question_answer1) A ray of light travels from an optically denser to a rarer medium. The critical angle for the two media is C. The maximum possible deviation of the ray will be :
A) \[2C\] done clear
B) \[\frac{\pi }{2}-C\] done clear
C) \[\pi -C\] done clear
D) \[\pi -2C\] done clear
View Answer play_arrowquestion_answer2) When one of the slits of Young's experiment is covered with a transparent sheet of thickness 4.8 mm, the central shifts to a position originally occupies by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe?
A) \[1.6\,mm\] done clear
B) \[3.8\,mm\] done clear
C) \[3.2\,mm\] done clear
D) \[7.6\,mm\] done clear
View Answer play_arrowquestion_answer3) Light passes successively through two polarimeter tubes each of length 0.29 m. The first tube contains dextro rotatory solution of concentration\[60\,kg\,{{m}^{-3}}\]and specific rotation 0.01 rad\[{{m}^{2}}\,k{{g}^{-1}}.\]The second tube contains laevo rotatory solution of concentration \[30\,kg\,{{m}^{-5}}\]and specific rotation 0\[0.02\,\]rad \[{{m}^{2}}k{{g}^{-1}}.\]The net rotation produced is:
A) \[{{0}^{o}}\] done clear
B) \[{{15}^{o}}\] done clear
C) \[{{10}^{o}}\] done clear
D) \[{{20}^{o}}\] done clear
View Answer play_arrowquestion_answer4) \[{{\upsilon }_{O}}\]and\[{{\upsilon }_{E}}\]represent the velocities, \[{{\mu }_{O}}\]and \[{{\mu }_{E}}\]he the refractive indices of ordinary and extraordinary rays for a double refracting crystal. Then:
A) \[{{\upsilon }_{O}}\le {{\mu }_{O}}\le {{\mu }_{E}},\]if the crystal is quartz done clear
B) \[{{\upsilon }_{O}}\ge {{\upsilon }_{E}},{{\mu }_{O}}\le {{\mu }_{E}},\]if the crystal is calcite done clear
C) \[{{\upsilon }_{o}}\ge {{\upsilon }_{E}},{{\mu }_{o}}\ge {{\mu }_{E}},\]if the crystal is quartz done clear
D) \[{{\upsilon }_{1}}\le {{\upsilon }_{E}},{{\mu }_{o}}\ge {{\mu }_{E}},\]if the crystal is calcite. done clear
View Answer play_arrowquestion_answer5) A racing car moving towards a cliff, sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If v is the velocity of sound, then the velocity of the car is:
A) \[\upsilon /2\] done clear
B) \[\upsilon /\sqrt{2}\] done clear
C) \[\upsilon /4\] done clear
D) \[\upsilon /3\] done clear
View Answer play_arrowquestion_answer6) The de-Broglie wavelength of an electron in the first Bohr orbit is:
A) equal to half the circumference of the first orbit done clear
B) equal to one fourth the circumference of the first orbit done clear
C) equal to the circumference of the first orbit done clear
D) equal to twice the circumference of the first orbit done clear
View Answer play_arrowquestion_answer7) Out of the following statements which is not true?
A) Infrared radiations arise due to minor electron transitions in atoms. done clear
B) Infrared radiations are used for long distance photography. done clear
C) Sun is the natural source of infrared radiation. done clear
D) Infrared radiations are detected by using a bolometer. done clear
View Answer play_arrowquestion_answer8) In nuclear fission the percentage of mass converted into energy is about:
A) \[0.01%\] done clear
B) \[10%\] done clear
C) \[1%\] done clear
D) \[0.1%\] done clear
View Answer play_arrowquestion_answer9) If \[{{l}_{1}},{{l}_{2}},{{l}_{3}},\]are the lengths of the emitter, base and collector of a transistor, then:
A) \[{{l}_{3}}<{{l}_{2}}<{{l}_{1}}\] done clear
B) \[{{l}_{1}}={{l}_{2}}={{l}_{3}}\] done clear
C) \[{{l}_{3}}<{{l}_{1}}<{{l}_{2}}\] done clear
D) (d \[{{l}_{3}}<{{l}_{1}}<{{l}_{2}}\] done clear
View Answer play_arrowquestion_answer10) When the conductivity of a semiconductor is only due to breaking of covalent bonds, the semiconductor is called:
A) intrinsic done clear
B) extrinsic done clear
C) p-type done clear
D) n-type done clear
View Answer play_arrowquestion_answer11) A very large number of balls are thrown vertically upwards in quick successions in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is 5 m, the number of balls thrown per minute is: (take\[g=10m/{{s}^{2}}\])
A) 80 done clear
B) 120 done clear
C) 40 done clear
D) 60 done clear
View Answer play_arrowquestion_answer12) The light reflected by a plane mirror may form a real image:
A) if the rays incident on the mirror are converging done clear
B) if the rays incident on the mirror are diverging done clear
C) under no circumstances done clear
D) if the object is placed very close to the mirror. done clear
View Answer play_arrowquestion_answer13) A convex is made up of three different materials as shown in the figure. For a point object places on its axis, the number of images formed are:
A) 5 done clear
B) 1 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer14) Light appears to travel in straight lines because:
A) light consists of very small particles done clear
B) the frequency of light is very small done clear
C) the velocity of light is different for different colours done clear
D) the wavelength of light is very small. done clear
View Answer play_arrowquestion_answer15) In Young's double slit experiment, the central bright fringe can be identified:
A) as it a narrower than other bright fringes done clear
B) by using white light instead of monochromatic light done clear
C) as it has a greater intensity than other bright fringes done clear
D) as it is wider than other bright fringes. done clear
View Answer play_arrowquestion_answer16) A railway engine whistling at a constant frequency moves with a constant speed. It goes past a stationary observer beside the railway track. Which of the following graphs best represent the variation of frequency of the sound n heard by the observer with the time t?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer17) The tension of a stretched string is increased by 69%. In order to keep its frequency of vibration constant, its length must be increased by:
