question_answer1) The following is the truth table for
A | B | Y |
0 | 0 | 1 |
1 | 0 | 1 |
0 | 1 | 1 |
1 | 1 | 0 |
A) NAND
B) AND
C) XOR
D) NOT
View Answer play_arrowquestion_answer2) In a full wave rectifier circuit operating from \[50\text{ }Hz\]main frequency, the fundamental frequency in the ripple would be
A) \[\text{25 }Hz\]
B) \[50\text{ }Hz\]
C) \[70.7\text{ }Hz\]
D) \[100\text{ }Hz\]
View Answer play_arrowquestion_answer3) The current gain a of a transistor is 0.9. The transistor is connected to common base configuration. What would be the change in collector current when base current changes by \[4mA\]?
A) \[1.2\,\,mA\]
B) \[12\,\,mA\]
C) \[24\,\,mA\]
D) \[36\,\,mA\]
View Answer play_arrowquestion_answer4) What is the name of the level formed due to impurity atom in p-type in the forbidden gap?
A) Donor level
B) Acceptor level
C) Conduction level
D) Forbidden level
View Answer play_arrowquestion_answer5) Which of the following is not true?
A) All unit cells are primitive
B) FCC structure is a closed packed structure
C) A unit cell is primitive if it contains lattice points only at its corner
D) A lattice does not contain any atom or molecule
View Answer play_arrowquestion_answer6) A radioactive element A decays into B with a half-life of 2 days. A fresh prepared sample of A has a mass of \[12\text{ }g\]. What mass of A and B are there in the sample after 4 days?
A) \[~A=3g,B=9g\]
B) \[A=6g,B=6g\]
C) \[A=12g,B=0g\]
D) \[A=9g,B=3g\]
View Answer play_arrowquestion_answer7) How many \[\alpha \]-particle and \[\beta \]-particles are emitted when uranium nucleus \[_{92}^{238}U\] decays to lead nucleus \[_{82}^{206}Pb\]?
A) \[\alpha =6,\beta =8\]
B) \[\alpha =10,\beta =8\]
C) \[\alpha =8,\beta =10\]
D) \[\alpha =8,\beta =6\]
View Answer play_arrowquestion_answer8) The angular speed of the electric in the nth orbit of Bohr hydrogen atom is
A) directly proportional to n
B) inversely proportional to \[\sqrt{n}\]
C) inversely proportional to \[{{n}^{2}}\]
D) inversely proportional to \[{{n}^{3}}\]
View Answer play_arrowquestion_answer9) If the electron in hydrogen atom jumps from the third to second orbit, the wavelength of the emitted radiation in terms of Rydberg constant R is given by
A) \[\lambda =\frac{36}{5R}\]
B) \[\lambda =\frac{5R}{36}\]
C) \[\lambda =\frac{5}{R}\]
D) \[\lambda =\frac{R}{6}\]
View Answer play_arrowquestion_answer10) When a monochromatic point source of light is at a distance of \[0.2\text{ }m\]from a photocell, the cut-off voltage and the saturation current are respectively \[{{\text{V}}_{0}}=0.6\]volt and\[{{I}_{s}}=18.0\,mA\]. If the same source is placed 0.6 m away from the photocell, then
A) stopping potential \[{{V}_{0}}\text{=}0.2\]volt and saturation current \[{{I}_{s}}=18.0\text{ }mA\]
B) stopping potential \[{{V}_{0}}=0.6\]volt and saturation current \[{{I}_{s}}=18.0\text{ }mA\]
C) stopping potential \[{{V}_{0}}=0.6\] volt and saturation current \[{{I}_{s}}=2.0\,mA\]
D) stopping potential \[{{V}_{0}}=2.0\] volt and saturation current \[{{I}_{s}}=2.0\,mA\]
View Answer play_arrowquestion_answer11) When light of wavelength \[300~nm\](nanometer) falls on a photoelectric emitter, photoelectrons are just liberated. For another emitter, however, light of \[600\text{ }nm\]wavelength is sufficient for creating photoemission. What is the ratio of the work function of the two emitters?
A) \[1:2\]
B) \[2:1\]
C) \[4:1\]
D) \[1:4\]
View Answer play_arrowquestion_answer12) In Millikan's oil drop experiment, a charged drop of mass \[1.8\times {{10}^{-14}}\text{ }kg\] is stationary between the plates. The distance between the plates \[0.9\text{ }cm\]and potential difference between the plates is\[2000\text{ }V\]. The number of electons on the oil drop is
A) \[10\]
B) \[5\]
C) \[50\]
D) \[20\]
View Answer play_arrowquestion_answer13) In the experiment for the determination of \[\frac{e}{m}\]of electrons by the Thomson method, electric and magnetic fields are
A) parallel and both are perpendicular to the motion of the electron
B) both mutually perpendicular and parallel to the motion of electron
C) both mutually perpendicular and also perpendicular to the motion of electron
D) both mutually perpendicular and have no relation with motion of the electron
View Answer play_arrowquestion_answer14) Blue colour of sky is due to
A) interference
B) scattering of light
C) dispersion of light
D) sun emits more of blue light
View Answer play_arrowquestion_answer15) In Young's double slit experiment distance between source is 1 mm and distance between the screen and source is 1 m. If the fringe width on the screen is 0.06 cm, then K is
A) \[6000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[4000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[1200\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[2400\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
View Answer play_arrowquestion_answer16) Angle of minimum deviation for a prism of refractive index \[1.5\] is equal to the angle of the prism. The angle of the prism is (given \[\cos \,{{41}^{o}}-24'-36''=0.75\])
A) \[{{82}^{o}}-49'-12''\]
B) \[{{72}^{o}}-48'-30''\]
C) \[{{41}^{o}}-24'-36''\]
D) \[{{31}^{o}}-49'-30''\]
View Answer play_arrowquestion_answer17) Two media having speeds of light \[2\times {{10}^{8}}\text{ }m/s\] and \[2.4\times {{10}^{8}}\text{ }m/s,\] are separated by a plane surface. What is the critical angle for a ray going from medium I to medium II ?
A) \[{{\sin }^{-1}}\left( \frac{5}{6} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{5}{12} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{2}} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
View Answer play_arrowquestion_answer18) When sunlight is incident son a prism, it produces a spectrum due to
A) interference of light
B) diffraction of light
C) total internal reflection
D) variation in speeds of different colours of light in the prism
View Answer play_arrowquestion_answer19) The transverse nature of light is shown by
A) interference of light
B) diffraction of light
C) polarization
D) radiation spectrum of black body
View Answer play_arrowquestion_answer20) An electromagnetic radiation of wavelength \[\lambda ,\] frequency v and propagating in air with velocity v is incident on a glass plate and is transmitted through. Which of the following statement is true for the wave inside the glass plate?
A) The velocity v remains unchanged but \[\lambda \]changes
B) The frequency v and wavelength remain unchanged but v changes
C) The wavelength \[\lambda \] remains unchanged but velocity v changes
D) The frequency v remains unchanged but \[\lambda \]changes
View Answer play_arrowquestion_answer21) The oscillating electric and magnetic vectors of an electromagnetic wave in vacuum are oriented along
A) the same direction but differ in phase by \[{{90}^{o}}\]
B) the same direction and are in phase
C) mutually perpendicular directions and differ in phase by \[{{90}^{o}}\]
D) mutually perpendicular directions and are in phase
View Answer play_arrowquestion_answer22) In an AC circuit the instantaneous values of emf and current are \[e=200\text{ }sin\text{ }300\,t\text{ }volt\] and \[i=2\,\sin \left( 300t+\frac{\pi }{3} \right)amp\] the average power consumed in watts is
A) \[200\]
B) \[100\]
C) \[50\]
D) \[400\]
View Answer play_arrowquestion_answer23) A transformer is used to light a 140 W, \[24\text{ }V\] lamp from \[240\text{ }VAC\]mains. The current in the mains cable of \[0.7\text{ }A\]. The efficiency of the transformer is
A) \[48%\]
B) \[63.8%\]
C) \[83.3%~\]
D) \[90%\]
View Answer play_arrowquestion_answer24) A solenoid has 2000 turns wound over a length of \[0.30\text{ }m\]. The area of its cross-section is \[1.2\times {{10}^{-3}}{{m}^{2}}\]. Around its central section a coil of 300 turns is wound. If an initial current of 2 A in the solenoid is reversed in \[0.25\text{ }s,\] the emf induced in the coil is
A) \[48\text{ }V\]
B) \[4.8\text{ }V\]
C) \[4.8\times {{10}^{-1}}\,V\]
D) \[4.8\times {{10}^{-2}}\,V\]
View Answer play_arrowquestion_answer25) A copper ring is held horizontally and a bar magnet with its length along the axis of the ring is dropped through the ring. The acceleration of the falling magnet is
A) less than that due to gravity
B) equal to that due to gravity
C) more than that due to gravity
D) depends on the length of the magnet and diameter of the ring
View Answer play_arrowquestion_answer26) The dimensional formula of Planck's constant (h) is
A) \[[M{{L}^{-2}}{{T}^{-3}}]\]
B) \[[M{{L}^{2}}{{T}^{-1}}]\]
C) \[[ML{{T}^{-2}}]\]
D) \[[M{{L}^{-2}}{{T}^{-1}}]\]
View Answer play_arrowquestion_answer27) A particle starts from rest and experiences constant acceleration for 6 s. If it travels a distance d-^ in the first two seconds, a distance \[{{d}_{2}}\] in the next two seconds and a distance \[{{d}_{3}}\] in the last two seconds, then
A) \[{{d}_{1}}:{{d}_{2}}:{{d}_{3}}=1:1:1\]
B) \[{{d}_{1}}:{{d}_{2}}:{{d}_{3}}=1:2:3\]
C) \[{{d}_{1}}:{{d}_{2}}:{{d}_{3}}=1:3:5\]
D) \[{{d}_{1}}:{{d}_{2}}:{{d}_{3}}=1:5:9\]
View Answer play_arrowquestion_answer28) A particle originally at rest at the highest point of a smooth circle in a vertical plane, is gently pushed and starts sliding/along the circle. It will leave the circle at a' vertical distance h. below the highest point such that
A) \[h=2R\]
B) \[h=\frac{R}{2}\]
C) \[h=R\]
D) \[h=\frac{R}{3}\]
View Answer play_arrowquestion_answer29) An inclined plane has an inclination \[\theta \] with horizontal. A body of mass m rests on it. If the coefficient of friction between the body and the plane is \[\mu ,\] then the minimum force that needs to be applied parallel to the inclined plane is
A) \[mg\,\,\sin \,\theta \]
B) \[\mu mg\,\,\cos \,\theta \]
C) \[\mu mg\,\,\cos \,\theta +mg\,\,\sin \,\theta \]
D) \[\mu mg\,\,\cos \,\theta -mg\,\,\sin \,\theta \]
View Answer play_arrowquestion_answer30) A \[60\text{ }kg\]man stands on a spring scale in a lift. At some instant he finds that the scale reading has changed from \[60\text{ }kg\] to \[50\text{ }kg\] for a while and then comes again to \[60\text{ }kg\] mark. What should he conclude?
