south-east done clear
View Answer play_arrowquestion_answer50) An inductor is connected to an AC source, When compared to voltage, the current in the lead wires
A) is ahead in phase by n done clear
B) lags in phase by n done clear
C) is ahead in phase by ? done clear
D) lags in phase by ? done clear
View Answer play_arrowquestion_answer51) Curie temperature is the one above which
A) paramagnetic substance changes to ferromagnetic done clear
B) paramagnetic changes to diamagnetic done clear
C) diamagnetic changes to paramagnetic done clear
D) ferromagnetic changes to paramagnetic done clear
View Answer play_arrowquestion_answer52) Energy in a current carrying coil is stored in the form of
A) electric field done clear
B) magnetic field done clear
C) heat done clear
D) None of the above done clear
View Answer play_arrowquestion_answer53) Graph of force per unit length between two long parallel currents carrying conductor and the distance between them is
A) straight line done clear
B) parabola done clear
C) ellipse done clear
D) rectangular hyperbola done clear
View Answer play_arrowquestion_answer54) A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it from this position. The angle of rotation is
A) \[{{60}^{o}}\] done clear
B) \[{{45}^{o}}\] done clear
C) \[{{30}^{o}}\] done clear
D) \[{{75}^{o}}\] done clear
View Answer play_arrowquestion_answer55) A point source of light is kept below the surface of water in a pond
A) light emerges from every point of the surface of the pond done clear
B) no light is transmitted from the surface of the pond done clear
C) all the light emitted by the source emerges from a circular region of the pond done clear
D) some of the light emitted by the source emerges from a circular region of the pond done clear
View Answer play_arrowquestion_answer56) If white light is used in Young's double slit experiment
A) no interference pattern is formed done clear
B) white fringes are formed done clear
C) central bright fringe is white done clear
D) central bright fringe is coloured done clear
View Answer play_arrowquestion_answer57) Electromagnetic waves can be deflected by
A) electric fields only done clear
B) magnetic fields only done clear
C) Both [a] and [b] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer58) Maximum lateral displacement of a ray of light incident on a slab of thickness t is
A) \[\frac{t}{2}\] done clear
B) \[\frac{t}{3}\] done clear
C) \[\frac{t}{4}\] done clear
D) \[t\] done clear
View Answer play_arrowquestion_answer59) Mercury vapour lamp gives
A) continuous spectrum done clear
B) line spectrum done clear
C) band spectrum done clear
D) absorption spectrum done clear
View Answer play_arrowquestion_answer60) Pick the correct statement from the following
A) Primary rainbow is a virtual image and secondary rainbow is a real image done clear
B) Primary rainbow is a real image and secondary rainbow is a virtual image done clear
C) Both primary and secondary rainbows are virtual images done clear
D) Both primary and secondary rainbows are real images done clear
View Answer play_arrowquestion_answer61) The refractive index of water, glass and diamond are \[1.33,1.50,\text{ }2.40\]respectively. The refractive index of diamond relative to water and of glass relative to diamond, respectively are nearly
A) \[1.80,0.625\] done clear
B) \[0.554,\text{ }0.625\] done clear
C) \[1.80,\text{ }1.6\] done clear
D) \[0.554,\text{ }1.6\] done clear
View Answer play_arrowquestion_answer62) In the diffraction pattern of a single slit
A) all bands are uniformly bright done clear
B) all bands are uniformly wide done clear
C) central band is narrower done clear
D) central band is wider done clear
View Answer play_arrowquestion_answer63) A radioactive substance has a half-life of four months. Three-fourth of the substance will decay in
A) \[3\text{ }months\] done clear
B) \[4\text{ }months\] done clear
C) \[~8\text{ }months\] done clear
D) \[\text{12 }months\] done clear
View Answer play_arrowquestion_answer64) Electrons in the atom are held to the nucleus by
A) Coulomb's forces done clear
B) nuclear forces done clear
C) van der Waals' forces done clear
D) gravitational forces done clear
View Answer play_arrowquestion_answer65) Mass of the nucleons together in a heavy nucleus is
A) greater than mass of nucleus done clear
B) equal to mass of nucleus done clear
C) same as mass of nucleus done clear
D) None of the above done clear
View Answer play_arrowquestion_answer66) Ratio of the radii of the nuclei with mass numbers 8 and 27 would be
A) \[27/8\] done clear
B) \[8/27\] done clear
C) \[2/3\] done clear
D) \[3/2\] done clear
View Answer play_arrowquestion_answer67) Stopping potential required to reduce the photoelectric current to zero
A) is directly proportional to the wavelength of the incident radiation done clear
B) increases uniformly with wavelength of the incident radiation done clear
C) is directly proportional to the frequency of the incident radiation done clear
D) decreases uniformly with the frequency of the incident radiation done clear
View Answer play_arrowquestion_answer68) The first member of the Ballmer?s series of the hydrogen has a wavelength \[\lambda ,\] the wavelength of the second member of its series is
A) \[\frac{27}{20}\lambda \] done clear
B) \[\frac{20}{27}\lambda \] done clear
C) \[\frac{27}{20}\lambda \] done clear
D) None of these done clear
View Answer play_arrowquestion_answer69) The photoelectric threshold frequency of a metal is v. When light of frequency \[4v\] is incident on the metal. The maximum kinetic energy of the emitted photoelectrons is
A) \[4\,\,hv\] done clear
B) \[3\,\,hv\] done clear
C) \[5\,\,hv\] done clear
D) \[\frac{5}{2}\,\,hv\] done clear
View Answer play_arrowquestion_answer70) The shortest wavelength in Lyman series is\[91.2\text{ }nm\]. The longest wavelength of the series is
A) \[121.6\text{ }nm\] done clear
B) \[182.4\text{ }nm\] done clear
C) \[243.4\text{ }nm\] done clear
D) \[364.8\text{ }nm\] done clear
View Answer play_arrowquestion_answer71) Energy gap of a semiconductor is of the order of
A) \[1\,\,eV\] done clear
B) \[10\,\,eV\] done clear
C) \[0.1\text{ }eV\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer72) Majority charge carriers in p-type material are
A) holes done clear
B) electrons done clear
C) Both and done clear
D) None of the above done clear
View Answer play_arrowquestion_answer73) Resistance of a semiconductor
A) increases with increase in temperature done clear
B) decreases with increase in temperature done clear
C) is not affected by change in temperature done clear
D) increases for germanium and decreases for silicon done clear
View Answer play_arrowquestion_answer74) Semiconductor material having fewer free electrons than pure germanium or silicon is
A) p-type done clear
B) n-type done clear
C) Both [a] and [b] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer75) The concentrations of impurities in a transistor are
A) equal for the emitter, base and collector regions done clear
B) least for the emitter region done clear
C) largest for the emitter region done clear
D) least for the base region done clear
View Answer play_arrowquestion_answer76) At \[\text{25}{{\,}^{\text{o}}}\text{C}\], the total pressure of an ideal solution obtained by mixing 3 moles of 'A? and 2 moles of 'B? is 184 Ton". What is the vapour pressure (in Torr) of pure 'B' at the same temperature? (vapour pressure of pure 'A? at \[25{{\,}^{o}}C,\] is 200 Torr)
A) 180 done clear
B) 160 done clear
C) 16 done clear
D) 100 done clear
View Answer play_arrowquestion_answer77) Relative lowering of vapour pressure of a dilute solution is 0.2. What is the mole fraction of the non-volatile solute?
A) 0.8 done clear
B) 0.5 done clear
C) 0.3 done clear
D) 0.2 done clear
View Answer play_arrowquestion_answer78) Match the following List ?A? List ?B? (1) \[PhC{{O}_{2}}C{{H}_{3}}\] [A]\[2,4-\text{DNP}\] (2) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}C{{O}_{2}}H\] [B] Arndt-Eistert synthesis (3)\[{{C}_{6}}{{H}_{5}}CHO\] [C] Hydrolysis Correct answer is
A) \[1-A,\,2-B,\,3-C\] done clear
B) \[1-B,\,2-C,\,3-A\] done clear
C) \[1-C,\,2-B,\,3-A\] done clear
D) \[1-B,\,2-A,\,3-C\] done clear
View Answer play_arrowquestion_answer79) 2-pentanone and 3-methyl-2-butanone are a pair of....... isomers.