A) \[30%\] done clear
B) \[~20%\] done clear
C) \[~69%\] done clear
D) \[\sqrt{69%}\] done clear
View Answer play_arrowquestion_answer18) Under the same conditions of temperature and pressure, the velocity of sound in oxygen and hydrogen are \[{{\upsilon }_{O}}\]and \[\upsilon H.\]Then:
A) \[{{\upsilon }_{O}}=4{{\upsilon }_{H}}\] done clear
B) \[{{\upsilon }_{H}}=4{{\upsilon }_{O}}\] done clear
C) \[{{\upsilon }_{O}}={{\upsilon }_{H}}\] done clear
D) \[{{\upsilon }_{H}}=16{{\upsilon }_{O}}\] done clear
View Answer play_arrowquestion_answer19) small drops of mercury, each of radius r and charge q coalesce to form a big drop. The ratio of the surface density of charge of each small drop with of the big drop is:
A) 64 : 1 done clear
B) 1 : 64 done clear
C) 1 : 4 done clear
D) 4 : 1 done clear
View Answer play_arrowquestion_answer20) Two capacitors of capacitances \[\text{3}\,\text{ }\!\!\mu\!\!\text{ F}\]and \[6\,\text{ }\!\!\mu\!\!\text{ F}\]are charged to a potential of 12 V each. They are now connected to each other, with the positive plate to each joined to the negative plate to the other. The potential difference across each will be:
A) 4V done clear
B) 6V done clear
C) zero done clear
D) 3 V done clear
View Answer play_arrowquestion_answer21) The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is:
A) \[{{120}^{o}}\] done clear
B) \[~{{60}^{o}}\] done clear
C) \[{{90}^{o}}\] done clear
D) \[{{150}^{o}}\] done clear
View Answer play_arrowquestion_answer22) The load versus elongation graph for four wires of the same meterials is shown in the figure. The thinnest wire is represented by the line:
A) OC done clear
B) OD done clear
C) OA done clear
D) OB done clear
View Answer play_arrowquestion_answer23) One kilogram of ice at \[\text{0}{{\,}^{\text{o}}}\text{C}\]is mixed with one kilogram of water at\[\text{80}{{\,}^{\text{o}}}\text{C}\text{.}\]The final temperature of the mixture is (take: specific heat of water \[=4200\,J\,k{{g}^{-1}}\,{{K}^{-1}},\] latent heat of ice\[=336\,kJ\,k{{g}^{-1}}\]).
A) \[40{{\,}^{o}}C\] done clear
B) \[~60{{\,}^{o}}C\] done clear
C) \[~0{{\,}^{o}}C\] done clear
D) \[~50{{\,}^{o}}C\] done clear
View Answer play_arrowquestion_answer24) A Carnot's engine is made to work between \[200{{\,}^{o}}C\]and\[0{{\,}^{o}}C\]first and then between \[0{{\,}^{o}}C\]and \[-200{{\,}^{o}}C.\]The ratio of efficiencies of the engine in the two cases is:
A) \[1:1.73\] done clear
B) \[1.73:1\] done clear
C) \[1:2\] done clear
D) \[1:1\] done clear
View Answer play_arrowquestion_answer25) An object is placed 12 cm to the left of a converging lens of focal length 8 cm. Another converging lens of 6 cm focal length is placed at a distance of 30 cm. to the right of the first lens. The second lens will produce:
A) virtual enlarged image done clear
B) no image done clear
C) a real inverted image done clear
D) a real enlarged image done clear
View Answer play_arrowquestion_answer26) The resistance of an incandescent lamp is:
A) smaller when switched on done clear
B) greater when switched off done clear
C) the same whether it is switch off or switch on done clear
D) greater when switched on done clear
View Answer play_arrowquestion_answer27) A superconductor exhibits perfect:
A) ferromagnetism done clear
B) ferrimagnetism done clear
C) diamagnetism done clear
D) paramagnetism done clear
View Answer play_arrowquestion_answer28) A magnet is dropped down an infinitely long vertical copper tube. Then:
A) the magnet moves with continuously decreasing velocity and ultimately comes to rest done clear
B) the magnet moves with continuously increasing velocity and ultimately acquires a constant terminal velocity done clear
C) the magnet moves with continuously increasing velocity and acceleration done clear
D) the magnet moves with continuously increasing velocity but constant acceleration. done clear
View Answer play_arrowquestion_answer29) Whenever a hydrogen atom emits a photon in the Balmer series, it:
A) may emit another photon in the Paschen series done clear
B) need not emit any more photon done clear
C) may emit another photon in the Balmer series done clear
D) must emit another photon in the Lyman series. done clear
View Answer play_arrowquestion_answer30) The SI unit of radioactivity is:
A) Rutherford done clear
B) Roentgen done clear
C) Becqueral done clear
D) Curie. done clear
View Answer play_arrowquestion_answer31) An ammeter and a voltmeter are joined in series to a cell. Their readings are A and V respectively. If a resistance is now joined in parallel with the voltmeter, then:
A) A will decrease, V will increase done clear
B) A will increase, V will decrease done clear
C) both A and V will increase done clear
D) both A and V will increase done clear
View Answer play_arrowquestion_answer32) If each of the resistance of the network shown in figure is R, the equivalent resistance between A and B is:
A) 3R done clear
B) 5R done clear
C) R/2 done clear
D) R done clear
View Answer play_arrowquestion_answer33) A cell supplies a current of 0.9 A through a \[2\Omega \]resistor and a current of 0-3 A through a \[7\Omega \]resistor. The internal resistance of the cell is:
A) \[1.2\,\Omega \] done clear
B) \[2.0\,\,\Omega \] done clear
C) \[0.5\,\,\Omega \] done clear
D) \[1.0\,\,\Omega \] done clear
View Answer play_arrowquestion_answer34) A wire carrying current\[i\]is shaped as shown. Section AB is a quarter circle of radius r. The magnetic field is directed:
A) perpendicular to the plane of the paper and directed into the paper done clear
B) at an angle \[\pi /4\]to the plane of the paper done clear
C) along the bisector of the angle ACB away from AB done clear
D) along the bisector of ACB towards AB. done clear