A) The lift was in constant motion upwards
B) The lift was in constant motion downwards
C) The lift while in motion suddenly stopped
D) The lift while in motion upwards suddenly' stopped
View Answer play_arrowquestion_answer31) A diatomic molecule is formed by two atoms which may be treated as mass points \[{{m}_{1}}\] and \[{{m}_{2}},\] joined by a massless rod of length r. Then the moment of inertia of the molecule about an axis passing through the centre of mass and perpendicular to rod is
A) zero
B) \[({{m}_{1}}+{{m}_{2}}){{r}^{2}}\]
C) \[\left( \frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}{{m}_{2}}} \right){{r}^{2}}\]
D) \[\left( \frac{{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{r}^{2}}\]
View Answer play_arrowquestion_answer32) If the polar ice caps of earth melt, how long it affect the length of day?
A) Length of day would remain unchanged
B) Length of day would increase
C) Length of day would decrease
D) None of the above
View Answer play_arrowquestion_answer33) A planet revolves in an elliptical orbit around the sun. The semi-major and semi-minor axes are a and b, their the period is given by
A) \[{{T}^{2}}\propto {{b}^{3}}\]
B) \[{{T}^{2}}\propto {{\left( \frac{a+b}{2} \right)}^{3}}\]
C) \[{{T}^{2}}\propto {{a}^{3}}\]
D) \[{{T}^{2}}\propto {{\left( \frac{a-b}{2} \right)}^{3}}\]
View Answer play_arrowquestion_answer34) In a capillary tube of which the lower end dips in a liquid, the liquid rises to a height of\[10\text{ }cm\]If a capillary of the same bore is taken, whose length is 5 cm and dipped in liquid, then
A) a fountain of liquid will be obtain
B) the liquid will not rise in the tube at all
C) the liquid will rise upto the top and slowly ooze out of it
D) the liquid will rise to the top and will stay there
View Answer play_arrowquestion_answer35) There relation between Y (Young's modulus), K (bulk modulus) and \[\eta \] (shear modulus) is
A) \[\frac{9}{Y}=\frac{1}{K}+\frac{3}{\eta }\]
B) \[\frac{1}{Y}=\frac{1}{3\lambda }+\frac{1}{9K}\]
C) \[\frac{9}{Y}=\frac{1}{\eta }+\frac{3}{K}\]
D) \[\frac{1}{\eta }=\frac{1}{K}+\frac{1}{Y}\]
View Answer play_arrowquestion_answer36) Solar radiation emitted by sun correspond to that emitted by black body at a temperature of \[6000\text{ }K\]. Maximum intensity is emitted at wavelength of\[4800\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]. If the sun was to cool down from \[6000\text{ }K\]to \[3000\text{ }K,\] then the peak intensity of emitted radiation would occur at a wavelength
A) \[4800\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[9600\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[2400\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[19200\overset{\text{o}}{\mathop{\text{A}}}\,\]
View Answer play_arrowquestion_answer37) An ideal gas heat engine operates in a Carnot cycle between \[{{227}^{o}}C\]and\[{{127}^{o}}C\]. It absorbs \[6\times {{10}^{4}}cal\] at the higher temperature. The amount of heat converted into work is
A) \[4.8\times {{10}^{4}}\text{ }cal\]
B) \[1.2\times {{10}^{4}}\text{ }cal\]
C) \[3.5\times {{10}^{4}}\text{ }cal\]
D) \[1.6\times {{10}^{4}}\text{ }cal\]
View Answer play_arrowquestion_answer38) A certain mass of gas at NTP is expanded to three times its volume under adiabatic conditions. The resulting temperature of gas ,' will be (7 for gas is \[1.40\])
A) \[273\times {{\left( \frac{1}{3} \right)}^{1.4}}\]
B) \[273\times {{(3)}^{0.4}}\]
C) \[273\times {{\left( \frac{1}{3} \right)}^{0.4}}\]
D) \[273\times {{(3)}^{1.4}}\]
View Answer play_arrowquestion_answer39) If for a gas \[\frac{R}{{{C}_{V}}}=0.67,\] this gas is made up of molecules which "are
A) monoatomic
B) diatomic
C) polyatomic
D) mixture of diatomic and polyatomic molecules
View Answer play_arrowquestion_answer40) The velocity of a small ball of mass M and density \[{{d}_{1}}\] when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \[{{d}_{2}},\] the viscous force acting on the ball is
A) \[Mg\left( 1-\frac{{{d}_{2}}}{{{d}_{1}}} \right)\]
B) \[Mg\frac{{{d}_{1}}}{{{d}_{2}}}\]
C) \[Mg({{d}_{1}}-{{d}_{2}})\]
D) \[Mg{{d}_{1}}{{d}_{2}}\]
View Answer play_arrowquestion_answer41) The length of an elastic spring is a meters when a force of \[4\text{ }N\]is applied, and b meters when the \[\text{5 }N\] force is applied. Then the length of the spring when the \[9N\] force is applied is
A) \[a+b\]
B) \[~9b-9a\]
C) \[5b-4a\]
D) \[4a-5b\]
View Answer play_arrowquestion_answer42) Moment of inertia of a uniform 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) \[5I\]
B) \[3I\]
C) \[4I\]
D) \[6I\]
View Answer play_arrowquestion_answer43) The escape velocity of a body from the surface of earth is \[11.2\text{ }km/s\]. It is thrown up with a velocity 4 times this velocity of escape. The velocity of the body when it has escaped the gravitational pull of earth (neglecting presence of all other heavenly bodies) is
A) \[4\times 11.2\text{ }km/s\]
B) \[\sqrt{15}\times 11.2\text{ }km/s\]
C) zero
D) \[3\times 11.2\text{ }km/s\]
View Answer play_arrowquestion_answer44) If a planet of given density were made larger (keeping its density unchanged) its force of attraction for an object on its surface would increase because of increased mass of the planet but would decrease because of larger separation between the centre of the planet and its surface. Which effect would dominate?
A) Increase in mass
B) Increase in radius
C) Both affect the attraction equally
D) None of the above
View Answer play_arrowquestion_answer45) Two balls each of mass m are placed on the vertices A and B of an equilateral triangle ABC of side\[1\text{ }m\]. A ball of mass \[2m\] is placed at vertex C. The centre of mass of this system from vertex A (located at origin) is
A) \[\left( \frac{1}{2}m,\,\frac{1}{2}m \right)\]
B) \[\left( \frac{1}{2}m,\sqrt{3}m \right)\]
C) \[\left( \frac{1}{2}m,\frac{\sqrt{3}}{4}m \right)\]
D) \[\left( \frac{\sqrt{3}}{4}m,\frac{\sqrt{3}}{4}m \right)\]
View Answer play_arrowquestion_answer46) A particle moves along the x-axis from \[x={{x}_{1}}\] to \[x={{x}_{2}}\] under the action of a force given by\[F=2\text{ }x\]. Then the work done in the process is
A) zero
B) \[{{x}_{2}}^{2}-{{x}_{1}}^{2}\]
C) \[2{{x}_{2}}({{x}_{2}}-{{x}_{1}})\]
D) \[2{{x}_{1}}({{x}_{1}}-{{x}_{2}})\]
View Answer play_arrowquestion_answer47) A body of mass 5 kg strikes another body of mass \[2.5\text{ }kg\]initially at rest. The bodies after collision coalesce and begin to move as whole with a kinetic energy of\[5\text{ }J\]. The kinetic energy of the first body before collision is
A) \[7.5\text{ }J\]
B) \[5\text{ }J\]
C) \[2.5\text{ }J\]
D) \[10\text{ }J\]
View Answer play_arrowquestion_answer48) For traffic moving at \[60\text{ }km/h\]along a circular track of radius \[0.1\text{ }km,\]the correct angle of banking is
A) \[{{\tan }^{-1}}\left( \frac{{{60}^{2}}}{0.1} \right)\]
B) \[{{\tan }^{-1}}\left( \frac{{{(50/3)}^{2}}}{100\times 9.8} \right)\]
C) \[{{\tan }^{-1}}{{(60\times 0.1\times 9.8)}^{1/2}}\]
D) \[{{\tan }^{-1}}\left( \frac{100\times 9.8}{{{(50/3)}^{2}}} \right)\]
View Answer play_arrowquestion_answer49) Two projectiles are fired at different angles with the same magnitude of velocity, such that they have the same range. At what angles they might have been projected?