A) functional done clear
B) chain done clear
C) positional done clear
D) stereo done clear
View Answer play_arrowquestion_answer80) What are the units of entropy?
A) \[\text{cal K}\] done clear
B) \[\text{Cal}\,{{\text{K}}^{-1}}\] done clear
C) \[\text{cm}\,{{\text{K}}^{-1}}\] done clear
D) \[\text{ }\!\!~\!\!\text{ cmK}\] done clear
View Answer play_arrowquestion_answer81) Calculate \[\Delta H\](in Joules) for, C (graphite) \[\to C\](diamond), from the following data C(graphite)\[+\,{{O}_{2}}(g)\to C{{O}_{2}}(g);\] \[\Delta H=-393.5\,kJ\] C (diamond)\[+\,{{O}_{2}}(g)\to C{{O}_{2}}(g);\] \[\Delta H=-395.4\,kJ\]
A) \[1,900\] done clear
B) \[~-788.9\times {{10}^{3}}\] done clear
C) \[1,90,000\] done clear
D) \[~+\,788.9\times \,{{10}^{3}}\] done clear
View Answer play_arrowquestion_answer82) \[C{{H}_{2}}Br+\bar{O}H\xrightarrow{{}}C{{H}_{3}}OH+B{{r}^{-}}\]reaction proceeds by\[{{S}_{N}}2-\]mechanism. Its rate is dependent on the concentration of
A) \[C{{H}_{3}}Br,\bar{O}H\] done clear
B) \[C{{H}_{3}}Br\]only done clear
C) \[~\bar{O}H\] only done clear
D) \[~C{{H}_{3}}Br,C{{H}_{3}}OH\] done clear
View Answer play_arrowquestion_answer83) The end products in the Cannizaro reaction of benzaldehyde is
A) \[~PhC{{O}_{2}}H,PhC{{H}_{2}}OH\] done clear
B) \[~PhC{{O}_{2}}H,PhC{{H}_{2}}C{{O}_{2}}H\] done clear
C) \[PhC{{H}_{2}}OH,PhCOC{{H}_{3}}\] done clear
D) \[PhCO{{}_{2}}H,PhCOC{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer84) For a chemicalreaction, the free energy change \[(\Delta G)\] is negative. The reaction is
A) a spontaneous reaction done clear
B) an equilibrium reaction done clear
C) a non-spontaneous reaction done clear
D) characterised by\[{{r}_{f}}-{{r}_{b}}\] (where\[{{r}_{f}}\]and\[{{r}_{b}}\] are rates of forward and backward reactions respectively) done clear
View Answer play_arrowquestion_answer85) In which of the following reactions, the heat liberated is known as "heat of combustion"?
A) \[{{H}^{+}}(aq)+O{{H}^{-}}(aq)\to {{H}_{2}}O(l)+heat\] done clear
B) \[C\text{(graphite)}+\frac{1}{2}{{O}_{2}}(g)\to CO(g)+\text{heat}\] done clear
C) \[C{{H}_{4}}(g)+2{{O}_{2}}(g)\to C{{O}_{2}}(g)+2{{H}_{2}}O(l)+\,heat\] done clear
D) \[{{H}_{2}}S{{O}_{4}}(aq)+{{H}_{2}}O(l)\to {{H}_{2}}S{{O}_{4}}(aq)+heat\] done clear
View Answer play_arrowquestion_answer86) The number of chiral centres in \[(+)-\]glucose
A) 4 done clear
B) 3 done clear
C) 2 done clear
D) 1 done clear
View Answer play_arrowquestion_answer87) Aniline on oxidation with \[\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}\]and \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]gives
A) benzoic acid done clear
B) \[m-\] amino benzoic acid done clear
C) Schiff?s base done clear
D) \[~p-\] benzoquinone done clear
View Answer play_arrowquestion_answer88) What are the units of equivalent conductivity of a solution?
A) \[\text{mho c}{{\text{m}}^{-1}}\] done clear
B) \[\text{ohm c}{{\text{m}}^{-1}}\text{ g equi}{{\text{v}}^{-1}}\] done clear
C) \[\text{mho c}{{\text{m}}^{-2}}\text{ g equi}{{\text{v}}^{-1}}\] done clear
D) \[\text{mho c}{{\text{m}}^{2}}\text{ g equi}{{\text{v}}^{-1}}\] done clear
View Answer play_arrowquestion_answer89) What is the cell reaction occurring in Daniel cell (Galvanic cell)?
A) \[Cu(s)+ZnS{{O}_{4}}(aq)\to CuS{{O}_{4}}(aq)+Zn(s)\] done clear
B) \[Zn(s)+CuS{{O}_{4}}(aq)\to Cu(s)+ZnS{{O}_{4}}(aq)\] done clear
C) \[Ni(s)+ZnS{{O}_{4}}(aq)\to NiS{{O}_{4}}(aq)+Zn(s)\] done clear
D) \[2Na(s)+CdS{{O}_{4}}(aq)\to N{{a}_{2}}S{{O}_{4}}(aq)\]\[+\,Cd(s)\] done clear
View Answer play_arrowquestion_answer90) \[n-\]propylamine yields a volatile compound X on warming with ale. alkali and chloroform. X has an offensive odour. The structure of X is
A) \[~C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CN\] done clear
B) \[~{{(C{{H}_{3}})}_{2}}CHCN\] done clear
C) \[~C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}NC\] done clear
D) \[{{(C{{H}_{3}})}_{2}}CHNC\] done clear
View Answer play_arrowquestion_answer91) The molecular formula of benzonitrile is
A) \[{{C}_{6}}{{H}_{5}}CN\] done clear
B) \[{{C}_{6}}{{H}_{5}}NC\] done clear
C) \[{{C}_{6}}{{H}_{5}}CNO\] done clear
D) \[{{C}_{6}}{{H}_{5}}NCO\] done clear
View Answer play_arrowquestion_answer92) Which of the following statements (or equation) is correct?
A) The units of cell emf are\[\text{V}\text{.c}{{\text{m}}^{-1}}\] done clear
B) \[\Delta G=-\frac{nF}{{{E}_{cell}}}\] done clear
C) In Galvanic cell, chemical energy is transformed into electrical energy done clear
D) Oxidation state of Mn in potassium permanganate is + 6 done clear
View Answer play_arrowquestion_answer93) Which of the following metal can be obtained by the electrolysis of the aqueous solution of its salts?
A) Cu done clear
B) Na done clear
C) Mg done clear
D) K done clear
View Answer play_arrowquestion_answer94) The magnetic moment (in BM) of \[\text{Z}{{\text{n}}^{\text{2+}}}\]ion according to spin-only formula is
A) zero done clear
B) 1.73 done clear
C) 2.84 done clear
D) 3.87 done clear
View Answer play_arrowquestion_answer95) The 3d-block element that exhibits maximum number of oxidation states is
A) Sc done clear
B) Ti done clear
C) Mn done clear
D) Zn done clear
View Answer play_arrowquestion_answer96) Which of the following molecule in its valence shell has three bond pairs of electrons and one lone pair of electrons?
A) \[N{{H}_{3}}\] done clear
B) \[~{{H}_{2}}O\] done clear
C) \[~B{{F}_{3}}\] done clear
D) \[~C{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer97) Which of the following set of properties belong to\[PC{{l}_{5}}\]?