View Answer play_arrowquestion_answer35) The wire loop formed by joining two semicircular sections of radii\[{{R}_{1}}\]and\[{{R}_{2}}\]and centre C, carries a current\[I\]as shown. The magnetic field at C has a magnitude:
A) \[\frac{{{\mu }_{0}}I}{2}\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)\] done clear
B) \[\frac{{{\mu }_{0}}I}{4}\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)\] done clear
C) \[\frac{{{\mu }_{0}}I}{2}\left( \frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}} \right)\] done clear
D) \[\frac{{{\mu }_{0}}I}{4}\left( \frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}} \right)\] done clear
View Answer play_arrowquestion_answer36) To increase both the resolving power and magnifying power of a telescope:
A) the focal length of the objective has to be increased done clear
B) both the focal length and aperture of the objective has to be increased done clear
C) the wavelength of light has to be decreased done clear
D) the aperture of the objective has to be increased done clear
View Answer play_arrowquestion_answer37) Forty one tuning forks are arranged in increasing order of frequencies such that every fork gives 5 beats with the next. The last fork has a frequency that is double the frequency of the first fork is:
A) 210 done clear
B) 400 done clear
C) 205 done clear
D) 200 done clear
View Answer play_arrowquestion_answer38) In a stationary wave all the particles:
A) in the region between two nodes vibrate in same phase done clear
B) on either side of a node vibrate in same phase done clear
C) of the medium vibrate in same phase done clear
D) in the region between two antinodes vibrate in same phase. done clear
View Answer play_arrowquestion_answer39) A cylindrical tube, open at both ends, has a fundamental frequency\[{{f}_{0}}\]in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is:
A) \[{{f}_{0}}\] done clear
B) \[3{{f}_{0}}/4\] done clear
C) \[2{{f}_{0}}\] done clear
D) \[{{f}_{0}}/2\] done clear
View Answer play_arrowquestion_answer40) A man \[x\]can hear upto 10 kHz and another man \[y\]upto 2 kHz. A note of frequency 500 Hz is produced before them from a stretched string then both will hear sounds of:
A) different pitch but same quality done clear
B) same pitch but different quality done clear
C) same pitch and same quality done clear
D) different pitch and different quality. done clear
View Answer play_arrowquestion_answer41) When 100 V D.C. is applied across a coil, a current of 1 A flows through it. When 100 V A.C. of 50 Hz is applied to the same, coil only 0.5 A flows. The inductance of the coil is:
A) \[5.5\,mH\] done clear
B) \[0.55\,mH\] done clear
C) \[55\text{ }mH\] done clear
D) \[~0.55\text{ }H.\] done clear
View Answer play_arrowquestion_answer42) In the circuit shown in the figure, the A.C. source gives a voltage \[y=20\,cos\text{ (}2000t\text{)}.\]Neglecting source resistance, the voltmeter and ammeter reading will be:
A) \[1.68\text{ }V,\text{ }0.47\text{ }A\] done clear
B) \[~0\text{ }V,\text{ }0.47\text{ }A\] done clear
C) \[5.6\,V,1.4\,A\] done clear
D) \[0\,V,\,1.4\,A\] done clear
View Answer play_arrowquestion_answer43) In the Bohr model of the hydrogen atom, let R, V and E represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantity is proportional to the quantum number\[n\]?
A) \[E/V\] done clear
B) \[R/E\] done clear
C) \[VR\] done clear
D) \[RE\] done clear
View Answer play_arrowquestion_answer44) In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life?
A) 63% done clear
B) \[69.3%\] done clear
C) 37% done clear
D) 50% done clear
View Answer play_arrowquestion_answer45) A caesium photocell, with a steady potential difference of 60V across it, is illuminated by a bright point source of light 50 cm away. When the same light is places 1cm. away, the photoelectrons emitted from the cell:
A) are half as numerous; done clear
B) are one quarter as numerous done clear
C) each carry one quarter of their previous energy done clear
D) each carry one quarter of their previous momentum. done clear
View Answer play_arrowquestion_answer46) The equation\[y=A{{\cos }^{2}}\left[ 2\pi nt-2\pi \frac{x}{y} \right]\] represents a wave with:
A) amplitude\[A/2,\]frequency\[2n\]and wavelength \[\lambda \] done clear
B) amplitude\[A/2,\]frequency\[2n\]and wavelength\[\lambda /2\] done clear
C) amplitude A, frequency \[n\]and wavelength done clear
D) amplitude A, frequency\[2n\]and wavelength \[2\lambda \] done clear
View Answer play_arrowquestion_answer47) A light points fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through 10 cm, the frequency of the tuning fork is:
A) 280 Hz done clear
B) 360 Hz done clear
C) 56 Hz done clear
D) 56.0 Hz done clear
View Answer play_arrowquestion_answer48) Three point charges are placed at the comers of an equilateral triangle. Assuming only electrostatic forces are acting. Then the system:
A) will be in equilibrium if the charges rotate about the centre of the triangle done clear
B) can never be in equilibrium done clear
C) will be in equilibrium if the charges have the same magnitudes but different signs done clear
D) will be in equilibrium if the charges have different magnitude and different signs. done clear
View Answer play_arrowquestion_answer49) Two copper balls, each weighing 10 g are kept in air 10 cm apart. If one electron from every \[{{10}^{6}}\] atoms is transferred from one ball to the other, the coulomb force between them is: (atomic weight of copper is 63.5)
A) \[2.0\times {{10}^{4}}N\] done clear
B) \[2.0\times {{10}^{10}}N\] done clear
C) \[2.0\,{{10}^{6}}N\] done clear
D) \[2.0\times {{10}^{8}}N\] done clear
View Answer play_arrowquestion_answer50) What fraction of the energy drawn from the charging battery is stored in a capacitor?