A) \[{{25}^{o}}\] and \[{{65}^{o}}\]
B) \[{{35}^{o}}\] and \[{{75}^{o}}\]
C) \[{{10}^{o}}\] and \[{{50}^{o}}\]
D) None of these
View Answer play_arrowquestion_answer50) If two non-zero vectors obey the relation \[|\vec{P}+\vec{Q}|=|\vec{P}-\vec{Q}|\].then the angle between the vectors \[\vec{P},\] \[\vec{Q}\] is
A) \[{{0}^{o}}\]
B) \[\pi \]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{2}\]
View Answer play_arrowquestion_answer51) A weightless spring which has a force constant k oscillates with a frequency r% when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2m is attached to one of the halves. The frequency of oscillation will not become
A) \[\sqrt{2n}\]
B) \[\frac{n}{\sqrt{2}}\]
C) \[2n\]
D) \[n\]
View Answer play_arrowquestion_answer52) A particle moves so that its acceleration a is given by \[a=-bx,\] where x is displacement from equilibrium position and b is a non-negative real constant. The time period of oscillation of the particle is
A) \[2\pi \sqrt{b}\]
B) \[\frac{2\pi }{b}\]
C) \[\frac{2\pi }{\sqrt{b}}\]
D) \[2\frac{\pi }{\sqrt{b}}\]
View Answer play_arrowquestion_answer53) A tuning fork of frequency \[500\text{ }cycles/s\]is sounded on a resonance tube. The first and second resonance is obtained at \[17\text{ }cm\]and\[52\text{ }cm\]. The velocity of sound in m/s is
A) \[175\]
B) \[350\]
C) \[525\]
D) \[700\]
View Answer play_arrowquestion_answer54) Which of the following characteristics does not change due to the damping of simple harmonic motion?
A) Angular frequency
B) Time period
C) Initial phase
D) Amplitude
View Answer play_arrowquestion_answer55) A hollow charged metal sphere has a radius r. If the potential difference between its surface and a point at a distance \[3\text{ }r\]from the centre is V, then electrical intensity at distance \[3\text{ }r\]from the centre is
A) \[\frac{V}{2r}\]
B) \[\frac{V}{3r}\]
C) \[\frac{V}{4r}\]
D) \[\frac{V}{6r}\]
View Answer play_arrowquestion_answer56) Current is flowing with a current density \[J=480\,A/c{{m}^{2}}\]in a copper wire. Assuming that each copper atom contributes one free electron and given that Avogadro number \[=6.0\times {{10}^{23}}\text{ }atoms/mol\] Density of copper \[=9.0\text{ }g/c{{m}^{3}}\] Atomic weight of copper \[=64\text{ }g/mol\] Electronic charge \[=1.6\times {{10}^{-19}}C\] The drift velocity of electrons is
A) \[1\text{ }mm/s\]
B) \[\text{2 }mm/s\]
C) \[0.5\text{ }mm/s\]
D) \[0.36\text{ }mm/s\]
View Answer play_arrowquestion_answer57) A tap supplies water at \[{{20}^{o}}C\]. A man takes \[1\text{ }L\]of water per minute at \[{{35}^{o}}C\]from a geyser connected to the tap. The power of geyser is
A) \[1050\text{ }W\]
B) \[2100\text{ }W\]
C) \[1500\text{ }W\]
D) \[3000\text{ }W\]
View Answer play_arrowquestion_answer58) A charge is fired through a magnetic field. The force acting on the charge is maximum when the angle between the direction of motion of charge and the magnetic field is
A) zero
B) \[\frac{\pi }{4}\]
C) \[\pi \]
D) \[\frac{\pi }{2}\]
View Answer play_arrowquestion_answer59) At a place the angle of dip is \[{{30}^{o}}\]. If the horizontal component of earth's magnetic field is H, then the total field intensity is
A) \[\frac{H}{2}\]
B) \[\frac{2H}{\sqrt{3}}\]
C) \[H\sqrt{2}\]
D) \[H\sqrt{3}\]
View Answer play_arrowquestion_answer60) A particle is vibrating in simple harmonic motion with an amplitude of\[4\text{ }cm\]. At what displacement from the equilibrium position is its energy half potential and half-kinetic?
A) \[2\sqrt{2}cm\]
B) \[\sqrt{2}cm\]
C) \[2\,cm\]
D) \[1\,cm\]
View Answer play_arrowquestion_answer61) A tuning fork of frequency \[480\text{ }Hz\]produces 10 beats/s, when sounded with a sonometer string. A slight increase in tension in the sonometer string produces fewer beats/s than before. What was the frequency of sonometer string?
A) \[470\text{ }Hz\]
B) \[490\text{ }Hz\]
C) \[480\text{ }Hz\]
D) \[460\text{ }Hz\]
View Answer play_arrowquestion_answer62) A hollow metal sphere of radius \[5\text{ }cm\]is charged such that potential at its surface is\[10\text{ }V\]. The potential at the centre of the sphere is
A) zero volt
B) \[10\text{ }V\]
C) same as at point \[5\text{ }cm\]away from the surface
D) same as at point \[\text{10 }cm\] away from the surface
View Answer play_arrowquestion_answer63) An electric dipole consisting of two opposite charges of \[2\times {{10}^{-6}}\text{ }C\]each, separated by a distance of \[3\text{ }cm\]is placed in an electric field of \[2\times {{10}^{5}}\text{ }N/C\]. The maximum torque on the dipole is
A) \[12\times {{10}^{-1}}\text{ }Nm\]
B) \[12\times {{10}^{-3}}\text{ }Nm\]
C) \[24\times {{10}^{-1}}Nm\]
D) \[24\times {{10}^{-3}}\text{ }Nm\]
View Answer play_arrowquestion_answer64) A given piece of wire of length I and radius r is having a resistance R. This wire is stretched uniformly to a wire of radius \[\frac{r}{2}\]. What is the new resistance?
A) \[4R\]
B) \[8R\]
C) \[16R\]
D) \[2R\]
View Answer play_arrowquestion_answer65) Two .thin long parallel wires separated by a distance b are carrying current i ampere each. The magnitude of the force per unit length exerted by one wire on the other is
A) \[\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}^{2}}}{b}\]
B) \[\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}^{2}}}{{{b}^{2}}}\]
C) \[\frac{{{\mu }_{0}}}{2\pi }\frac{i}{b}\]
D) \[\frac{{{\mu }_{0}}}{2\pi }\frac{i}{{{b}^{2}}}\]
View Answer play_arrowquestion_answer66) To increase the range of a voltmeter, we need to connect a suitable
A) high resistance in parallel
B) high resistance in series
C) low resistance in series
D) low resistance in parallel
View Answer play_arrowquestion_answer67) Two wires made up of the same material are of equal lengths but their radii are in the ratio of\[1:2\]. On stretching each of these two strings by the same tension, the ratio between the fundamental frequencies is
A) \[1:4\]
B) 4 : 1
C) \[2:1\]
D) \[1:2\]
View Answer play_arrowquestion_answer68) An object producing a pitch of \[400\text{ }Hz\]flies past a stationary person. The object was moving in a straight line with a velocity 200 m/s. The velocity of sound is 300 m/s. What is the change in frequency noted by the person as the object flies past him?
A) \[1440\text{ }Hz\]
B) \[240\text{ }Hz\]
C) \[1200\text{ }Hz\]
D) \[960\text{ }Hz\]
View Answer play_arrowquestion_answer69) Four capacitors each of \[1\mu F\] are connected as shown. The equivalent capacitance between P and Q is
A) \[4\mu F\]
B) \[\frac{1}{4}\mu F\]
C) \[\frac{3}{4}\mu F\]
D) \[\frac{4}{3}\mu F\]
View Answer play_arrowquestion_answer70) The magnitude of electric field at distance r from an infinitely thin rod having a linear charge density \[\lambda ,\]is (use Gauss's law)
A) \[E=\frac{\lambda }{2\pi {{\varepsilon }_{0}}r}\]
B) \[E=\frac{2\lambda }{\pi {{\varepsilon }_{0}}r}\]
C) \[E=\frac{2\lambda }{4\pi {{\varepsilon }_{0}}r}\]
D) \[E=\frac{4\lambda }{\pi {{\varepsilon }_{0}}r}\]
View Answer play_arrowquestion_answer71) A \[200\text{ }W\]and a \[100\text{ }W\]bulb, both. meant for operation at \[220\text{ }V\]are connected in series. When connected to a \[220\text{ }V\] supply the power consumed by the, combination is
A) \[33.3\text{ }W\]
B) \[66.7\text{ }W\]
C) \[300W\]
D) \[100W\]
View Answer play_arrowquestion_answer72) The sensitivity of a moving coil galvanometer depends on
A) angle of deflection -
B) earth's magnetic field
C) torsional constant of the spring
D) None of the above
View Answer play_arrowquestion_answer73) Domain formation is the necessary feature of
A) diamagnetic substances
B) paramagnetic substances
C) ferromagnetic substances
D) All of the above
View Answer play_arrowquestion_answer74) In a charged capacitor the energy stored in
A) the positive charges
B) the negative charges
C) the field between the plates
D) None of the above
View Answer play_arrowquestion_answer75) For a given temperature difference which of the following pairs will generate maximum thermo-emf?