A) \[s{{p}^{3}},\] tetrahedral, 4 valence shell pairs of electrons done clear
B) trigonal bipyramidal, 5 valence shell pairs of electrons done clear
C) \[s{{p}^{3}}{{d}^{2}},\]octahedral, 6 valence shell pairs of electrons done clear
D) \[s{{p}^{3}}d,\]square planar, 4 valence shell pairs of electrons done clear
View Answer play_arrowquestion_answer98) The metal ion in complex \[\underset{\scriptscriptstyle-}{A}\]has BAN identical to the atomic number of krypton. \[\underset{\scriptscriptstyle-}{A}\]is (At. no. of\[Cr=24,\,Fe=26,\,Pd=46\])
A) \[[Pd{{(N{{H}_{3}})}_{6}}]C{{l}_{4}}\] done clear
B) \[[Cr{{(N{{H}_{3}})}_{5}}Cl]S{{O}_{4}}\] done clear
C) \[N{{a}_{4}}[Fe{{(CN)}_{6}}]\] done clear
D) \[{{K}_{3}}[Fe{{(CN)}_{6}}]\] done clear
View Answer play_arrowquestion_answer99) The complex that does not give a precipitate wit\[\text{ }\!\!~\!\!\text{ AgN}{{\text{O}}_{\text{3}}}\]solution
A) \[[Co{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]\] done clear
B) \[[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}\] done clear
C) \[\text{ }\!\![\!\!\text{ Ag(N}{{\text{H}}_{\text{3}}}{{\text{)}}_{\text{2}}}\text{ }\!\!]\!\!\text{ Cl}\] done clear
D) \[[Cr{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl\] done clear
View Answer play_arrowquestion_answer100) According to bond order concept, the correct order of stability of\[{{\text{O}}_{\text{2}}}\text{,O}_{\text{2}}^{\text{+}}\] and \[\text{O}_{2}^{-}\] is
A) \[{{O}_{2}}>O_{2}^{+}>O_{2}^{-}\] done clear
B) \[O_{2}^{-}>{{O}_{2}}>O_{2}^{+}\] done clear
C) \[{{O}_{2}}>O_{2}^{-}>O_{2}^{+}\] done clear
D) \[O_{2}^{+}>{{O}_{2}}<O_{2}^{-}\] done clear
View Answer play_arrowquestion_answer101) Zero dipole moment is possessed by
A) \[PC{{l}_{3}}\] done clear
B) \[~B{{F}_{3}}\] done clear
C) \[Cl{{F}_{3}}\] done clear
D) \[~N{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer102) The number of moles of ions given on complete ionisation of one mole of \[[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}\] is/are
A) 4 done clear
B) 3 done clear
C) 2 done clear
D) 1 done clear
View Answer play_arrowquestion_answer103) The coordination number in a/an........ complex may increase to 8.
A) cobalt done clear
B) osmium done clear
C) nickel done clear
D) iron done clear
View Answer play_arrowquestion_answer104) The radius ratio \[\left( \frac{{{r}^{+}}}{{{r}^{-}}} \right)\] of an ionic solid\[({{A}^{+}}{{B}^{-}})\]is 0.69. What is the coordination number of\[{{B}^{-}}\]?
A) 6 done clear
B) 8 done clear
C) 2 done clear
D) 10 done clear
View Answer play_arrowquestion_answer105) A, B and C are ideal gases. Their molecular weights are 2, 4 and 28 respectively. The ran of diffusion of these gases follow the order
A) \[C>A>B\] done clear
B) \[~C>B>A\] done clear
C) \[A=B=C\] done clear
D) \[~A>B>C\] done clear
View Answer play_arrowquestion_answer106) Among the following ions (hydrated), the colourless metal ion is
A) \[C{{u}^{+}}\] done clear
B) \[C{{u}^{2+}}\] done clear
C) \[F{{e}^{2+}}\] done clear
D) \[M{{n}^{2+}}\] done clear
View Answer play_arrowquestion_answer107) German silver is an alloy of
A) \[Cu,Zn\] done clear
B) \[~Cu,Ni,\,Zn\] done clear
C) \[~Cu,Sn,Zn\] done clear
D) \[~Cu,Zn\] done clear
View Answer play_arrowquestion_answer108) Which of the following Statements is not correct?
A) The units of surface tension are dynes \[c{{m}^{-1}}\] done clear
B) The units of viscosity coefficient of a liquid are "poise" done clear
C) \[\text{CsCl}\]crystallizes in body centred cubic type of lattice done clear
D) The coordination number of \[{{\text{S}}^{2-}}\]in ZnS is 6 done clear
View Answer play_arrowquestion_answer109) Which of the following is not a method of preparation of colloidal solution?
A) Electrical dispersion done clear
B) Peptization done clear
C) Coagulation done clear
D) Mechanical dispersion done clear
View Answer play_arrowquestion_answer110) Pauling's equation for determining the electronegativity of an element, is
A) \[{{X}_{A}}-{{X}_{B}}=0.208\sqrt{\Delta }\] done clear
B) \[{{X}_{A}}+{{X}_{B}}=0.208\sqrt{\Delta }\] done clear
C) \[{{X}_{A}}-{{X}_{B}}=0.208{{\Delta }^{2}}\] done clear
D) \[{{X}_{A}}-{{X}_{B}}=\sqrt{\Delta }\] \[{{X}_{A}},{{X}_{B}}=\]electronegativity values of elements AandB \[\Delta =\]represents polarity of \[A-B\]bond done clear
View Answer play_arrowquestion_answer111) The ionic radii\[(\overset{\text{o}}{\mathop{A}}\,)\]of \[{{C}^{4-}}\]and\[{{O}^{2-}}\]respectively are 2.60 and 1.40. The ionic radius of th6 isoelectronic ion \[{{N}^{3-}}\]would be
A) 2.6 done clear
B) 1.71 done clear
C) 1.4 done clear
D) 0.95 done clear
View Answer play_arrowquestion_answer112) The gold numbers of some colloidal solution are given below Colloidal solution Gold number A 0.01 B 2.5 C 20 The protective nature of these colloidal solutions follow the order
A) \[~C>B>A\] done clear
B) \[~A>B>C\] done clear
C) \[~A=B=C\] done clear
D) \[~B>A>C\] done clear
View Answer play_arrowquestion_answer113) Which of the following reaction is an example for homogeneous catalysis?
A) \[2{{H}_{2}}{{O}_{2}}(l)\xrightarrow{Mn{{O}_{2}}(s)}2{{H}_{2}}O(l)+{{O}_{2}}(g)\] done clear
B) \[2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g)\] done clear
C) \[2CO(g)+{{O}_{2}}(g)\xrightarrow{NO(g)}2C{{O}_{2}}(g)\] done clear
D) \[{{H}_{2}}(g)+{{C}_{2}}{{H}_{4}}(g)\xrightarrow{Ni(s)}{{C}_{3}}{{H}_{6}}(g)\] done clear
View Answer play_arrowquestion_answer114) Consider the following abbreviations for hydrated alkali ions \[X={{[Li{{({{H}_{2}}O)}_{n}}]}^{+}}\] \[X={{[K{{({{H}_{2}}O)}_{n}}]}^{+}}\] \[Z={{[Cs{{({{H}_{2}}O)}_{n}}]}^{+}}\] What is the correct order of size of these hydrated alkali ions?
A) \[~X>Y>Z\] done clear
B) \[~Z>Y>X\] done clear
C) \[~X=Y=Z\] done clear
D) \[~Z>X>Y\] done clear
View Answer play_arrowquestion_answer115) What is the product formed when phosphorus trioxide is dissolved in water?
A) \[~HP{{O}_{3}}\] done clear
B) \[~{{H}_{3}}P{{O}_{4}}\] done clear
C) \[~{{H}_{3}}P{{O}_{3}}\] done clear
D) \[~HP{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer116) The molecular formula of dithionic acid is
A) \[~{{H}_{2}}{{S}_{2}}{{O}_{4}}\] done clear
B) \[~{{H}_{2}}{{S}_{2}}{{O}_{6}}\] done clear
C) \[~{{H}_{2}}{{S}_{2}}{{O}_{5}}\] done clear
D) \[{{H}_{2}}{{S}_{2}}{{O}_{7}}\] done clear
View Answer play_arrowquestion_answer117) The bond dissociation energy of \[\text{C}{{\text{l}}_{\text{2}}}\text{, B}{{\text{r}}_{\text{2}}}\]and \[{{\text{I}}_{\text{2}}}\]follow the order
A) \[~C{{l}_{2}}>{{I}_{2}}>B{{r}_{2}}\] done clear
B) \[{{I}_{2}}>B{{r}_{2}}>C{{l}_{2}}\] done clear
C) \[{{I}_{2}}=C{{l}_{2}}=B{{r}_{2}}\] done clear
D) \[C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}\] done clear
View Answer play_arrowquestion_answer118) During the extraction of copper, the impurity \[(FeS)\]is removed as slag by mixing the contaminated copper ore with silica and coke. The molecular formula of slag is
A) \[~FeSi{{O}_{3}}\] done clear
B) \[~F{{e}_{2}}{{O}_{3}}\] done clear
C) \[FeSi\](solid) done clear
D) \[~FeSi\] (vapour) done clear
View Answer play_arrowquestion_answer119) Which of the following is used as indelible ink?