A) 75% done clear
B) 100% done clear
C) 25% done clear
D) 50% done clear
View Answer play_arrowquestion_answer51) A projectile is moving at \[20\,\text{m}{{\text{s}}^{-1}}\]at its highest point, where it breaks into equal parts due to an internal explosion. One part moves vertically up at \[30\,\text{m}{{\text{s}}^{-1}}\]with respect to the ground. Then the other part will move at:
A) \[20\,m{{s}^{-1}}\] done clear
B) \[10\sqrt{31}\,m{{s}^{-1}}\] done clear
C) \[50\,m{{s}^{-1}}\] done clear
D) \[30\,m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer52) A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
A) R/2 done clear
B) R/3 done clear
C) R/5 done clear
D) R/4 done clear
View Answer play_arrowquestion_answer53) From the top of a tower a stone is thrown up which reaches the ground in a time h. A second stone thrown down with the same speed reaches the ground in a time \[{{t}_{2}}.\]A third stone released from rest from the same between reaches the ground in a time \[{{t}_{3}}.\]Then:
A) \[\frac{1}{{{t}_{3}}}=\frac{1}{{{t}_{2}}}-\frac{1}{{{t}_{1}}}\] done clear
B) \[t_{3}^{2}=t_{1}^{2}-t_{2}^{2}\] done clear
C) \[{{t}_{3}}=\frac{{{t}_{1}}+{{t}_{2}}}{2}\] done clear
D) \[{{t}_{3}}=\sqrt{{{t}_{1}}{{t}_{2}}}\] done clear
View Answer play_arrowquestion_answer54) Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities and \[{{k}_{5}}\] when points A and B are maintained at different temperatures. No heat flows through the central rod if:
A) \[{{k}_{1}}{{k}_{4}}={{k}_{2}}{{k}_{3}}\] done clear
B) \[{{k}_{1}}={{k}_{4}}\]and \[{{k}_{2}}={{k}_{3}}\] done clear
C) \[\frac{{{k}_{1}}}{{{k}_{4}}}=\frac{{{k}_{2}}}{{{k}_{3}}}\] done clear
D) \[{{k}_{1}}{{k}_{2}}={{k}_{3}}{{k}_{4}}\] done clear
View Answer play_arrowquestion_answer55) The energy spectrum of a black body exhibits a maximum around a wavelength\[{{\lambda }_{0}}.\]The temperature of the black body is now changed such that the energy is maximum around a wavelength\[3{{\lambda }_{0}}/4.\] The power radiated by the black body will now increase by a factor of:
A) 64/27 done clear
B) 256/81 done clear
C) 4/3 done clear
D) 16/9 done clear
View Answer play_arrowquestion_answer56) \[n\]identical bulbs, each designated to draw a power P from a certain voltage supply. The total power which they will draw is:
A) \[P/n\] done clear
B) \[P/{{n}^{2}}\] done clear
C) \[np\] done clear
D) \[P\] done clear
View Answer play_arrowquestion_answer57) A and B are two conductors carrying a current \[\text{I}\]in the same direction,\[x\]and\[~y\]are two electron beams moving in the same direction. Then there will be :
A) attraction between A and B, repulsion between \[x\] and \[y\] done clear
B) repulsion between A and B, attraction between \[x\]and \[y\] done clear
C) attraction between A and B and \[x\]and \[y\] done clear
D) repulsion between A and B and \[x\]and \[y\] done clear
View Answer play_arrowquestion_answer58) The current-voltage graph for a given metallic conductor at two different temperature \[{{\text{T}}_{\text{1}}}\]and \[{{\text{T}}_{2}}\]are as shown in the figure. Then:
A) \[{{T}_{1}}<{{T}_{2}}\] done clear
B) nothing can be said about \[{{T}_{1}}\]and \[{{T}_{2}}\] done clear
C) \[{{T}_{1}}={{T}_{2}}\] done clear
D) \[{{T}_{1}}>{{T}_{2}}\] done clear
View Answer play_arrowquestion_answer59) The variation of the intensity of magnetisation \[(I)\] with respect to the magnetising field (H) in a diamagnetic substance is described by the graph:
A) OC done clear
B) OD done clear
C) OA done clear
D) OB done clear
View Answer play_arrowquestion_answer60) An aluminium ring B faces an electromagnet A. The current \[I\]through A can be altered. Then which of the following statements is correct?
A) If \[I\]decreases, A will repel B done clear
B) Whether \[I\] increases or decreases, B will not experience any force done clear
C) If \[I\] increases, A will repel B done clear
D) If \[I\] increases, A will attract B done clear
View Answer play_arrowquestion_answer61) Glacial acetic acid is obtained by:
A) chemically separating acetic acid done clear
B) treating vinegar with dehydrating agents done clear
C) crystallising, separating and melting acetic acid done clear
D) distilling vinegar. done clear
View Answer play_arrowquestion_answer62) An organic acid without a carboxylic acid group is:
A) picric acid done clear
B) oxalic acid done clear
C) vinegar done clear
D) ascorbic acid done clear
View Answer play_arrowquestion_answer63) An ester used as medicine is:
A) ethyl benzoate done clear
B) methyl salicylate done clear
C) methyl acetate done clear
D) ethyl acetate done clear
View Answer play_arrowquestion_answer64) Reaction of aniline with benzaldehyde is:
A) polymerisation done clear
B) condensation done clear
C) addition done clear
D) substitution done clear
View Answer play_arrowquestion_answer65) Halo alkane in the presence of alcoholic KOH undergoes:
A) elimination done clear
B) poly merisation done clear
C) dimerisation done clear
D) substitution done clear
View Answer play_arrowquestion_answer66) The simplest way to check whether a system is colloidal is by:
A) electrodialysis done clear
B) finding out particle size done clear
C) Tyndall effect done clear
D) Brownian movement. done clear
View Answer play_arrowquestion_answer67) An example for a strong electrolyte is:
A) urea done clear