A) lead-nickel
B) copper-iron
C) gold-silver
D) antimony-bismuth
View Answer play_arrowquestion_answer76) The electrons identified by quantum numbers:
(I) \[n=4,l=1\] |
(II) \[n=4,l=0\] |
(III) \[n=3,l=2\] |
(IV) \[n=2,l=1\] |
A) \[(IV)<(II)<(III)<(I)\]
B) \[(II)<(IV)<(I)<(III)\]
C) \[(I)<(III)<(II)<(IV)\]
D) \[(III)<(I)<(IV)<(II)\]
View Answer play_arrowquestion_answer77) Ground state electronic configuration of nitrogen atom can be represented as
A)
B)
C)
D)
View Answer play_arrowquestion_answer78) The first emission line in the electronic spectrum of hydrogen in the Balmer series appears at\[c{{m}^{-1}}\]
A) \[\frac{9R}{400}c{{m}^{-1}}\]
B) \[\frac{7R}{144}c{{m}^{-1}}\]
C) \[\frac{3R}{4}c{{m}^{-1}}\]
D) \[\frac{5R}{36}c{{m}^{-1}}\]
View Answer play_arrowquestion_answer79) \[\text{KMn}{{\text{O}}_{\text{4}}}\]reacts with oxalic acid according to the equation \[2MnO_{4}^{-}+5{{C}_{2}}O_{4}^{2-}+16{{H}^{+}}\xrightarrow{{}}2M{{n}^{2+}}\]\[+\,10C{{O}_{2}}+8{{H}_{2}}O\] Here, 20 mL of \[\text{0}\text{.1}\,\text{M}\,\text{KMn}{{\text{O}}_{\text{4}}}\] is equivalent to
A) \[\text{20 mL}\]of \[\text{0}\text{.5}\,\text{M }{{\text{H}}_{\text{2}}}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}}\]
B) \[\text{50}\,\text{mL}\]of \[\text{0}\text{.1}\,\text{M}\,{{\text{H}}_{\text{2}}}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}}\]
C) \[\text{ }\!\!~\!\!\text{ 50 mL}\]of \[\text{0}\text{.01}\,\text{M}\,{{\text{H}}_{2}}{{C}_{2}}{{O}_{4}}\]
D) \[\text{20}\,\text{mL}\]of \[\text{0}\text{.1 M}\,{{\text{H}}_{\text{2}}}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}}\]
View Answer play_arrowquestion_answer80) Half-life of a sample is 160 days. After 800 days, 1 g of the sample shall be reduced to
A) \[\frac{1}{2}g\]
B) \[\frac{1}{5}g\]
C) \[\frac{1}{4}g\]
D) \[\frac{1}{32}g\]
View Answer play_arrowquestion_answer81) Radio-carbon dating was discovered by
A) GN Lewis
B) J Williard Gibbs
C) WF Libby
D) W Nernst
View Answer play_arrowquestion_answer82) An aqueous solution of 6.3 g oxalic acid dihydrate is made up to 250 mL. The volume of N sodium hydroxide required to completely neutralise 10 mL of this solution is
A) 40 mL
B) 20 mL
C) 10 mL
D) 4 mL
View Answer play_arrowquestion_answer83) How will increase of pressure affect the equation? \[C(s)+{{H}_{2}}O(g)CO(g)+{{H}_{2}}(g)\]
A) Shift in the forward direction
B) Shift in the reverse direction
C) Increase in the yield of hydrogen
D) No effect
View Answer play_arrowquestion_answer84) For which of the following reactions,\[{{K}_{p}}={{K}_{c}}?\]
A) \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}\]
B) \[{{N}_{2}}+{{O}_{2}}2NO\]
C) \[PC{{l}_{5}}PC{{l}_{3}}+C{{l}_{2}}\]
D) \[2S{{O}_{3}}2S{{O}_{2}}+{{O}_{2}}\]
View Answer play_arrowquestion_answer85) Which of the following salts is most soluble?
A) \[B{{i}_{2}}{{S}_{3}}({{K}_{sp}}=1\times {{10}^{-17}})\]
B) \[MnS({{K}_{sp}}=7\times {{10}^{-16}})\]
C) \[CuS({{K}_{sp}}=8\times {{10}^{-37}})\]
D) \[A{{g}_{2}}S({{K}_{sp}}=6\times {{10}^{-51}})\]
View Answer play_arrowquestion_answer86) Ostwald dilution law is applicable to
A) strong electrolytes only
B) weak electrolytes only
C) non-electrolytes only
D) strong as well as weak electrolytes
View Answer play_arrowquestion_answer87) In the reaction \[2A+B\xrightarrow{{}}{{A}_{2}}B,\] if the concentration of A is doubled and that of B is halved, then the rate of reaction will
A) increase by 4 times
B) decrease by 2 times
C) increase by 2 times
D) remains the same
View Answer play_arrowquestion_answer88) The Arrhenius equation expressing the effect of temperature on the rate constant of a reaction is
A) \[k={{e}^{-E/RT}}\]
B) \[k=\ln \frac{E}{RT}\]
C) \[k=\frac{A.E}{RT}\]
D) \[k=A.{{e}^{-{{E}_{a}}/RT}}\]
View Answer play_arrowquestion_answer89) If the half-time for a particular reaction is found to be constant and independent of the initial concentration of the reactants, then the reaction is of
A) first order
B) zero order
C) second order
D) none of these
View Answer play_arrowquestion_answer90) Normality of \[\text{2}\,\text{M}{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\] is
A) \[\text{2N}\]
B) \[\text{4}\,\text{N}\]
C) \[\frac{N}{2}\]
D) \[\frac{N}{4}\]
View Answer play_arrowquestion_answer91) Which of the following is a non-colligative property?
A) Elevation in boiling point
B) Osmotic pressure
C) Optical activity
D) Depression in freezing point
View Answer play_arrowquestion_answer92) The freezing point of equimolal aqueous solution will be highest for
A) \[{{C}_{6}}{{H}_{5}}N{{H}_{3}}Cl\]
B) \[La{{(N{{O}_{3}})}_{3}}\]
C) glucose
D) \[Ca{{(N{{O}_{3}})}_{2}}\]
View Answer play_arrowquestion_answer93) The van't Hoff factor for \[\text{0}\text{.1}\,\text{M}\,\text{Ba(N}{{\text{O}}_{\text{3}}}{{\text{)}}_{\text{2}}}\] solution is 2.74. The degree of dissociation is
A) 91.3%
B) 87%
C) 100%
D) 74%
View Answer play_arrowquestion_answer94) The enthalpy of vaporisation of liquid water using the data \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l)\] \[\Delta H=-285.77\,kJ/mol\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(g);\] \[\Delta H=-241.84\,kJ/mol\]is
A) \[+\,43.93\,kJ/mol\]
B) \[-43.93\,kJ/mol\]
C) \[527.61\,kJ/mol\]
D) \[-527.61\,kJ/mol\]
View Answer play_arrowquestion_answer95) The enthalpy change for the transition of liquid water to steam is \[40.8\,kJ\,mo{{l}^{-1}}\]at \[373\,K.\] Calculate the entropy of vaporisation of water.
A) \[109.4\,J{{K}^{-1}}\,mo{{l}^{-1}}\]
B) \[-109.4\,J{{K}^{-1}}\,mo{{l}^{-1}}\]
C) \[218.8\,J{{K}^{-1}}\,mo{{l}^{-1}}\]
D) \[-218.8\,J{{K}^{-1}}\,mo{{l}^{-1}}\]
View Answer play_arrowquestion_answer96) The occurrence of the reaction is impossible if
A) \[\Delta H\] is\[+\,ve;\Delta S\] is also \[+\,ve\]
B) \[\Delta H\]is\[~-ve;\text{ }\Delta S\] is also \[-ve\]
C) \[\Delta H\]is \[-ve;\Delta \,S\]is \[+\,ve\]
D) \[\Delta H\] is \[+\,ve;\Delta S\]is \[-ve\]
View Answer play_arrowquestion_answer97) The bond energy of an\[O-H\] bond is 109 kcal/mol. When a mole of water is formed, then
A) 109 kcal is released
B) 218 kcal is absorbed
C) 109 kcal is absorbed
D) 218 kcal is released
View Answer play_arrowquestion_answer98) Of the following reaction, only one is a redox reaction. Identify this reaction.
A) \[Ca{{(OH)}_{2}}+2HCl\xrightarrow{{}}CaC{{l}_{2}}+2{{H}_{2}}O\]
B) \[2{{S}_{2}}O_{7}^{2-}+2{{H}_{2}}O\xrightarrow{{}}2SO_{4}^{2-}+4{{H}^{+}}\]
C) \[BaC{{l}_{2}}+MgS{{O}_{4}}\xrightarrow{{}}BaS{{O}_{4}}+MgC{{l}_{2}}\]
D) \[C{{u}_{2}}S+2FeO\xrightarrow{{}}2Cu+2Fe+S{{O}_{2}}\]
View Answer play_arrowquestion_answer99) Oxidation number of nitrogen is highest in
A) \[{{N}_{3}}H\]
B) \[{{N}_{2}}{{O}_{4}}\]
C) \[N{{H}_{2}}OH\]
D) \[N{{H}_{3}}\]
View Answer play_arrowquestion_answer100) Correct order of first ionization potential among the following elements Be, B, C, N, O is
A) \[B<Be<C<O<N\]
B) \[B<Be<C<N<O\]
C) \[~Be<B<C<N<\text{O}\]
D) \[~Be<B<C<O<N\]
View Answer play_arrowquestion_answer101) The unit of equivalent conductivity is
A) ohm cm
B) \[~oh{{m}^{-1}}c{{m}^{2}}\text{ }g\text{ }equi{{v}^{-1}}\]
C) \[oh{{m}^{-2}}c{{m}^{-2}}\text{ }g\text{ }equiv\]
D) \[oh{{m}^{-2}}c{{m}^{-2}}g\,equiv\]
View Answer play_arrowquestion_answer102) In which of the following crystals of ionic compounds would you expect maximum distance between the centres of cations and anions?