A) Aqueous \[\text{CuS}{{\text{O}}_{\text{4}}}\]solution done clear
B) Aqueous \[\text{AgN}{{\text{O}}_{\text{3}}}\]solution done clear
C) Aqueous \[\text{NaCl}\]solution done clear
D) Aqueous \[\text{NaOH}\]solution done clear
View Answer play_arrowquestion_answer120) Which of the following ore is an ore of copper?
A) Argentite done clear
B) Haematite done clear
C) Malachite done clear
D) Calamine done clear
View Answer play_arrowquestion_answer121) \[\text{KMn}{{\text{O}}_{\text{4}}}(mol\,wt.=158)\]oxidizes oxalic acid in acid medium to \[\text{C}{{\text{O}}_{\text{2}}}\]and water as follows \[5{{C}_{2}}O_{4}^{2-}+2MnO_{4}^{-}+16{{H}^{+}}\to 10C{{O}_{2}}+2M{{n}^{2+}}\]\[\text{+}\,\,\text{8}{{\text{H}}_{\text{2}}}\text{O}\] What is the equivalent weight of\[\text{KMn}{{\text{O}}_{\text{4}}}\]?
A) 158 done clear
B) 31.6 done clear
C) 39.5 done clear
D) 79 done clear
View Answer play_arrowquestion_answer122) Sodium bicarbonate on heating decomposes to form sodium carbonate, \[\text{C}{{\text{O}}_{\text{2}}}\]and water. If 0.2 moles of sodium bicarbonate is completely decomposed, how many moles of sodium carbonate is formed?
A) 0.1 done clear
B) 0.2 done clear
C) 0.05 done clear
D) 0.025 done clear
View Answer play_arrowquestion_answer123) What is the energy (in eV) required to excite the electron from\[n=1\]to\[n=2\]state in hydrogen atom? (\[n=\]principal quantum number)
A) 13.6 done clear
B) 3.4 done clear
C) 17.0 done clear
D) 10.2 done clear
View Answer play_arrowquestion_answer124) According to aufbau principle, the correct order of energy of 3d, 4s and 4p orbitals is
A) \[~4p<3d<4s\] done clear
B) \[~4s<4p<3d\] done clear
C) \[~4s<3d<4p\] done clear
D) \[~3d<4s<4p\] done clear
View Answer play_arrowquestion_answer125) \[n-\]pentane and 2-methylbutane are a pair of
A) enantiomers done clear
B) stereoisomers done clear
C) diastereomers done clear
D) constitutional isomers done clear
View Answer play_arrowquestion_answer126) Compound can exhibit
A) geometrical isomerism done clear
B) tautomerism done clear
C) optical isomerism done clear
D) geometrical and optical isomerism done clear
View Answer play_arrowquestion_answer127) The activity of a radioactive nuclide is \[2\times {{10}^{7}}\] disintegrations per minute (dpm). After 23.03 min, its activity is reduced to\[2\times {{10}^{6}}\text{ dpm}\text{.}\] What is the average life (in min) of this nuclide?
A) 100 done clear
B) 10 done clear
C) 1 done clear
D) 0.1 done clear
View Answer play_arrowquestion_answer128) What' is the correct order of velocity of alpha \[(\alpha ),\]beta \[(\beta )\]and gamma\[(\gamma )\]rays?
A) \[\alpha >\,\beta >\gamma \] done clear
B) \[\alpha >\,\gamma >\beta \] done clear
C) \[\gamma >\,\alpha >\beta \] done clear
D) \[\gamma >\beta >\alpha \] done clear
View Answer play_arrowquestion_answer129) The isomers which are interconverted through rotation around a single bond are
A) conformers done clear
B) diastereomers done clear
C) enantiomers done clear
D) position isomers done clear
View Answer play_arrowquestion_answer130) The major product in the reaction of 2-butyne with \[\text{Li/liq}\text{.N}{{\text{H}}_{\text{3}}}\]is
A) done clear
B) done clear
C) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\] done clear
D) \[{{H}_{2}}C=CH-C{{H}_{2}}-C{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer131) What is X in the following nuclear reaction? \[_{11}N{{a}^{23}}+{{\,}_{0}}{{n}^{1}}\to {{\,}_{11}}N{{a}^{24}}+X\]
A) \[{{\,}_{1}}{{H}^{1}}\] done clear
B) \[{{\,}_{2}}H{{e}^{4}}\] done clear
C) \[{{\,}_{1}}{{H}^{2}}\] done clear
D) \[\gamma -\]ray (gamma ray) done clear
View Answer play_arrowquestion_answer132) HA is a weak acid. The pH of 0.1 M HA solution is 2. What is the degree of dissociation \[(\alpha )\]of HA?
A) 0.5 done clear
B) 0.2 done clear
C) 0.1 done clear
D) 0.301 done clear
View Answer play_arrowquestion_answer133) In the following reaction, A and B, respectively are \[A\xrightarrow{\text{HBr}}{{C}_{2}}{{H}_{5}}Br\xrightarrow{B}A\]
A) \[{{C}_{2}}{{H}_{4}},alc\,KOH/\Delta \] done clear
B) \[{{C}_{2}}{{H}_{5}}Cl,aq\,KOH/\Delta \] done clear
C) \[C{{H}_{3}}OH,aq\,KOH/\Delta \] done clear
D) \[{{C}_{2}}{{H}_{2}},PB{{r}_{3}}\] done clear
View Answer play_arrowquestion_answer134) The reagent(s) used in the preparation of aspirin from salicylic acid
A) \[\text{SOC}{{\text{l}}_{\text{2}}}\text{,}\]pyridine done clear
B) \[{{\text{(C}{{\text{H}}_{3}}\text{CO)}}_{2}}O,{{H}^{+}}\] done clear
C) \[C{{H}_{3}}C{{O}_{2}}H,HCl\] done clear
D) \[C{{H}_{3}}Cl,AlC{{l}_{3}}\] done clear
View Answer play_arrowquestion_answer135) The equilibrium reaction that is not influenced by volume change at constant temperature is
A) \[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\] done clear
B) \[{{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)\] done clear
C) \[{{N}_{2}}{{O}_{4}}(g)2N{{O}_{2}}(g)\] done clear
D) \[2NO(g)+{{O}_{2}}2N{{O}_{2}}(g)\] done clear
View Answer play_arrowquestion_answer136) Consider the following solutions of equal concentrations \[A=N{{H}_{4}}Cl\] \[B=C{{H}_{3}}COONa\] \[C=N{{H}_{2}}OH\] \[D=C{{H}_{2}}COOH\] A buffer solution can be obtained by mixing equal volumes of
A) C and D done clear
B) A and B done clear
C) A and C done clear
D) C and D done clear
View Answer play_arrowquestion_answer137) In the following reaction, X and Y respectively are \[{{C}_{2}}{{H}_{5}}OH\xrightarrow{KMn{{O}_{4}}/{{H}^{+}}}X\frac{Y}{{{H}_{2}}S{{O}_{4}}/\Delta }C{{H}_{3}}C{{O}_{2}}{{C}_{2}}{{H}_{5}}\]
A) \[C{{H}_{3}}OH,{{C}_{2}}{{H}_{5}}OH\] done clear
B) \[~C{{H}_{3}}CHO,C{{H}_{3}}OH\] done clear
C) \[~C{{H}_{3}}C{{O}_{2}}H,\text{ }{{C}_{2}}{{H}_{5}}OH\] done clear
D) \[~{{C}_{2}}{{H}_{4}},C{{H}_{3}}CO{{}_{2}}H\] done clear
View Answer play_arrowquestion_answer138) The reaction conditions used for converting 1, 2-dibromopropane to propylene are
A) \[KOH,alcohol/\Delta \] done clear
B) \[KOH,\text{ }water/\Delta \] done clear
C) \[~Zn,\text{ }alcohol/\Delta \] done clear
D) \[~Na,\text{ }alcohol/\Delta \] done clear
View Answer play_arrowquestion_answer139) Which of the following's a Lewis acid?
A) \[AlC{{l}_{3}}\] done clear
B) \[C{{l}^{-}}\] done clear
C) \[CO\] done clear
D) \[{{C}_{2}}{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer140) If "a" and\[''{{t}_{1/2}}''\] are initial concentration of reactant and half-life of a zero order reaction respectively, which of the following is correct?