B) ammonium hydroxide done clear
C) sugar done clear
D) sodium acetate done clear
View Answer play_arrowquestion_answer68) An example of a salt that will not hydrolyse is:
A) \[C{{H}_{3}}COON{{H}_{4}}\] done clear
B) \[C{{H}_{3}}COOK\] done clear
C) \[N{{H}_{4}}Cl\] done clear
D) \[KCl\] done clear
View Answer play_arrowquestion_answer69) \[C{{}^{14}}\]is:
A) a natural non-radioactive isotope done clear
B) an artificial non-radioactive isotope done clear
C) an artificial radioactive isotope done clear
D) a natural radioactive isotope. done clear
View Answer play_arrowquestion_answer70) A cuprous ore among the following is:
A) cuprite done clear
B) malachite done clear
C) chalcopyrites done clear
D) azurite done clear
View Answer play_arrowquestion_answer71) van der Waal's equation for \[n\]moles of a gas is:
A) \[\left( P+\frac{{{n}^{2}}a}{{{V}^{2}}} \right)(V-nb)=RT\] done clear
B) \[\left( P+\frac{na}{{{V}^{2}}} \right)(V-nb)=RT\] done clear
C) \[\left( P+\frac{a}{{{V}^{2}}} \right)(V-b)=nRT\] done clear
D) \[\left( P+\frac{{{n}^{2}}a}{{{V}^{2}}} \right)(V-b)=RT\] done clear
View Answer play_arrowquestion_answer72) Smallest among these species is:
A) lithium done clear
B) lithium ion done clear
C) hydrogen done clear
D) helium done clear
View Answer play_arrowquestion_answer73) Sodium chloride is an ionic compound where as hydrogen chloride gas is mainly convalent because :
A) electronegativity difference in the case of hydrogen is less than 2.1. done clear
B) hydrogen chloride is a gas done clear
C) hydrogen is a non-metal done clear
D) sodium is reactive. done clear
View Answer play_arrowquestion_answer74) Covalent compounds have low melting point because:
A) covalent molecules are held by weak van der Waal?s force of attraction done clear
B) covalent bond is less exothermic done clear
C) covalent bond is weaker than ionic bond done clear
D) covalent molecules have definite shape. done clear
View Answer play_arrowquestion_answer75) A neutral fertilizer among these compounds is:
A) ammonium nitrate done clear
B) urea done clear
C) CAN done clear
D) ammonium sulphate done clear
View Answer play_arrowquestion_answer76) A condensation polymer among the following polymers is:
A) teflon done clear
B) polysterene done clear
C) PVC done clear
D) decron done clear
View Answer play_arrowquestion_answer77) A compound that undergoes bromination easily is:
A) toluene done clear
B) benzoic acid done clear
C) phenol done clear
D) benzene done clear
View Answer play_arrowquestion_answer78) A sugar that is not a disacharide among the following is:
A) galactose done clear
B) lactose done clear
C) maltose done clear
D) sucrose done clear
View Answer play_arrowquestion_answer79) DryiAg soil invariably contains:
A) butyric acid done clear
B) stearic acid done clear
C) lauric acid done clear
D) linoleic acid done clear
View Answer play_arrowquestion_answer80) Hetrocyclic amino acid among these compound is:
A) lysine done clear
B) tyrosin done clear
C) proline done clear
D) serine done clear
View Answer play_arrowquestion_answer81) Aluminium oxide is not reduced by chemical reactions since:
A) reducing agent contaminate done clear
B) the process pollute the environment done clear
C) aluminium oxide is highly stable done clear
D) aluminium oxide is reactive. done clear
View Answer play_arrowquestion_answer82) Iron loses magnetic property at:
A) melting point done clear
B) 1000 K done clear
C) Curie point done clear
D) boiling point done clear
View Answer play_arrowquestion_answer83) An example for a double salt is:
A) potassium ferricyanide done clear
B) cobalt hexamine chloride done clear
C) cuprous sulphate done clear
D) Mohr's salt. done clear
View Answer play_arrowquestion_answer84) The set of compounds in which the reactivity of halogen atom in the ascending order is:
A) vinyl chloride, chloroethane, chlorobenzene done clear
B) vinyl chloride, chlorobenzene, chloroethane done clear
C) chloroethane, chlorobenzene, vinyl chloride done clear
D) chlorobenzene, vinyl chloride, chloroethane. done clear
View Answer play_arrowquestion_answer85) Methanal is:
A) \[C{{H}_{3}}CHO\] done clear
B) \[C{{H}_{3}}COC{{H}_{3}}\] done clear
C) \[C{{H}_{2}}OH\] done clear
D) \[HCHO.\] done clear
View Answer play_arrowquestion_answer86) In the case of auto catalysis:
A) product catalysis done clear
B) solvent catalysis done clear
C) reactant catalysis done clear
D) heat produced in the reaction catalysis. done clear
View Answer play_arrowquestion_answer87) Which of the following statements is true?
A) \[\Delta E\]is always greater than \[\Delta H\] done clear
B) \[\Delta E\]is always less than \[\Delta H\] done clear
C) \[\Delta E\]may be lesser or greater or equal to \[\Delta H\] done clear
D) \[\Delta E\]is always proportional to \[\Delta H\] done clear
View Answer play_arrowquestion_answer88) Order of reaction is decided by:
A) molecularity done clear
B) pressure done clear
C) temperature done clear
D) mechanism of reaction as well as relative concentration of reactants done clear
View Answer play_arrowquestion_answer89) Half-life of a reaction is found to be inversely proportional to the cube of initial concentration. The order of reaction is:
A) 5 done clear
B) 2 done clear
C) 4 done clear
D) 3 done clear
View Answer play_arrowquestion_answer90) Which among the following statement is false?