A) \[\text{ }\!\!~\!\!\text{ LiF}\]
B) \[\text{CsF}\]
C) \[CsI\]
D) \[LiI\]
View Answer play_arrowquestion_answer103) 50 mL of hydrogen diffuses through small hole from a vessel in 20 min time. Time taken for 40 mL of oxygen to diffuse out under similar conditions will be
A) 12 min
B) 32 min
C) 8 min
D) 64 min
View Answer play_arrowquestion_answer104) A gas will approach ideal behaviour at
A) low temperature and high pressure
B) low temperature and low pressure
C) high temperature and low pressure
D) high temperature and high pressure
View Answer play_arrowquestion_answer105) A colloidal system in which gas bubbles are dispersed in a liquid is known as
A) foam
B) aerosol
C) sol
D) emulsion
View Answer play_arrowquestion_answer106) In which of the following, Tyndall effect is not observed?
A) Smoke
B) Emulsions
C) Sugar solution
D) Gold sol
View Answer play_arrowquestion_answer107) Which is not correct regarding the adsorption of a gas on surface of a solid?
A) Enthalpy and entropy change is negative
B) Adsorption is more for some specific substance
C) On increasing temperature, adsorption increases progressively
D) It is a reversible reaction
View Answer play_arrowquestion_answer108) The ionic radii of isoelectronic species\[{{N}^{3-}},{{O}^{2-}}\]and \[{{F}^{-}}\]are in the order
A) 1.36, 1.40, 1.71
B) 1.36, 1.71, 1.40
C) 1.71, 1.40, 1.36
D) 1.71, 1.36, 1.40
View Answer play_arrowquestion_answer109) Which of the following element is most electropositive?
A) Al
B) Mg
C) P
D) S
View Answer play_arrowquestion_answer110) The compound in which carbon atom uses only \[s{{p}^{3}}-\]hybrid orbitals for bond formation is
A) \[HCOOH\]
B) \[N{{H}_{2}}CON{{H}_{2}}\]
C) \[{{(C{{H}_{3}})}_{3}}COH\]
D) \[C{{H}_{3}}CHO\]
View Answer play_arrowquestion_answer111) The only molecule having dipole moment is
A) 2,2-dimethylpropane
B) trans-2-pentene
C) trans-3-hexene
D) 2,2,3,3-tetramethylbutane
View Answer play_arrowquestion_answer112) \[{{N}_{2}}\]and\[{{O}_{2}}\]are converted into\[N_{2}^{+}\]and \[O_{2}^{+}\]respectively. Which of the following is .not correct?
A) In \[{{N}_{2}}^{+},\]the N?N bond weakens
B) In \[O_{2}^{+},O-O\] bond order increases
C) ln \[{{O}_{2}}^{+},\] paramagnetism decreases
D) \[{{\text{N}}_{\text{2}}}^{\text{+}}\]becomes diamagnetic
View Answer play_arrowquestion_answer113) The hybridisation of carbon atoms in C?C single bond of\[HC\equiv C-CH=C{{H}_{2}}\]is
A) \[s{{p}^{3}}-s{{p}^{3}}\]
B) \[s{{p}^{2}}-s{{p}^{2}}\]
C) \[sp-s{{p}^{2}}\]
D) \[s{{p}^{3}}-sp\]
View Answer play_arrowquestion_answer114) Chemical A is used for water softening to remove temporary hardness. A reacts with sodium carbonate to generate caustic soda. When\[\text{C}{{\text{O}}_{\text{2}}}\] is bubbled through A, it turns cloudy. What is A?
A) \[\text{CaC}{{\text{O}}_{3}}\]
B) \[CaO\]
C) \[Ca{{(OH)}_{2}}\]
D) \[Ca{{(HC{{O}_{3}})}_{3}}\]
View Answer play_arrowquestion_answer115) Which of the following pentafluorides can't be formed?
A) \[P{{F}_{5}}\]
B) \[As{{F}_{5}}\]
C) \[Sb{{F}_{5}}\]
D) \[Bi{{F}_{5}}\]
View Answer play_arrowquestion_answer116) The correct order of increasing oxidising power is
A) \[~{{F}_{2}}<C{{l}_{2}}<{{I}_{2}}>B{{r}_{2}}\]
B) \[~{{F}_{2}}<B{{r}_{2}}<C{{l}_{2}}<{{I}_{2}}\]
C) \[~C{{l}_{2}}<B{{r}_{2}}<{{F}_{2}}<{{I}_{2}}\]
D) \[{{I}_{2}}<B{{r}_{2}}<C{{l}_{2}}<{{F}_{2}}\]
View Answer play_arrowquestion_answer117) Amongst \[TiF_{6}^{2-},CoF_{6}^{3-},C{{u}_{2}}C{{l}_{2}}\]and \[NiCl_{4}^{2-}\]at. no.\[Ti=22,Co=27,Cu=29,Ni=28\]). The. colourless species are
A) \[CoF_{6}^{3-}\]and \[NiCl_{4}^{2-}\]
B) \[TiF_{6}^{2-}\]and \[CoF_{6}^{3-}\]
C) \[C{{u}_{2}}C{{l}_{2}}\] and \[NiCl_{4}^{2-}\]
D) \[TiF_{6}^{2-}\] and \[C{{u}_{2}}C{{l}_{2}}\]
View Answer play_arrowquestion_answer118) The number of S?S bonds in sulphur trioxide is
A) three
B) two
C) one
D) zero
View Answer play_arrowquestion_answer119) Choose the correct statement.
A) Transition elements have low melting point
B) Transition elements do not have catalytic activity
C) Transition elements exhibit variable oxidation states
D) Transition elements show inert pair effect
View Answer play_arrowquestion_answer120) Two of the constituents of German silver are
A) \[Ag+Cu\]
B) \[Ag+Zn\]
C) \[Cu+Zn\]
D) \[Cu+Sn\]
View Answer play_arrowquestion_answer121) Aufbau principle does not Jgrve the correct arrangement of filling Up T of atomic orbitals in
A) Cu and Zn
B) Co and Zn
C) Mn and Cr
D) Cu and Cr
View Answer play_arrowquestion_answer122) Which of the following compounds exhibit linkage isomerism?
A) \[[Co{{(en)}_{3}}]C{{l}_{3}}\]
B) \[[Co{{(en)}_{3}}]C{{l}_{3}}\]
C) \[[Co{{(en)}_{2}}N{{O}_{2}}Cl]Br\]
D) \[[Co{{(N{{H}_{3}})}_{5}}Cl]B{{r}_{2}}\]
View Answer play_arrowquestion_answer123) IUPAC name of\[[Pt{{(N{{H}_{3}})}_{3}}Br(N{{O}_{2}})Cl]Cl\]
A) triamminechlorobromonitro platinum (IV) chloride
B) triamminebromonitrochloro platinum (IV) chloride
C) triamminebromochloronitro platinum (IV) chloride
D) triamminenitrochlorobromo platinum (IV)chloride
View Answer play_arrowquestion_answer124) According to postulates ofWemefs theory for coordination compounds, which of the following is true?
A) Primary valencies are ionisable
B) Secondary valencies are ionisable
C) Only primary valencies are non-ionizable
D) Primary and secondary valencies are non- ionisable
View Answer play_arrowquestion_answer125) Ferrocene is an example of
A) sand-wiched complex
B) pi-bonded complex
C) a complex in which all the five carbon atoms of cyclopentadiene anion are bonded to the metal
D) all of the above
View Answer play_arrowquestion_answer126) Which form of iron is least ductile?
A) Hard steel
B) Cast iron
C) Mild steel
D) Wrought steel
View Answer play_arrowquestion_answer127) Which of the following is known as Lunar caustic when in the fused state?
A) Silver nitrate
B) Silver sulphate
C) Silver chloride
D) Sodium sulphate
View Answer play_arrowquestion_answer128) One of the following metals is obtained by leaching its ore with dilute cyanide solution. Identify it.
A) Titanium
B) Vanadium
C) Silver
D) Zinc
View Answer play_arrowquestion_answer129) Which of the following species could be expected to exhibit aromatic character? Select the correct answer from the following
A) I and IV
B) II and IV
C) I and III
D) II and III
View Answer play_arrowquestion_answer130) The correct IUPAC name of the following compound is \[C{{H}_{3}}C{{H}_{2}}\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-C=\underset{{{C}_{2}}{{H}_{5}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-\underset{{{C}_{2}}{{H}_{5}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,HC{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\]
A) 5, 6-dimethyl-8-methyl dec-6-ene
B) 6-butyl-5-ethyl-3-methyl oct-4-ene
C) 5, 6-diethyl-3-methyl dec-4-ene
D) 2, 4, 5-triethyl non-3-ene
View Answer play_arrowquestion_answer131) The kind of delocalisation involving sigma bond is called
A) inductive effect
B) hyperconjugation effect
C) electromeric effect
D) mesomeric effect
View Answer play_arrowquestion_answer132) Which of the following compounds react with HBr obeying Markownikoff?s rule?
A) \[C{{H}_{2}}=C{{H}_{2}}\]
B)
C)
D)
View Answer play_arrowquestion_answer133) How many cyclic isomers of \[{{\text{C}}_{\text{5}}}{{\text{H}}_{\text{10}}}\]are possible?