A) \[{{t}_{1/2}}\propto \frac{1}{a}\] done clear
B) \[{{t}_{1/2}}\propto a\] done clear
C) \[{{t}_{1/2}}\propto \frac{1}{{{a}^{2}}}\] done clear
D) \[{{t}_{1/2}}\propto {{a}^{2}}\] done clear
View Answer play_arrowquestion_answer141) All monosaccharides ....... Tollen's reagent.
A) oxidises done clear
B) condense with done clear
C) reduces done clear
D) add to done clear
View Answer play_arrowquestion_answer142) The product formed in the reaction of glycine with benzoyl chloride \[\text{+ aq NaOH}\]is
A) \[~PhCOC{{H}_{2}}N{{H}_{2}}\] done clear
B) \[~PhC{{H}_{2}}N{{H}_{2}}\] done clear
C) \[~PhCONHC{{H}_{3}}\] done clear
D) \[~PhCONHC{{H}_{2}}C{{O}_{2}}H\] done clear
View Answer play_arrowquestion_answer143) The rate constant of a reaction is found to be \[3\times {{10}^{-3}}\,mol\,{{L}^{-1}}\,{{\min }^{-1}}.\]The order of the reaction is
A) zero done clear
B) 1 done clear
C) 2 done clear
D) 1.5 done clear
View Answer play_arrowquestion_answer144) What is the two third life of a first order reaction having \[k=5.48\times {{10}^{-14}}{{s}^{-1}}\]
A) \[2.01\times {{10}^{11}}s\] done clear
B) \[2.01\times {{10}^{13}}s\] done clear
C) \[8.08\times {{10}^{13}}\,s\] done clear
D) \[16.04\times {{10}^{11}}\,s\] done clear
View Answer play_arrowquestion_answer145) Which of the following solvents are aprotic? [A]\[N{{H}_{3}}\] [B]\[S{{O}_{2}}\] [C] \[C{{H}_{3}}CN\] [D] \[C{{H}_{3}}C{{O}_{2}}H\]
A) \[A,B,C\] done clear
B) \[A,C,D\] done clear
C) \[B,C\] done clear
D) \[A,C\] done clear
View Answer play_arrowquestion_answer146) Chlorobenzene is o, p -directing in electrophilic substitution reaction. The directing influence is explained by
A) \[+\text{ }M\]of\[Ph\] done clear
B) \[+\,I\]of \[Cl\] done clear
C) \[+\text{ }M\]of\[Cl\] done clear
D) \[-I\]of \[Ph\] done clear
View Answer play_arrowquestion_answer147) 5 L of a solution contains\[\text{25}\,\text{mg}\] of \[\text{CaC}{{\text{O}}_{3}}.\]What is its concentration in ppm? (mol. wt. of \[\text{CaC}{{\text{O}}_{\text{3}}}\]is 100)
A) 25 done clear
B) 1 done clear
C) 5 done clear
D) 2500 done clear
View Answer play_arrowquestion_answer148) Observe the following abbrevations \[{{\pi }_{obs}}=\]observed colligative property \[{{\pi }_{cal}}=\]theoretical colligative property assuming normal behaviour of solute. van't Hoff factor \[(i)\]is given by
A) \[i={{\pi }_{obs}}\times {{\pi }_{cal}}\] done clear
B) \[i={{\pi }_{obs}}+{{\pi }_{cal}}\] done clear
C) \[i={{\pi }_{obs}}-{{\pi }_{cal}}\] done clear
D) \[i=\frac{{{\pi }_{obs}}}{{{\pi }_{cal}}}\] done clear
View Answer play_arrowquestion_answer149) The correct order for homolytic bond dissociation energies (\[\Delta H\]in kcal/mol) for \[C{{H}_{4}}(A),{{C}_{2}}{{H}_{6}}(B)\]and\[C{{H}_{3}}Br(C),\]under identical experimental conditions
A) \[C>B>A\] done clear
B) \[B>C>A\] done clear
C) \[~C>A>B\] done clear
D) \[~A>B>C\] done clear
View Answer play_arrowquestion_answer150) \[RX+{{I}^{-}}\xrightarrow{{}}R-I+X\]is an example of....... reaction.
A) nucleophilic addition done clear
B) nucleophilic substitution done clear
C) electrophilic addition done clear
D) elimination done clear
View Answer play_arrowquestion_answer151) If \[a{{x}^{3}}+b{{x}^{2}}+ex+d=0\]has a repeated root \[\alpha ,\] then a is also a root of
A) \[3a{{x}^{2}}+2bx+d=0\] done clear
B) \[a{{x}^{2}}+b\,x+c=0\] done clear
C) \[3a{{x}^{2}}+2bx+c=0\] done clear
D) \[6ax+2b=0\] done clear
View Answer play_arrowquestion_answer152) If the roots of \[{{x}^{3}}-3{{x}^{2}}-6x+8=0\] are in arithmetic progression, then the roots of the equation are
A) \[3,4,5\] done clear
B) \[4,7,10\] done clear
C) \[-2,1,4\] done clear
D) \[1,4,7\] done clear
View Answer play_arrowquestion_answer153) If \[\alpha ,\beta ,\gamma \] are the roots of the cubic equation \[{{x}^{3}}-{{x}^{2}}+x-1=0,\]then \[{{\alpha }^{-3}}+{{\beta }^{-3}}+{{\gamma }^{-3}}\] is equal to
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer154) If \[\alpha ,\beta ,\gamma \] are the roots of \[{{x}^{3}}+bx+c=0,\]then \[{{\alpha }^{2}}\beta +\alpha {{\beta }^{2}}+{{\beta }^{2}}\gamma +{{\gamma }^{2}}\alpha +\gamma {{\alpha }^{2}}\] is equal to
A) \[c\] done clear
B) \[-c\] done clear
C) \[-3c\] done clear
D) \[3c\] done clear
View Answer play_arrowquestion_answer155) \[\underset{x\to \infty }{\mathop{\lim }}\,(\sqrt{x+\sqrt{x}}-\sqrt{x})\]
A) \[-1/2\] done clear
B) \[1/2\] done clear
C) \[1\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer156) \[\underset{x\to 1}{\mathop{\lim }}\,\frac{2{{x}^{2}}+x-3}{3{{x}^{2}}+2x-2}\]is equal to
A) \[1\] done clear
B) \[2\] done clear
C) \[-1\] done clear
D) \[-2\] done clear
View Answer play_arrowquestion_answer157) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\sin }^{-1}}x-x}{{{x}^{3}}\,\cos x}\]is equal to
A) \[1/2\] done clear
B) \[1/3\] done clear
C) \[1/6\] done clear
D) \[1/12\] done clear
View Answer play_arrowquestion_answer158) If \[f:R\to R\] given by \[f(x)=\left\{ \begin{matrix} 2\,\cos x, & if & x\le -\frac{\pi }{2} \\ a\,\sin \,x+b, & if & -\frac{\pi }{2}<x<\frac{\pi }{2} \\ 1+{{\cos }^{2}}x, & if & x\ge \frac{\pi }{2} \\ \end{matrix} \right.\] is a continuous function on R, then (a, b) is equal to
A) \[(1/2,\,1/2)\] done clear
B) \[(0,-1)\] done clear
C) \[(0,2)\] done clear
D) \[(1,0)\] done clear
View Answer play_arrowquestion_answer159) \[\frac{d}{dx}\left\{ \begin{align} & {{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)+{{\tan }^{-1}}\left( \frac{3x-{{x}^{2}}}{1-3{{x}^{2}}} \right) \\ & -{{\tan }^{-1}}\left( \frac{4x-4{{x}^{2}}}{1-6{{x}^{2}}+{{x}^{4}}} \right) \\ \end{align} \right\}\]equal to
A) \[\frac{1}{\sqrt{1-{{x}^{2}}}}\] done clear
B) \[-\frac{1}{\sqrt{1-{{x}^{2}}}}\] done clear
C) \[\frac{1}{1+{{x}^{2}}}\] done clear
D) \[-\frac{1}{1+{{x}^{2}}}\] done clear
View Answer play_arrowquestion_answer160) If \[2{{x}^{2}}-3xy+{{y}^{2}}+x-2y-8=0,\]then \[\frac{dy}{dx}\] is equal to
A) \[\frac{3y-4x-1}{2y-3x-2}\] done clear
B) \[\frac{3y+4x-1}{2y+3x+2}\] done clear
C) \[\frac{3y+4x+1}{2y-3x+2}\] done clear