A) The adsorption may be mono layered or multilayered. done clear
B) Particle size of adsorbent will not affect the amount of adsorption. done clear
C) Increase of pressure increases amount of adsorption. done clear
D) Increase of temperature may decrease the amount of adsorption. done clear
View Answer play_arrowquestion_answer91) Purine derivative among the following bases is:
A) cytosine done clear
B) guanine done clear
C) uracil done clear
D) thymine. done clear
View Answer play_arrowquestion_answer92) A drug that is antipyretic as well as analgesic is:
A) penicillin done clear
B) chloroquin done clear
C) para acetamidophenol done clear
D) chloropromazine hydrochloride. done clear
View Answer play_arrowquestion_answer93) For a \[f-\]orbital the values of \[m\]are:
A) \[=1,0,+1\] done clear
B) \[0,+1,0,+1,+\,2\] done clear
C) \[-2,-1,0+1,+\,2\] done clear
D) \[-3,-2,-1,0,+1,+\,2,+\,3\] done clear
View Answer play_arrowquestion_answer94) Chloride ion and potassium ion are isoelectronic. Then:
A) potassium ion is relatively bigger done clear
B) depends on the other cation and anion done clear
C) their size are same done clear
D) chloride ion is bigger than potassium ion. done clear
View Answer play_arrowquestion_answer95) In a reversible reaction a catalyst will affect:
A) the rate of forward reaction and reverse reaction done clear
B) neither the forward reaction nor the rate of reverse reaction done clear
C) the rate of forward reaction done clear
D) the rate of reverse reaction. done clear
View Answer play_arrowquestion_answer96) Pentavalence in phosphorous is more stable when compared to that of nitrogen even through they belong to same group is due to:
A) reactivity of phosphorous done clear
B) inert nature of nitrogen done clear
C) dissimilar electronic configuration done clear
D) larger size of phosphorous atom. done clear
View Answer play_arrowquestion_answer97) Aqueous solutions of hydrogen sulphide and sulphurdioxide when mixed together, yield:
A) sulphur trioxide and water done clear
B) hydrogen and sulphurous acid done clear
C) sulphur and water done clear
D) hydrogen peroxide and sulphur. done clear
View Answer play_arrowquestion_answer98) A salt producing hydrocarbon among these compounds is:
A) ethane done clear
B) methane done clear
C) ethene done clear
D) ethyne done clear
View Answer play_arrowquestion_answer99) Octane number is zero for:
A) \[n-\]octane done clear
B) \[iso-\]octane done clear
C) \[n-\]heptane done clear
D) \[iso-\] heptane done clear
View Answer play_arrowquestion_answer100) The intensive property among these quantities is:
A) enthalpy done clear
B) mass/volume done clear
C) mass done clear
D) volume done clear
View Answer play_arrowquestion_answer101) 30g of Mg and 30g of oxygen are reacted and the residual mixture contains:
A) \[45\text{ }g\]of \[MgO\]and\[~15\text{ }g\] of\[{{O}_{2}}\] done clear
B) \[50\text{ }g\]of\[~MgO\] and \[10\text{ }g\]of\[~{{O}_{2}}\] done clear
C) \[60\text{ }g\] of\[MgO\]only done clear
D) \[~40\text{ }g\] of \[MgO\]and \[20\text{ }g\]of \[{{O}_{2}}.\] done clear
View Answer play_arrowquestion_answer102) 3g of oxide of a metal is converted to chloride completely and it yielded 5 g of chloride. The equivalent weight of metal is:
A) \[12\] done clear
B) \[~20\] done clear
C) \[33.25~~~~~~~~~~\] done clear
D) \[2.325\] done clear
View Answer play_arrowquestion_answer103) 20 ml of \[\text{0}\text{.25}\,\text{N}\]strong acid and 30 ml \[\text{0}\text{.2}\,\text{N}\]of strong base are mixed; the resulting solution is:
A) \[\text{0}\text{.02 N}\]acidic done clear
B) \[0.025\]N basic done clear
C) \[\text{ }\!\!~\!\!\text{ 0}\text{.02 N}\] basic done clear
D) \[\text{ }\!\!~\!\!\text{ 0}\text{.025 N}\]acidic done clear
View Answer play_arrowquestion_answer104) The rate of forward reaction is two times that of reverse reaction at a given temperature and identical concentration. \[{{K}_{\text{equilibrium}}}\]is:
A) \[2.5\] done clear
B) \[2.0\] done clear
C) \[0.5\] done clear
D) \[1.5\] done clear
View Answer play_arrowquestion_answer105) A chemical reaction was carried out at 300 K and 280 K. The rate constants were found to be \[{{K}_{1}}\]and \[{{K}_{2}}\]respectively. Then:
A) \[{{K}_{2}}=0.25\,{{K}_{1}}\] done clear
B) \[{{K}_{2}}\approx 0.5\,{{K}_{1}}\] done clear
C) \[{{K}_{2}}\approx 4{{K}_{1}}\] done clear
D) \[{{K}_{2}}\approx 2{{K}_{1}}\] done clear
View Answer play_arrowquestion_answer106) Ammonium ion is:
A) neither an acid nor base done clear
B) both an acid and a base done clear
C) a conjugate acid done clear
D) a conjugate base done clear
View Answer play_arrowquestion_answer107) Water is a:
A) amphoteric acid done clear
B) aprotic solvent done clear
C) protophobic solvent done clear
D) protophilic solvent done clear
View Answer play_arrowquestion_answer108) A smuggler could not carry gold by depositing iron on gold surface since:
A) gold has higher standard reduction potential than iron done clear
B) gold has lower standard reduction potential than iron done clear
C) gold is denser done clear
D) iron rusts. done clear
View Answer play_arrowquestion_answer109) A, is an aqueous acid; B is an aqueous base. They are diluted separately, then:
A) pH of A decreases and pH of B increases done clear
B) pH of A increases and pH of B decreases till pH in each case is 7 done clear