A) Four
B) Three
C) Two
D) Six
View Answer play_arrowquestion_answer134) The (R) and (S) enantiomers of an optically active compound differ in
A) their reactivity
B) their optical rotation of plane polarized light
C) their melting point
D) their solubility in achiral reagents
View Answer play_arrowquestion_answer135) Which of the following organic compounds exhibit acidic character?
A) \[{{H}_{3}}C-C\equiv CH\]
B) \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\]
C) \[{{H}_{2}}C=C{{H}_{2}}\]
D) \[{{H}_{3}}C-C{{H}_{3}}\]
View Answer play_arrowquestion_answer136) Methane is produced by the hydrolysis of
A) \[A{{l}_{4}}{{C}_{3}}\]
B) \[Ca{{C}_{2}}\]
C) Dry ice
D) \[n-{{C}_{3}}{{H}_{7}}MgBr\]
View Answer play_arrowquestion_answer137) In the reaction of phenol with chloroform and aqueous solution of\[\text{NaOH}\]at \[\text{70}{{\,}^{o}}C,\] the electrophile attacking the ring is
A) \[CHC{{l}_{3}}\]
B) \[CHC{{l}_{2}}\]
C) \[_{.}^{.}CC{{l}_{2}}\]
D) \[COC{{l}_{2}}\]
View Answer play_arrowquestion_answer138) Which of the following compounds can exist in optically active form?
A) 1-butanol
B) 2-butanol
C) 3-pentanol
D) 4-heptanol
View Answer play_arrowquestion_answer139) Chloroform is slowly oxidised by air in the presence of light and air to form
A) formyl chloride
B) trichloro methanol
C) phosgene
D) formaldehyde
View Answer play_arrowquestion_answer140) Chlorination of toluene in the presence of light and heat followed by treatment with aqueous NaOH solution gives
A) o-cresol
B) p-cresol
C) benzoic acid
D) 2, 4-dihydroxytoluene
View Answer play_arrowquestion_answer141) Formation of cyanohydrin from the reaction of acetone with HCN is called
A) electrophilic addition
B) nucleophilic addition
C) electrophilic substitution
D) nucleophilic substitution
View Answer play_arrowquestion_answer142) In the following reaction, \[C{{H}_{3}}COCl\frac{BaS{{O}_{4}}}{Pd/{{H}_{2}}}X\] Identify X out of the following
A) acetaidehyde
B) propionaldehyde
C) acetone
D) acetic anhydride
View Answer play_arrowquestion_answer143) Reaction of t-butyl bromide with sodium methoxide produces
A) isobutane
B) isobutylene
C) sodium-t-butoxide
D) t-butylmethylether
View Answer play_arrowquestion_answer144) The acid which does not contain \[-\text{COOH}\] group is
A) ethanoic acid
B) picric acid
C) lactic acid
D) palmitic acid
View Answer play_arrowquestion_answer145) The decreasing order of basic character of the three amines and ammonia is
A) \[N{{H}_{3}}>C{{H}_{3}}N{{H}_{2}}>{{C}_{2}}{{H}_{5}}N{{H}_{2}}>{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]
B) \[{{C}_{2}}{{H}_{5}}N{{H}_{2}}>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}>{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]
C) \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}>{{C}_{2}}{{H}_{5}}N{{H}_{2}}>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}\]
D) \[C{{H}_{3}}N{{H}_{2}}>{{C}_{2}}{{H}_{5}}N{{H}_{2}}>{{C}_{6}}{{H}_{5}}N{{H}_{2}}>N{{H}_{3}}\]
View Answer play_arrowquestion_answer146) Aniline is treated with a mixture of sodium nitrite and hypophosphorus acid, the product formed is
A) aniline diazonium hypophosphate
B) benzene
C) anilinium hypophosphite
D) aniline diazonium hypophosphite
View Answer play_arrowquestion_answer147) Nitrosoamines \[({{R}_{2}}N-N=O)\] are soluble in water. On heating them with cone \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{,}\]they give secondary amines. The reaction is called
A) Perkin's reaction
B) Fries reaction
C) Libermann nitroso reaction
D) Etard reaction
View Answer play_arrowquestion_answer148) The compound obtained by heating a mixture of\[{{\text{1}}^{\text{o}}}\]amine and chloroform with ethanolic potassium hydroxide is
A) an alkyl isocyanide
B) an alkyl isothiocyanate
C) an amide
D) an amide and nitro compound
View Answer play_arrowquestion_answer149) Which of the following is not an amino acid?
A) Glycine
B) Alanine
C) Histidine
D) Benzidine
View Answer play_arrowquestion_answer150) Which of the following is a fat soluble vitamin?
A) Vitamin A
B) Riboflavin
C) Pyridoxin
D) Thiamine
View Answer play_arrowquestion_answer151) \[\int_{0}^{1}{{{\cot }^{-1}}(1-x+{{x}^{2}})dx}\] is equal to
A) \[\pi -\log 2\]
B) \[\pi +\log 2\]
C) \[\frac{\pi }{2}+\log 2\]
D) \[\frac{\pi }{2}-\log 2\]
View Answer play_arrowquestion_answer152) \[\int_{0}^{1}{\log \,\left\{ \sin \left( \frac{\pi \,\,x}{2} \right) \right\}}\,\,dx\] is equal to
A) \[-\frac{\pi }{2}\log \,2\]
B) \[-\,\log \,\,\,2\]
C) \[-\frac{\pi }{2}\,\log \,2\]
D) \[\frac{\pi }{2}\,\log \,2\]
View Answer play_arrowquestion_answer153) The value of \[2\cos \frac{\pi }{13}.\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}\] is
A) \[-1\]
B) \[0\]
C) \[1\]
D) None of these
View Answer play_arrowquestion_answer154) In a triangle ABC, \[a=5,\] \[b=4\] and \[\cos (A+B)=\frac{31}{32}\] In this triangle, c is equal to
A) \[\sqrt{6}\]
B) \[36\]
C) \[6\]
D) None of these
View Answer play_arrowquestion_answer155) The locus of the centre of a circle of radius 2 which rolls on the outside of the circle \[{{x}^{2}}+{{y}^{2}}+3x-6y-9=0\]is
A) \[{{x}^{2}}+{{y}^{2}}+3x-6y+5=0\]
B) \[{{x}^{2}}+{{y}^{2}}+3x-6y-31=0\]
C) \[{{x}^{2}}+{{y}^{2}}+3x-6y+\frac{29}{4}=0\]
D) None of these
View Answer play_arrowquestion_answer156) \[\int{x|x|\,dx}\] is
A) \[\frac{{{x}^{2}}}{3}\]
B) \[-\frac{{{x}^{2}}}{3}\]
C) \[\frac{{{x}^{2}}|x|}{3}\]
D) None of these
View Answer play_arrowquestion_answer157) The solution set of the equation \[\sqrt{3{{x}^{2}}-7x-30}-\sqrt{2{{x}^{2}}-7x-5}=x-5\] is
A) \[\{6\}\]
B) \[\left\{ 6,-\frac{5}{2} \right\}\]
C) \[\{5,6\}\]
D) \[\left\{ 5,\frac{7}{2} \right\}\]
View Answer play_arrowquestion_answer158) If one root of the equation \[{{x}^{2}}+px+q=0\]is \[2+\sqrt{3},\] then the value of p and q are
A) \[-4,1\]
B) \[4,-1\]
C) \[2,\,\,\,\sqrt{3}\]
D) \[-2,-\,\,\,\sqrt{3}\]
View Answer play_arrowquestion_answer159) In an AP the sum of any two terms, such that the distance of one of them from the beginning is same as that of the other from the end, is
A) first term
B) sum of first and last terms
C) last term
D) half of the sum of the series
View Answer play_arrowquestion_answer160) If \[x,\,2x+2,\,\,3x+3,.....\] are in GP, then the fourth term is
A) \[27.5\]
B) \[4x+5\]
C) \[-13.5\]
D) \[4x+4\]
View Answer play_arrowquestion_answer161) The third term of a GP is 4. The product of its first five terms is
A) \[{{4}^{5/2}}\]
B) \[{{4}^{5}}\]
C) \[{{4}^{3}}\]
D) None of these
View Answer play_arrowquestion_answer162) The number of terms in the expansion of \[{{[{{(a+4b)}^{3}}{{(-4b+a)}^{3}}]}^{2}}\]are
A) \[6\]
B) \[7\]
C) \[8\]
D) \[18\]
View Answer play_arrowquestion_answer163) The coefficient of \[{{x}^{4}}\] in \[{{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}\]is
A) \[\frac{405}{256}\]
B) \[\frac{504}{259}\]
C) \[\frac{450}{263}\]
D) None of these
View Answer play_arrowquestion_answer164) Let A and B be two events such that \[P(A)=0.3,\]\[P(A\cup B)=0.8,\]if A and B are independent events, then \[P(B)\] is equal to
A) \[5/7\]
B) \[5/13\]
C) \[1/3\]
D) \[1/2\]
View Answer play_arrowquestion_answer165) If for some real number k \[\underset{x\to 0}{\mathop{\lim }}\,kx\,\,\text{cosec (x) =}\underset{x\to 0}{\mathop{\text{lim}}}\,\,\,x\,\,\text{cosec}\,\,(kx),\] then the possible values of k are
A) \[1,-1\]
B) \[0,\,\,\,1\]
C) \[1,\,\,\,2\]
D) \[0,\,\,\,\pi \]
View Answer play_arrowquestion_answer166) If \[{{\log }_{2}}[{{\log }_{3}}\{lo{{g}_{4}}({{\log }_{5}}x)\}]=0,\]then the value of x is
A) \[{{5}^{24}}\]
B) \[1\]
C) \[{{2}^{25}}\]
D) \[{{5}^{64}}\]
View Answer play_arrowquestion_answer167) The tangent to the curve \[y=2{{x}^{2}}-x+1\]is parallel to the line \[y=3x+9\]at the point
A) \[(3,\,\,9)\]
B) \[(2,\,\,-1)\]
C) \[(2,\,1)\]
D) \[(1,\,2)\]
View Answer play_arrowquestion_answer168) The system of equations \[x+3y+2z=0\] \[3x+y+z=0\] and \[2x-2y-z=0\]
A) possesses a trivial solution only
B) possesses a non-zero unique solution
C) does not have a common non-zero solution
D) has infinitely many solutions
View Answer play_arrowquestion_answer169) If \[\omega \] is a cube root of unity, then a root of the equation \[\left| \begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix} \right|=0\] is
A) \[x=0\]
B) \[x=1\]
C) \[x=\omega \]
D) \[x={{\omega }^{2}}\]
View Answer play_arrowquestion_answer170) If A is a square matrix, then AA' is a (A' is the transpose of the matrix A)
A) unit matrix
B) null matrix
C) symmetric matrix
D) skew-symmetric matrix
View Answer play_arrowquestion_answer171) If A is a \[3\times 3\] non-singular matrix, then \[\det \,\,({{A}^{-1}}\,adj\,A)\] is equal to
A) \[det\text{ }A\]
B) \[1\]
C) \[{{(det\text{ }A)}^{2}}\]
D) \[{{(det\text{ }A)}^{-1}}\]
View Answer play_arrowquestion_answer172) In case of a linear programming problem, feasible region is always
A) a convex set
B) a concave set
C) a bounded convex set
D) a bounded concave set
View Answer play_arrowquestion_answer173) Which of the following is an odd function?