D) \[\frac{3y+4x+1}{2y-3x-2}\] done clear
View Answer play_arrowquestion_answer161) The equation of the tangent at \[(1,5)\] to the curve \[y=5{{x}^{4}}\] is
A) \[20x-y=15\] done clear
B) \[x+20y=101\] done clear
C) \[20x+y=15\] done clear
D) \[x-20y=101\] done clear
View Answer play_arrowquestion_answer162) The length of the sub tangent at any point \[({{x}_{1}},\,{{y}_{1}})\] on the curve \[y={{a}^{x}},\]\[(a>0)\] is
A) \[2\,\,\log \,a\] done clear
B) \[1/\,\,\log \,a\] done clear
C) \[\log \,a\] done clear
D) \[{{a}^{{{2}_{{{x}_{1}}}}}}\log \,a\] done clear
View Answer play_arrowquestion_answer163) The set \[\{{{x}^{3}}-12x:-3\le x\le 3\}\] is equal to
A) \[\{x:-16\le x\le 16\}\] done clear
B) \[\{x:-12\le x\le 12\}\] done clear
C) \[\{x:-9\le x\le 9\}\] done clear
D) \[\{x:0\le x\le 10\}\] done clear
View Answer play_arrowquestion_answer164) The set of all local maxima for \[y=\cos \,\,x\]is
A) \[\{n\pi :n\in I\}\] done clear
B) \[\{2n\pi :n\in I\}\] done clear
C) \[\{n\pi /2:n\in I\}\] done clear
D) \[\{n\pi /3:n\in I\}\] done clear
View Answer play_arrowquestion_answer165) The absolute maximum of \[{{x}^{40}}-{{x}^{20}}\]on the interval \[[0,1]\] is
A) \[-1/4\] done clear
B) \[0\] done clear
C) \[1/4\] done clear
D) \[1/2\] done clear
View Answer play_arrowquestion_answer166) \[\int_{-2}^{2}{(x-|x|)}\,\,dx\] is equal to
A) \[0\] done clear
B) \[2\] done clear
C) \[4\] done clear
D) \[-4\] done clear
View Answer play_arrowquestion_answer167) If \[\int{\frac{dx}{x\,\log \,x}}=f(x)+\] constant, then \[f(x)\] is equal to
A) \[1/\,\log \,x\] done clear
B) \[\log \,x\] done clear
C) \[\log \,\,\log \,x\] done clear
D) \[x/\,\log \,x\] done clear
View Answer play_arrowquestion_answer168) If \[\int{\text{cosec x}\,\text{dx =f(x)+}}\] constant, then \[f(x)\] is equal to
A) \[\tan \,x/2\] done clear
B) \[\log \,|\tan \,(x/2)|\] done clear
C) \[\log |\sin \,x|\] done clear
D) \[\log |cos\,x|\] done clear
View Answer play_arrowquestion_answer169) \[{{I}_{n}}=\int{{{\tan }^{n}}x}\,\,dx\] for \[n\ge 2,\] then \[{{I}_{n}}+{{I}_{n-2}}\] is equal to
A) \[{{\tan }^{n\,}}x+c\] done clear
B) \[\frac{({{\tan }^{n-1}}x)}{n-1}+c\] done clear
C) \[\frac{{{\tan }^{n}}x}{n}+c\] done clear
D) \[n\,\,{{\tan }^{n}}x+c\] done clear
View Answer play_arrowquestion_answer170) \[\int_{0}^{\pi /2}{x\,\sin \,x}\,\,dx\]is equal to
A) \[0\] done clear
B) \[1\] done clear
C) \[-1\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer171) The area (in square unit) of the region bounded by the y-axis and the curve \[2x={{y}^{2}}-1\]is
A) \[1/3\] done clear
B) \[2/3\] done clear
C) \[1\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer172) The solution of the differential equation \[({{x}^{2}}+{{y}^{2}})dx=2xy\,\,dy\]is
A) \[{{x}^{2}}+{{y}^{2}}=cy\] done clear
B) \[c({{x}^{2}}-{{y}^{2}})=x\] done clear
C) \[{{x}^{2}}-{{y}^{2}}=cy\] done clear
D) \[{{x}^{2}}+{{y}^{2}}=cx\] (here c is an arbitrary constant) done clear
View Answer play_arrowquestion_answer173) A number n is chosen at random from the set \[\{11,12,13,.....30\}.\]The probability that n is neither divisible by 3 nor divisible by 5 is
A) \[7/20\] done clear
B) \[9/20\] done clear
C) \[11/20\] done clear
D) \[13/20\] done clear
View Answer play_arrowquestion_answer174) The probability that a number n chosen at random from 1 to 30, to satisfy \[n+(50/n)>27\]is
A) \[7/30\] done clear
B) \[3/10\] done clear
C) \[3/5\] done clear
D) \[1/5\] done clear
View Answer play_arrowquestion_answer175) If a random variable X has the distribution given below, then the value of c is
\[x=k\] | \[-2\] | \[-1\] | \[0\] | \[1\] | \[2\] | \[3\] |
\[P(X=k)\] | \[\frac{1}{10}\] | \[\frac{1}{10}\] | \[2c\] | \[\frac{3}{10}\] | \[\frac{1}{5}\] | \[c\] |
A) \[1/5\] done clear
B) \[2/5\] done clear
C) \[1/10\] done clear
D) \[3/10\] done clear
View Answer play_arrowquestion_answer176) A random variable X can attain only the value 1, 2, 3, 4, 5 with respective probabilities k, 2k, 3k, 2k, k. If m is the mean of the probability distribution, then (k, m) is equal to
A) \[(3,\,1/9)\] done clear
B) \[(\,1/9,3)\] done clear
C) \[(\,1/8,4)\] done clear
D) \[(\,1,3)\] done clear
View Answer play_arrowquestion_answer177) If \[f(x)=\lambda {{e}^{-ax}}\,\,(a>0)\] for \[0\le x<\infty \] is a probability density, then 'k is equal to
A) \[a\] done clear
B) \[{{a}^{2}}\] done clear
C) \[1/a\] done clear
D) \[{{a}^{2}}\] done clear
View Answer play_arrowquestion_answer178) Two unbiased dice are thrown simultaneously- The probability to get a sum more than 8 is
A) \[5/36\] done clear
B) \[5/18\] done clear
C) \[5/12\] done clear
D) \[2/9\] done clear
View Answer play_arrowquestion_answer179) The moment generating function of a random variable X is
A) \[E({{e}^{-1X}})\] done clear
B) \[E({{e}^{itX}})\] done clear
C) \[E({{e}^{tX}})\] done clear
D) \[E({{e}^{-it\,X}})\] done clear
View Answer play_arrowquestion_answer180) It \[\sigma \] is the standard deviation of a random variable X, then the standard deviation of the random variable \[aX+b,\]where \[a,\text{ }b\in R\]is
A) \[a\sigma +b\] done clear
B) \[|a|\sigma \] done clear
C) \[|a|\sigma +b\] done clear
D) \[{{a}^{2}}\sigma \] done clear
View Answer play_arrowquestion_answer181) If A and B are two sets, then \[A-(A-B)\]is equal to
A) \[B\] done clear
B) \[A\cup B\] done clear
C) \[A\cap B\] done clear
D) \[B-A\] done clear
View Answer play_arrowquestion_answer182) For any real number y the greatest integers not exceeding y is denoted by [y]. If \[f:R\to R\] is defined by \[f(x)=[2x]-2[x]\] for \[x\in R,\] then the range of f is
A) \[\{x\in R:x>0\}\] done clear
B) \[\{x\in R:x\le 0\}\] done clear
C) \[\{x\in R:0\le x\le 1\}\] done clear
D) \[\{0,\,1\}\] done clear
View Answer play_arrowquestion_answer183) The argument of \[\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\] is
A) \[2\pi /3\] done clear
B) \[\pi /3\] done clear
C) \[-\pi /3\] done clear
D) \[-2\pi /3\] done clear
View Answer play_arrowquestion_answer184) If \[S=\left\{ z\in C:\arg \left( \frac{z-2}{z+2} \right)=\frac{\pi }{3} \right\},\] then S is