C) pH of A and B increase done clear
D) pH of B and A decrease. done clear
View Answer play_arrowquestion_answer110) \[_{z}{{X}^{M}}+{{\,}_{2}}H{{e}^{4}}\to {{\,}_{15}}{{P}^{30}}+{{\,}_{0}}{{n}^{1}}.\]Then:
A) \[Z=12,M=27\] done clear
B) \[Z=13,M=27\] done clear
C) \[Z=12,M=17\] done clear
D) \[Z=13,M=28\] done clear
View Answer play_arrowquestion_answer111) Kinetic theory of gases presumes that collision between the molecules to be perfectly elastic because:
A) collisions will not split the molecule done clear
B) the molecules are tiny done clear
C) the molecules are rigid done clear
D) the temperature remains constant irrespective of collisions. done clear
View Answer play_arrowquestion_answer112) Bio-gas production is more useful when compared to the direct use of dung because:
A) both fuel value and fertilizer value are effectively utilized done clear
B) production of bio-gas involves less labour done clear
C) fuel is quickly produced done clear
D) the fertilizer produced is a fluid. done clear
View Answer play_arrowquestion_answer113) Compounds with high heat of formation are less stable because:
A) high temperature is required to synthesise them done clear
B) molecules of such compounds are distorted done clear
C) it is difficult to synthesise them done clear
D) energy rich state leads to instability. done clear
View Answer play_arrowquestion_answer114) In the case of a radio isotope the value of \[{{T}_{1/2}}\]and \[\lambda \]are identical in magnitude. The value is:
A) \[0.693\] done clear
B) \[{{(0.693)}^{1/2}}\] done clear
C) \[1/0.693\] done clear
D) \[{{(0.693)}^{2}}\] done clear
View Answer play_arrowquestion_answer115) Heat of neutralisation of weak acid and strong base is less than the heat of neutralisation of strong acid and strong base due to:
A) energy has to be spent for the total dissociation of weak acid done clear
B) salt of weak acid and strong base is not stable done clear
C) incomplete dissociation of weak acid done clear
D) incomplete neutralisation of weak acid. done clear
View Answer play_arrowquestion_answer116) A radio isotope will not emit:
A) gamma and alpha rays simultaneously done clear
B) gamma rays only done clear
C) alpha and beta rays simultaneously done clear
D) beta and gamma rays simultaneously. done clear
View Answer play_arrowquestion_answer117) Heat treatment alters the properties of steel due to:
A) chemical reaction on heating done clear
B) partial rusting done clear
C) change in the residual energy done clear
D) change in the lattice structure due to differential rate of cooling. done clear
View Answer play_arrowquestion_answer118) Chemical bond implies:
A) attraction and repulsion done clear
B) attraction and repulsion balanced at a particular distance done clear
C) attraction done clear
D) repulsion. done clear
View Answer play_arrowquestion_answer119) Grignard reagent is not prepared in aqueous medium but prepared in either medium. Because:
A) the reagent reacts with water done clear
B) the reagent becomes inactive in water done clear
C) it is insoluble in water done clear
D) the reagent is highly reactive in water. done clear
View Answer play_arrowquestion_answer120) A lone pair of electrons in an atom implies:
A) a pair of valence electrons not involved in bonding done clear
B) a pair of electrons involved in bonding done clear
C) a pair of electrons done clear
D) a pair of valence electrons done clear
View Answer play_arrowquestion_answer121) The value of \[\underset{x\to \pi }{\mathop{\lim }}\,\frac{\sqrt{2+\cos x}-1}{{{(\pi -x)}^{2}}}\]is :
A) 1/4 done clear
B) 2 done clear
C) 1/2 done clear
D) zero done clear
View Answer play_arrowquestion_answer122) If \[{{\tan }^{-1}}\frac{x+1}{x-1}+{{\tan }^{-1}}\frac{x-1}{x}={{\tan }^{-1}}(-7)\] then the value of \[x\] is:
A) zero done clear
B) \[~-2\] done clear
C) 1 done clear
D) 2 done clear
View Answer play_arrowquestion_answer123) Let the function\[f:R\to R\] be defined by \[f(x)=2x+\cos x\]then \[f:\]
A) has maximum at \[x=0\] done clear
B) has minimum at \[x=\pi \] done clear
C) is an increasing function done clear
D) is a decreasing done clear
View Answer play_arrowquestion_answer124) If \[{{\cos }^{-1}}\sqrt{p}+{{\cos }^{-1}}\sqrt{1-p}+{{\cos }^{-1}}\sqrt{1-q}\]\[=\frac{3\pi }{4}\] then the value of \[q\] is:
A) \[2/\sqrt{2}\] done clear
B) \[1\] done clear
C) \[1/2\] done clear
D) \[1/3\] done clear
View Answer play_arrowquestion_answer125) If the equation \[3{{x}^{2}}+xy-{{y}^{2}}-3x+6y+k=0\]represents a pair of lines, then the value of k is:
A) 9 done clear
B) 1 done clear
C) \[-9\] done clear
D) zero done clear
View Answer play_arrowquestion_answer126) The acute angle in radians between the minute the hour hand of a clock when the time is 4 hours 20 minutes is:
A) \[\pi /18\] done clear
B) zero done clear
C) \[\pi /6\] done clear
D) \[\pi /9\] done clear
View Answer play_arrowquestion_answer127) Let \[n\ge 5\]and\[b\ne 0.\]In the binomial expansion of \[{{(a-b)}^{n}},\] the sum of the 5th and 6th terms is zero then a/b equals:
A) \[\frac{5}{n-4}\] done clear
B) \[\frac{1}{5(n-4)}\] done clear
C) \[\frac{n-5}{6}\] done clear
D) \[\frac{n-4}{5}\] done clear
View Answer play_arrowquestion_answer128) In a H.P. \[pth\]term is q and \[qth\]term is p. Then the \[pqth\]term is:
A) zero done clear