A) \[|x|+1\]
B) \[\sin x+\cos x\]
C) \[{{x}^{2}}\,\,\sec x+x\,{{\tan }^{2}}x\]
D) \[{{x}^{2}}\cot x+4{{x}^{4}}\,\text{cosec x+}{{\text{x}}^{5}}\]
View Answer play_arrowquestion_answer174) The incentre of the triangle with vertices \[(1,\sqrt{3}),\,(0,0)\]and \[(2,0)\]is
A) \[(1,\,\sqrt{3}/2)\]
B) \[(2/3,\,\,\,1\,\sqrt{3})\]
C) \[(2/3,\,\,\sqrt{3}/2)\]
D) \[(1,\,\,1/\sqrt{3})\]
View Answer play_arrowquestion_answer175) If r is Karl Pearson's coefficient of correlation between two sets of variates, then
A) \[r<1\]
B) \[r>1\]
C) \[r<-1\]
D) \[|r|\,\le \,1\]
View Answer play_arrowquestion_answer176) Three dice are thrown simultaneously, then probability of throwing a total greater than 4 is
A) \[1/54\]
B) \[53/54\]
C) \[5/108\]
D) None of these
View Answer play_arrowquestion_answer177) An approximate evaluation of \[\int_{a}^{b}{f(x)\,\,dx}\] using trapezoidal rule requires the division of \[[a,b]\] into
A) an even number of sub-intervals
B) an odd number of sub-intervals
C) any number of sub-intervals
D) None of the above
View Answer play_arrowquestion_answer178) In a triangle ABC, \[C={{90}^{o}}\]. If r is the in radius and R is the circum radius of the triangle, then \[2\,(r+R)\]is equal to
A) \[a+c\]
B) \[a+b+c\]
C) \[b+c\]
D) \[a+b\]
View Answer play_arrowquestion_answer179) The relation \[{{\tan }^{-1}}\left( \frac{1+x}{1-x} \right)=\frac{\pi }{4}+{{\tan }^{-1}}x\] holds true for all
A) \[x\,\in R\]
B) \[x\,\in (-\infty ,\,1)\]
C) \[x\,\in (-1,\,\,\infty )\]
D) \[x\,\in (-\,\infty ,-1)\]
View Answer play_arrowquestion_answer180) \[\int_{0}^{\pi /2}{\frac{1}{1+{{\tan }^{3}}x}}dx\]is equal to
A) \[\pi /2\]
B) \[\pi /4\]
C) \[\pi \]
D) None of these
View Answer play_arrowquestion_answer181) A letter is taken out at random from the word 'ASSISTANT and another is taken-out from the word 'STATISTICS'. The chance that the two selected letters are identical, is
A) \[19/45\]
B) \[19/90\]
C) \[89/90\]
D) \[1/90\]
View Answer play_arrowquestion_answer182) The probability that the 6th day of a randomly chosen month of a year is a Sunday, is
A) \[1/12\]
B) \[1/17\]
C) \[1/84\]
D) None of these
View Answer play_arrowquestion_answer183) \[\underset{x\to \infty }{\mathop{\lim }}\,\left( \sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x} \right)\] is equal to
A) \[1/2\]
B) \[0\]
C) \[1\]
D) None of these
View Answer play_arrowquestion_answer184) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+2} \right)}^{x}}\] is equal to
A) \[e\]
B) \[{{e}^{2}}\]
C) \[{{e}^{3}}\]
D) \[{{e}^{4}}\]
View Answer play_arrowquestion_answer185) If \[{{b}^{2}}-4ac=0\]and \[a>0,\]then domain of the function \[f(x)=\log \{(a{{x}^{2}}+bx+c)\,\,(x+1)\}\] is
A) \[R-\left( -\frac{b}{2a} \right)\]
B) \[R-(-\infty ,\,\,-1)\]
C) \[(-1,\infty )-\left\{ -\frac{b}{2a} \right\}\]
D) \[R-\left( \left\{ -\frac{b}{2a} \right\}\cap (-\infty ,-1) \right)\]
View Answer play_arrowquestion_answer186) \[\int{\frac{1}{{{({{x}^{4}}+1)}^{5/4}}}}\] is equal to
A) \[-\frac{4}{{{({{x}^{4}}+1)}^{1/4}}}+c\]
B) \[\frac{1}{{{({{x}^{4}}+1)}^{1/4}}}+c\]
C) \[\frac{x}{{{({{x}^{4}}+1)}^{1/4}}}+c\]
D) None of the above
View Answer play_arrowquestion_answer187) Let \[f(x)=\left\{ \begin{matrix} |x|,\,\,for\,\,0<|x|\le 2 \\ 1,\,\,\,\,\,for\,\,\,\,x=0 \\ \end{matrix} \right.\], then at \[x=0,\] \[f\] has
A) a local maximum
B) a local minimum
C) no local extremum
D) no local maximum
View Answer play_arrowquestion_answer188) There are n different books and m copies of each in a college library. The number of ways in which a student can make a selection of one or more books is
A) \[{{(m+1)}^{n}}\]
B) \[\frac{(mn)!}{{{(m!)}^{n}}}\]
C) \[^{mn}{{C}_{n}}{{\times }^{n}}{{C}_{1}}\]
D) \[{{(m+n)}^{n}}-1\]
View Answer play_arrowquestion_answer189) Five digited numbers with distinct digits arc formed by using the digits,\[5,4,3,2,1,0\]. The number of those numbers which are multiples of 3, is
A) \[720\]
B) \[240\]
C) \[216\]
D) \[120\]
View Answer play_arrowquestion_answer190) If \[A+B+C=\pi ,\]then the value of \[\left| \begin{matrix} \sin \,(A+B+C) & \sin B & \cos \,C \\ -\sin \,B & 0 & \tan \,A \\ \cos \,(A+B) & -\tan \,A & 0a \\ \end{matrix} \right|\] is
A) 0
B) 1
C) 2 sin B tan A cos C
D) None of the above
View Answer play_arrowquestion_answer191) If A and B are two matrices such that both \[A+B\]and AB are defined, then
A) A and B are of same order
B) A is of order \[m\times m\]and B is of order \[n\times n\]
C) both A and B are of same order \[n\times n\]
D) A is of order m x n and B is of order \[n\times m\]
View Answer play_arrowquestion_answer192) The number of dissimilar terms in expansion of \[{{(a+b)}^{n}}\] is \[n+1,\] therefore number of dissimilar terms of the expansion \[{{(a+b+c)}^{12}}\] is
A) \[13\]
B) \[39\]
C) \[78\]
D) \[91\]
View Answer play_arrowquestion_answer193) If \[|x|<1,\] then \[1+n\left( \frac{2x}{1+x} \right)+\frac{n\,\,(n+1)}{2!}\]\[{{\left( \frac{2x}{1+x} \right)}^{2}}+.......\] is equal to
A) \[{{\left( \frac{2x}{1+x} \right)}^{n}}\]
B) \[{{\left( \frac{1+x}{2x} \right)}^{n}}\]
C) \[{{\left( \frac{1-x}{1+x} \right)}^{n}}\]
D) \[{{\left( \frac{1+x}{1-x} \right)}^{n}}\]
View Answer play_arrowquestion_answer194) Eccentricity of the curve \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]is equal to
A) \[2\]
B) \[\sqrt{2}\]
C) \[4\]
D) None of these
View Answer play_arrowquestion_answer195) If forces of \[12,\text{ }5\] and \[13\] unit weight balance at a point, two of them are inclined at
A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{90}^{o}}\]
View Answer play_arrowquestion_answer196) If the resultant of two forces P and Q acting on a particle is at right angle to Q, then the angle between the forces is
A) \[{{\cos }^{-1}}\left( \frac{P}{Q} \right)\]
B) \[\pi -{{\cos }^{-1}}\left( \frac{Q}{P} \right)\]
C) \[\pi -{{\cos }^{-1}}\left( \frac{P}{Q} \right)\]
D) None of these
View Answer play_arrowquestion_answer197) To open a lock, a key is taken out from a collection of n keys at random. If the lock is not opened with this key, it is put back into the collection and another key is tried. The process is repeated again and again. If it is given that with only one key in the collection, the lock can be opened, then the probability that the lock will open in n trials, is
A) \[{{\left( \frac{1}{n} \right)}^{n}}\]
B) \[{{\left( \frac{n-1}{n} \right)}^{n}}\]
C) \[1-{{\left( \frac{n-1}{n} \right)}^{n}}\]
D) None of these
View Answer play_arrowquestion_answer198) The function \[f(x)=x+\frac{1}{x}\] has