A) an ellipse done clear
B) a straight line. done clear
C) a circle done clear
D) a parabola done clear
View Answer play_arrowquestion_answer185) If \[ac\ne 0\] and \[\alpha ,\beta \] are the roots of the equation \[a{{x}^{2}}+bx+c=0,\]then the quadratic equation with \[1/\alpha \] and \[1/\beta \] as its root is
A) \[{{x}^{2}}/a+x/b+1/c=0\] done clear
B) \[c{{x}^{2}}+bx+a=0\] done clear
C) \[b{{x}^{2}}+cx+a=0\] done clear
D) \[a{{x}^{2}}+cx+b=0\] done clear
View Answer play_arrowquestion_answer186) If \[\left\{ {{a}_{n}} \right\}_{n}^{x}\] is a sequence with \[{{a}_{0}}=p\] and \[{{a}_{n}}-{{a}_{n-1}}=r{{a}_{n-1}}\] for \[n\ge 1,\] then the terms of the sequence are in
A) an arithmetic progression done clear
B) a geometric progression done clear
C) a harmonic progression done clear
D) an arithmetico-geometric progression done clear
View Answer play_arrowquestion_answer187) The coefficient of \[{{x}^{-17}}\]in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\]is
A) \[^{15}{{C}_{11}}\] done clear
B) \[^{15}{{C}_{12}}\] done clear
C) \[^{-15}{{C}_{11}}\] done clear
D) \[^{-15}{{C}_{3}}\] done clear
View Answer play_arrowquestion_answer188) The term independent of x in the expansion of \[{{\left( {{x}^{3}}+\frac{2}{{{x}^{2}}} \right)}^{15}}\] is
A) \[{{T}_{7}}\] done clear
B) \[{{T}_{8}}\] done clear
C) \[{{T}_{9}}\] done clear
D) \[{{T}_{10}}\] done clear
View Answer play_arrowquestion_answer189) The ortho centre of the \[\Delta \,OAB,\]where O is the origin,\[A(6,0)\] and \[B(3,\,3\sqrt{3})\] is
A) \[(9/2,\,\sqrt{3}/2)\] done clear
B) \[(3,\,\sqrt{3})\] done clear
C) \[(\,\sqrt{3},3)\] done clear
D) \[(3,-\sqrt{3})\] done clear
View Answer play_arrowquestion_answer190) The distance between the pair of parallel lines given by \[{{x}^{2}}-1005x+2006=0\]is
A) \[1001\] done clear
B) \[1000\] done clear
C) \[1005\] done clear
D) \[2006\] done clear
View Answer play_arrowquestion_answer191) The radical axis of the coaxial system of circles with limiting points \[(1,2)\] and \[(-2,1)\] is
A) \[x+3y=0\] done clear
B) \[3x+y=0\] done clear
C) \[2x+3y=0\] done clear
D) \[3x+2y=0\] done clear
View Answer play_arrowquestion_answer192) The equation of the circle that can be inscribed in the square OABC, where O is the origin \[A(-2,0),\,B(-2,2)\] and \[C(0,2)\] is
A) \[{{x}^{2}}+{{y}^{2}}+2x-2y=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+2x-2y+1=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2x-2y-1=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-2x+2y+1=0\] done clear
View Answer play_arrowquestion_answer193) The curve with parametric equation \[x={{e}^{t}}+{{e}^{-t}}\] and \[y={{e}^{t}}-{{e}^{-t}}\] is
A) a circle done clear
B) an ellipse done clear
C) a hyperbola done clear
D) a parabola done clear
View Answer play_arrowquestion_answer194) If \[(-1,\,2\sqrt{2})\] is one of extremity of a focal chord of the parabola \[{{y}^{2}}=-8x,\] then the other extremity is
A) \[(-1,-\sqrt{2})\] done clear
B) \[(2\sqrt{2},-1)\] done clear
C) \[(-4,4\sqrt{2})\] done clear
D) \[(4,4\sqrt{2})\] done clear
View Answer play_arrowquestion_answer195) The equation of the pair of straight lines perpendicular to the pair \[2{{x}^{2}}+3xy+2{{y}^{2}}+10x+5y=0\] and passing through the origin is
A) \[2{{x}^{2}}+5xy+2{{y}^{2}}=0\] done clear
B) \[2{{x}^{2}}-3xy+2{{y}^{2}}=0\] done clear
C) \[2{{x}^{2}}+3xy+{{y}^{2}}=0\] done clear
D) \[2{{x}^{2}}-5xy+2{{y}^{2}}=0\] done clear
View Answer play_arrowquestion_answer196) If two angles of a triangle are \[{{45}^{o}}\] and \[{{\tan }^{-1}}(2),\] then the third angle is
A) \[{{60}^{o}}\] done clear
B) \[{{75}^{o}}\] done clear
C) \[{{\tan }^{-1}}3\] done clear
D) \[{{90}^{o}}\] done clear
View Answer play_arrowquestion_answer197) \[\frac{\tan A}{1+\sec A}+\frac{1+\sec A}{\tan A}\]is equal to
A) \[2\text{ }sin\text{ }A\] done clear
B) \[2\text{ }cos\text{ }A\] done clear
C) \[2\text{ }cosec\text{ }A\] done clear
D) \[2\text{ }sec\text{ }A\] done clear
View Answer play_arrowquestion_answer198) If \[\sin \theta +\cos \theta =h,\] then the quadratic equation having \[\sin \theta \] and \[\cos \theta \] as its roots is
A) \[{{x}^{2}}-hx+({{h}^{2}}-1)=0\] done clear
B) \[2{{x}^{2}}-2hx+({{h}^{2}}-1)=0\] done clear
C) \[{{x}^{2}}-hx+2({{h}^{2}}-1)=0\] done clear
D) \[{{x}^{2}}-2hx+({{h}^{2}}-1)=0\] done clear
View Answer play_arrowquestion_answer199) In a triangle, if \[{{r}_{1}}+{{r}_{3}}=k\,\,{{\cos }^{2}}\,B/2,\]then k is equal to
A) \[R\] done clear
B) \[2R\] done clear
C) \[3R\] done clear
D) \[4R\] done clear
View Answer play_arrowquestion_answer200) If \[\tan (k+1)\theta =\tan \theta ,\] then \[\theta \] belongs to the set
A) \[\{n\pi :n\in I\}\] done clear
B) \[\{n\pi /2:n\in I\}\] done clear
C) \[\{n\pi /k:n\in I\}\] done clear
D) \[\{n\pi /2k:n\in I\}\] done clear
View Answer play_arrowquestion_answer201) \[{{\tan }^{-1}}\left( \frac{3x-{{x}^{3}}}{1-3{{x}^{2}}} \right)-{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)\] is equal to
A) \[0\] done clear
B) \[1\] done clear
C) \[{{\tan }^{-1}}(x)\] done clear
D) \[{{\tan }^{-1}}(2x)\] done clear
View Answer play_arrowquestion_answer202) If \[sin\text{ }A:sin\text{ }B:sin\text{ }C=3:4:5,\] then \[cos\text{ }A:cos\text{ }B\]is equal to
A) \[4:3\] done clear
B) \[5:3\] done clear
C) \[3:4\] done clear
D) \[3:5\] done clear
View Answer play_arrowquestion_answer203) If A is a matrix such that \[{{A}^{2}}=A+I,\]where I is the unit matrix, then \[{{A}^{5}}\]is equal to
A) \[5A+I\] done clear
B) 5A + 21 done clear
C) \[5A+3I\] done clear
D) \[5A+4I\] done clear
View Answer play_arrowquestion_answer204) The inverse of \[\left[ \begin{matrix} 0 & 0 & 2 \\ 0 & 2 & 0 \\ 2 & 0 & 0 \\ \end{matrix} \right]\] is
A) \[\left[ \begin{matrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & \frac{1}{2} \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} 0 & 0 & 2 \\ 0 & 2 & 0 \\ 2 & 0 & 0 \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} 0 & 0 & \frac{1}{2} \\ 0 & \frac{1}{2} & 0 \\ \frac{1}{2} & 0 & 0 \\ \end{matrix} \right]\] done clear
View Answer play_arrowquestion_answer205) \[\left| \begin{matrix} 1 & 2 & 3 \\ {{1}^{3}} & {{2}^{3}} & {{3}^{3}} \\ {{1}^{5}} & {{2}^{5}} & {{3}^{5}} \\ \end{matrix} \right|\] equal to
A) \[1!\,\,2\,\,1\,\,\,3\] done clear
B) \[1\,\,!\,\,\,3\,\,!\,\,\,5\,\,!\] done clear
C) \[6\,\,!\] done clear
D) \[9\,\,!\] done clear
View Answer play_arrowquestion_answer206) \[\left| \begin{matrix} a & b & a+b \\ b & a+b & a \\ a+b & a & b \\ \end{matrix} \right|\] is equal to
A) \[{{a}^{3}}+{{b}^{3}}\] done clear
B) \[-({{a}^{3}}+{{b}^{3}})\] done clear
C) \[2\,({{a}^{3}}+{{b}^{3}})\] done clear
D) \[-2\,({{a}^{3}}+{{b}^{3}})\] done clear
View Answer play_arrowquestion_answer207) If \[A\left[ \begin{matrix} a & b & 0 \\ -b & a & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],\] where \[{{a}^{2}}+{{b}^{2}}=1,\] then adj is equal to
A) \[{{A}^{-1}}\] done clear
B) \[{{A}^{T}}\] done clear
C) \[A\] done clear
D) \[-A\] (Here, \[{{A}^{T}}\] is the transpose of A) done clear
View Answer play_arrowquestion_answer208) If A is a non-singular matrix such that \[{{A}^{3}}=A+I,\] then the inverse of \[B={{A}^{6}}-{{A}^{5}}\]is
A) \[A\] done clear
B) \[{{A}^{-1}}\] done clear
C) \[-A\] done clear
D) \[-{{A}^{-1}}\] done clear
View Answer play_arrowquestion_answer209) The value of \[\lambda \] such that \[x+3y+\lambda z=0,\]\[2x+4y-z=0,\,\,\,\,\,\,\,x+5y-2z=0\]has a non-trivial solution is
A) \[-1\] done clear
B) \[0\] done clear
C) \[1\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer210) If \[A=\left[ \begin{matrix} 0 & -3 & -4/3 \\ 3 & 0 & -1/4 \\ 4/3 & 1/4 & 0 \\ \end{matrix} \right],\] then det \[(A+{{A}^{T}})\] is equal to
A) \[0\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer211) If the position vector of A with respect to O is \[3\hat{i}-2\hat{j}+4\hat{k}\]and \[\overrightarrow{AB}=3\hat{i}-\hat{j}+\hat{k},\] then the position vector of B with respect to 0 is
A) \[-\hat{j}+3\hat{k}\] done clear
B) \[6\hat{i}-3\hat{j}+5\hat{k}\] done clear
C) \[\hat{j}-3\hat{k}\] done clear
D) \[\hat{i}-3\hat{j}+5\hat{k}\] done clear
View Answer play_arrowquestion_answer212) If \[|\vec{a}|=|\vec{b}|=|\vec{a}-\vec{b}|=1,\] then \[|\vec{a}+\vec{b}|\]is equal to
A) \[1\] done clear
B) \[2\] done clear
C) \[\sqrt{2}\] done clear
D) \[\sqrt{3}\] done clear
View Answer play_arrowquestion_answer213) If the vectors \[2\hat{i}-3\hat{j}+4\hat{k},\,\,\hat{i}+2\hat{j}-\hat{k}\] and \[\lambda \hat{i}-\hat{j}+2\hat{k}\]are coplanar, then X is equal to
A) \[0\] done clear
B) \[5/8\] done clear
C) \[8/5\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer214) If \[\vec{a}=2\hat{i}+2\hat{j}+\hat{k},\,\vec{a}.\vec{b}=14\] and \[\vec{a}\times \vec{b}=3\hat{i}+\hat{j}-8\hat{k},\] then \[\vec{b}\] equals
A) \[\hat{i}+5\hat{j}+2\hat{k}\] done clear
B) \[\hat{i}-2\hat{j}+16\hat{k}\] done clear
C) \[5\hat{i}+\hat{j}+2\hat{k}\] done clear
D) \[5\hat{i}-\hat{j}+2\hat{k}\] done clear
View Answer play_arrowquestion_answer215) If \[\vec{a},\vec{b},\vec{c}\] are non-coplanar vectors and \[(\vec{a}-\lambda \vec{b}).(\vec{b}-2\vec{c})\times (\vec{c}+2\vec{a})=0,\] then \[\lambda \] is equal to
A) \[1\] done clear
B) \[1/4\] done clear
C) \[0\] done clear
D) \[-1/4\] done clear
View Answer play_arrowquestion_answer216) If \[\vec{a},\vec{b},\vec{c}\] are non-coplanar and \[[\vec{a}+\vec{b}\,\,\,\vec{b}+\vec{c}\,\,\,\,\vec{c}+\vec{a}]=k[\vec{a}\vec{b}\vec{c}],\]then k is equal to
A) \[0\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer217) If \[\vec{a}+2\vec{b}+2\vec{c}=\vec{0}\] and \[(\vec{a}\times \vec{b})+(\vec{b}\times \vec{c})+(\vec{c}\times \vec{a})=\lambda (\vec{b}\times \vec{c}),\] then \[\lambda \] is equal to
A) \[4\] done clear
B) \[7\] done clear
C) \[8\] done clear
D) \[9\] done clear
View Answer play_arrowquestion_answer218) The line segment adjoining the points A , B makes projection 1,4,3 on X,Y,Z axis respectively. Then the direction cosines of AB are
A) \[1,4,3\] done clear
B) \[1/\sqrt{26},\,\,4/\sqrt{26},\,\,3/\sqrt{26}\] done clear
C) \[-1/\sqrt{26},\,\,4/\sqrt{26},\,\,3/\sqrt{26}\] done clear
D) \[1/\sqrt{26},-\,\,4/\sqrt{26},\,\,3/\sqrt{26}\] done clear
View Answer play_arrowquestion_answer219) The length of the projection of the line segment joining \[(3,-1,0)\] and \[(-3,5,\sqrt{2})\] on a line with direction cosines \[1/2,\,\,1/2,\,\,1/\sqrt{2}\] is
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer220) The line perpendicular to the plane s\[2x-y+5z=4\] passing through the point \[(-1,0,1)\] is
A) \[\frac{x+1}{2}=-y=\frac{z-1}{-5}\] done clear
B) \[\frac{x+1}{2}=-y=\frac{z-1}{-5}\] done clear
C) \[\frac{x+1}{2}=-y=\frac{z-1}{5}\] done clear
D) \[\frac{x+1}{2}=y=\frac{z-1}{5}\] done clear
View Answer play_arrowquestion_answer221) The shortest distance between the lines \[\frac{x-2}{3}=\frac{y+3}{4}=\frac{z-1}{5}\] and \[\frac{x-5}{1}=\frac{y-1}{2}=\frac{z-6}{3}\] is
A) \[3\] done clear
B) \[2\] done clear
C) \[1\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer222) Angle between the line \[\frac{x+1}{1}=\frac{y}{2}=\frac{z-1}{1}\] and a normal to the plane \[x-y+z=0\] is
A) \[{{0}^{o}}\] done clear
B) \[{{30}^{o}}\] done clear
C) \[{{45}^{o}}\] done clear
D) \[{{90}^{o}}\] done clear
View Answer play_arrowquestion_answer223) A point on x-axis which is equidistant from both the points \[(1,\,2,3)\] and \[(3,5,-2)\] is
A) \[(-6,0,0)\] done clear
B) \[(5,0,0)\] done clear
C) \[(-5,0,0)\] done clear
D) \[(6,0,0)\] done clear
View Answer play_arrowquestion_answer224) Foot of the perpendicular from \[(-2,1,4)\] to a plane is \[(3,1,2)\], then the equation of the plane is
A) \[4x-2y=11\] done clear
B) \[5x-2y=10\] done clear
C) \[5x-2z=11\] done clear
D) \[5x+2z=11\] done clear
View Answer play_arrowquestion_answer225) If \[\theta \] is the angle between the planes \[2x-y+z-1=0\] and \[x-2y+z+2=0,\] then \[\cos \,\theta \] is equal to
A) \[2/3\] done clear
B) \[3/4\] done clear
C) \[4/5\] done clear
D) \[5/6\]s done clear
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