A) a local maxima at \[x=1\]and a local minima at \[x=-1\]
B) a local minima at \[x=1\] and a local maxima at \[x=-1\]
C) absolute maxima at \[x=1\] and absolute minima at \[x=-1\]
D) Absolute minima at \[x=1\] and absolute maxima at \[x=-1\]
View Answer play_arrowquestion_answer199) If the sides of a triangle are \[13,7,8,\] then the greatest angle of the triangle is
A) \[\frac{\pi }{2}\]
B) \[\frac{3\pi }{2}\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{\pi }{3}\]
View Answer play_arrowquestion_answer200) \[\underset{h\to \frac{x}{4}}{\mathop{\lim }}\,\frac{\tan \,x-1}{x-\frac{\pi }{4}}\]is equal to
A) \[1\]
B) \[1/2\]
C) \[2\]
D) \[0\]
View Answer play_arrowquestion_answer201) \[\underset{h\to 0}{\mathop{lim}}\,\frac{\sin \,\sqrt{x+h}-\sin \,\sqrt{x}}{h}\] is equal to
A) \[\cos \,\,\sqrt{x}\]
B) \[1/(2\,\sin \sqrt{x})\]
C) \[(\cos \sqrt{x})/2\sqrt{x}\]
D) \[\sin \sqrt{x}\]
View Answer play_arrowquestion_answer202) If \[f(x)={{x}^{2}}+4x+1,\] then
A) \[f(x)=f(-x),\] for all x
B) \[f(x)\ne 1,\] for \[x=0\]
C) \[f''(x)>0,\] for all x
D) \[f(x)>1,\] for \[x\le 1\]
View Answer play_arrowquestion_answer203) If a, b, c are different real numbers and \[a\,\,\hat{i}+b\,\,\hat{j}+c\,\,\hat{k},\]\[b\,\,\hat{i}+c\,\,\hat{j}+a\,\,\hat{k}\] and \[c\,\,\hat{i}+a\,\,\hat{j}+b\,\,\hat{k}\]are position vectors of three non-collinear points, then
A) centroid of \[\Delta ABC\] is s\[\frac{a+b+c}{3}\,(\hat{i}+\hat{j}+\hat{k})\]
B) \[(\hat{i}+\hat{j}+\hat{k})\] is not really inclined to three vectors
C) triangle ABC is a scalene triangle
D) perpendicular from the origin to the plane of the triangle does not meet it at the centroid
View Answer play_arrowquestion_answer204) Given four lines with equations \[x+2y-3=0,\] \[2x+3y-4=0,\] \[3x+4y-5=0,\] \[4x+5y-6=0.\] These lines are
A) concurrent
B) the sides of quadrilateral
C) the sides of a parallelogram
D) the sides of a square
View Answer play_arrowquestion_answer205) The equations of lines through the point \[(1,\,1)\] and making angles of \[{{45}^{o}}\]with the line \[x+y=0\]are
A) \[x-1=0,\,\,x-y=0\]
B) \[x-1=0,\,\,y-1=0\]
C) \[x-y=0,\,\,y-1=0\]
D) \[x+y-2=0,\,\,\,y-1=0\]
View Answer play_arrowquestion_answer206) If a function F is such that \[f(0)=2,\,\,F(1)=3,\] \[F(n+2)=2F(n)-F(n+1)\]for \[n\ne 0,\] then \[F(5)\] is equal to
A) \[-7\]
B) \[-3\]
C) \[7\]
D) \[13\]
View Answer play_arrowquestion_answer207) If \[f(x)=\frac{1}{\sqrt{-x}},\] then domain of fof is
A) \[(0,\,\,\infty )\]
B) \[(-\,\infty ,\,\,0)\]
C) \[\{0\}\]
D) \[\{\,\,\}\]
View Answer play_arrowquestion_answer208) If x and y are odd integers, then \[{{x}^{2}}+{{y}^{2}}\]is
A) an odd integer
B) an even integer divisible by 4
C) an even integer not divisible by 4
D) None of the above
View Answer play_arrowquestion_answer209) The minimum value of \[sin{{\,}^{4}}x+co{{s}^{4}}x\]is
A) \[1\]
B) \[0\]
C) \[1/2\]
D) None of these
View Answer play_arrowquestion_answer210) The locus of the point of intersection of the lines \[x\,cot\,\theta +y\,cosec\,\theta \text{=}2\]and \[x\,cosec\,\theta +y\,cot\,\theta =6\]is
A) a straight line
B) circle
C) a hyperbola
D) an ellipse
View Answer play_arrowquestion_answer211) If \[2/3,\,k,\,5/8\]are in AP, find the value of k.
A) \[15\]
B) \[21\]
C) \[12\]
D) \[31/48\]
View Answer play_arrowquestion_answer212) If \[x=\sqrt{3018+\sqrt{36+\sqrt{169}}},\] then the value of x is
A) \[55\]
B) \[44\]
C) \[63\]
D) \[42\]
View Answer play_arrowquestion_answer213) The number of diagonals that can be drawn by joining the vertices of an octagon, is
A) \[28\]
B) \[48\]
C) \[20\]
D) \[15\]
View Answer play_arrowquestion_answer214) If the fourth term in the expansion of \[{{\left( ax+\frac{1}{x} \right)}^{n}}\] is \[\frac{5}{2},\] then find the value of a and n.
A) \[a=1/2\]and \[n=6\]
B) \[a=1/3\] and \[n=5\]
C) \[a=2\]and \[n=3\]
D) \[a=1/4\]and \[n=1\]
View Answer play_arrowquestion_answer215) If \[{{e}^{x}}=y+\sqrt{1+{{y}^{2}}},\] then the value of y is
A) \[{{e}^{x}}-{{e}^{-x}}\]
B) \[\frac{1}{2}({{e}^{x}}-{{e}^{-x}})\]
C) \[{{e}^{x}}+{{e}^{-x}}\]
D) None of these
View Answer play_arrowquestion_answer216) In the group \[G=\{1,3,7,9\}\]under multiplication modulo 10, the inverse of 7 is
A) \[7\]
B) \[3\]
C) \[9\]
D) \[1\]
View Answer play_arrowquestion_answer217) If A and B are two mutually exclusive events then
A) \[P(A)<P(\bar{B})\]
B) \[P(A)>P(\bar{B})\]
C) \[P(A)<P(B)\]
D) None of these
View Answer play_arrowquestion_answer218) The equation of the directrix of the parabola \[{{y}^{2}}+4y+4x+2=0\] is
A) \[-1\]
B) \[x=1\]
C) \[x=-3/2\]
D) \[x=3/2\]
View Answer play_arrowquestion_answer219) Let \[{{T}_{n}}\] denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If \[{{T}_{n+1}}-{{T}_{n}}=21,\] then n equals
A) \[5\]
B) \[7\]
C) \[6\]
D) \[4\]
View Answer play_arrowquestion_answer220) In a triangle ABC, \[2ca\,\sin \left( \frac{A-B+C}{2} \right)\] is equal to
A) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]
B) \[{{c}^{2}}+{{a}^{2}}-{{b}^{2}}\]
C) \[{{b}^{2}}-{{c}^{2}}-{{a}^{2}}\]
D) \[{{c}^{2}}-{{a}^{2}}-{{b}^{2}}\]
View Answer play_arrowquestion_answer221) A fair die is tossed eight times. The probability that a third six is observed on the eight throw is
A) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]
B) \[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{8}}}\]
C) \[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{6}}}\]
D) None of these
View Answer play_arrowquestion_answer222) The greatest distance of the point from the circle \[{{x}^{2}}+{{y}^{2}}-4x-2y-20=0\]is
A) \[10\]
B) \[15\]
C) \[5\]
D) None of these
View Answer play_arrowquestion_answer223) The vectors \[\overrightarrow{AB}=3\hat{i}+4\hat{k}\] and \[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\] are the sides of a triangle ABC. The length of the median through A is
A) \[\sqrt{18}\]
B) \[\sqrt{72}\]
C) \[\sqrt{33}\]
D) \[\sqrt{288}\]
View Answer play_arrowquestion_answer224) A particle acted on by constant forces \[4\hat{i}+\hat{j}-3\hat{k}\] and \[3\hat{i}+\hat{j}-\hat{k}\] is displaced from the point \[\hat{i}+2\hat{j}+3\hat{k}\] to the point \[5\hat{i}+4\hat{j}+\hat{k}\]. The total work done by the forces is
A) 20 unit
B) 30 unit
C) 40 unit
D) 50 unit
View Answer play_arrowquestion_answer225) If \[f(x)\] is a differentiable function, then \[\underset{x\to a}{\mathop{\lim }}\,\] \[\frac{a\,\,f(x)-x\,f(a)}{x-a}\] is equal to
A) \[a\,\,f'(a)-f(a)\]
B) \[a\,\,f(a)-f'(a)\]
C) \[a\,\,f'(a)+f(a)\]
D) \[\,f'(a)+a\,f(a)\]
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