B) \[\frac{p+q}{pq}\] done clear
C) 1 done clear
D) \[\frac{pq}{p+q}\] done clear
View Answer play_arrowquestion_answer129) Orbit of the earth around the sun is an ellipse with sun at one of its foci. If the semi-major axis is 150 million kilometers and the eccentricity is 1/60. The difference between the maximum and the minimum distance between the earth and the sun is:
A) 20 million km. done clear
B) 5 million km. done clear
C) 50 million km. done clear
D) 2.5 million km. done clear
View Answer play_arrowquestion_answer130) If \[{{\log }_{2}}7=x,\]then \[x\]is:
A) a rational number such that \[0<x<2\] done clear
B) an rational number done clear
C) a rational number such that \[2<x<3\] done clear
D) a prime number of the form \[7x+2\] done clear
View Answer play_arrowquestion_answer131) The value of \[{{\cos }^{2}}\frac{\pi }{12}+{{\cos }^{2}}\frac{\pi }{4}+{{\cos }^{2}}\frac{5\pi }{12}\]is
A) \[2/3\] done clear
B) \[\frac{2}{3+\sqrt{3}}\] done clear
C) \[3/2\] done clear
D) \[\frac{3+\sqrt{3}}{2}\] done clear
View Answer play_arrowquestion_answer132) If \[0<x<\frac{\pi }{2},\]then the largest angle of a triangle whose sides are \[1,\,\sin x,\cos x\]is:
A) \[\pi /3\] done clear
B) \[\pi /2\] done clear
C) \[\pi \] done clear
D) \[\frac{\pi }{2}-x\] done clear
View Answer play_arrowquestion_answer133) The general solution of the equation \[\sin \theta +\cos \theta =1\]is:
A) \[\theta =2n\pi +\frac{\pi }{2},n=0,\pm 1,\,\pm 2\] done clear
B) \[\theta -n\pi +\{{{(-1)}^{n}}+1\}\pi /4,n=0,\pm \,1,\pm \,2\] done clear
C) \[\theta =n\pi +\{{{(-1)}^{n}}-1\}\frac{\pi }{4},n=0,\pm \,1,\,\pm 2\] done clear
D) \[\theta =2n\pi ,n=0,\pm 1,\,\pm 2+...\] done clear
View Answer play_arrowquestion_answer134) If \[y={{\tan }^{-1}}\left( \frac{\cos x-\sin x}{\cos x+\sin x} \right),\]then \[\frac{dy}{dx}=\]
A) \[-1\] done clear
B) \[\sin 2\pi \] done clear
C) \[\cos 2x\] done clear
D) zero done clear
View Answer play_arrowquestion_answer135) The differential of \[{{e}^{{{x}^{3}}}}\]with respect to \[\log x\] is:
A) \[{{e}^{{{x}^{3}}}}\] done clear
B) \[3{{x}^{2}}{{e}^{{{x}^{3}}}}+3{{x}^{2}}\] done clear
C) \[3{{x}^{3}}{{e}^{{{x}^{3}}}}\] done clear
D) \[3{{x}^{3}}{{e}^{{{x}^{3}}}}\] done clear
View Answer play_arrowquestion_answer136) If 5 is one root of the equations \[\left| \begin{matrix} x & 3 & 7 \\ 2 & x & -2 \\ 7 & 8 & x \\ \end{matrix} \right|=0,\] then the other two roots of the equation are:
A) \[-2,-7\] done clear
B) \[-2,7\] done clear
C) \[2,-7\] done clear
D) \[2,7\] done clear
View Answer play_arrowquestion_answer137) The value of\[\sum\limits_{k=1}^{6}{\left( \sin \frac{2\pi k}{7}-i\cos \frac{2\pi k}{7} \right)}\]is:
A) \[i\] done clear
B) zero done clear
C) \[-i\] done clear
D) \[-1\] done clear
View Answer play_arrowquestion_answer138) If \[x=2\cot \,t+\cos 2t,\]\[y=2\sin t-\sin 2t\]then \[\frac{dy}{dx}\]at \[t=\frac{\pi }{4}\]is:
A) \[1-\sqrt{2}\] done clear
B) \[-(1+\sqrt{2})\] done clear
C) \[\sqrt{2}\] done clear
D) \[1/\sqrt{2}\] done clear
View Answer play_arrowquestion_answer139) If \[\vec{a},\vec{b},\vec{c}\]are mutually perpendicular unit vectors, then \[|\vec{a}+\vec{b}+\vec{c}|\]is equal to:
A) 3 done clear
B) \[\sqrt{3}\] done clear
C) zero done clear
D) 1 done clear
View Answer play_arrowquestion_answer140) If ABCDEF is a regular hexagon then \[\overrightarrow{AD}+\overrightarrow{EB}+\overrightarrow{FC}\] equals:
A) zero done clear
B) \[2\overrightarrow{AB}\] done clear
C) \[4\overrightarrow{AB}\] done clear
D) \[3\overrightarrow{AB}\] done clear
View Answer play_arrowquestion_answer141) The value of \[\int_{{}}^{{}}{\frac{dx}{\sqrt{2x-{{x}^{2}}}}}\]is:
A) \[{{\sin }^{-1}}(1-x)+c\] done clear
B) \[{{\sin }^{-1}}(x-1)+c\] done clear
C) \[{{\sin }^{-1}}(1+x)+c\] done clear
D) \[-\sqrt{2x-{{x}^{2}}}+c\] done clear
View Answer play_arrowquestion_answer142) Which of the following functions is a solution of the differential equation\[{{\left( \frac{dy}{dx} \right)}^{2}}-x\left( \frac{dy}{dx} \right)+y=0\]
A) \[y=2x-4\] done clear
B) \[y=2{{x}^{2}}-4\] done clear
C) \[y=2\] done clear
D) \[y=2x\] done clear
View Answer play_arrowquestion_answer143) \[y=a{{e}^{mx}}+b{{e}^{-mx}}\]satisfies which of the following differential equations:
A) \[\frac{dy}{dx}+my=0\] done clear
B) \[\frac{dy}{dx}-my=0\] done clear
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\] done clear
D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{m}^{2}}y=0\] done clear
View Answer play_arrowquestion_answer144) Solution of the differential equation\[\frac{dx}{x}+\frac{dy}{y}=0\]is:
A) \[\frac{1}{x}+\frac{1}{y}=c\] done clear
B) \[\log x\log y=c\] done clear
C) \[xy=c\] done clear
D) \[x+y=c\] done clear
View Answer play_arrowquestion_answer145) The value of \[\int_{{}}^{{}}{{{x}^{3}}\log x\,dx}\]is:
A) \[\frac{1}{16}(4{{x}^{4}}\log x-{{x}^{4}}+c)\] done clear
B) \[\frac{1}{8}({{x}^{4}}\log x-4{{x}^{4}}+c)\] done clear
C) \[\frac{1}{16}(4{{x}^{4}}\log x+{{x}^{4}}+c)\] done clear
D) \[\frac{{{x}^{4}}\log x}{4}+c\] done clear
View Answer play_arrowquestion_answer146) The equation to the tangent to the curve \[y=b{{e}^{-x/a}}\]at the point where it crosses the \[y-\]axis is:
A) \[ax+by=1\] done clear
B) \[\frac{x}{a}-\frac{y}{b}=1\] done clear
C) \[\frac{x}{a}+\frac{y}{b}=1\] done clear
D) \[ax-by=1\] done clear
View Answer play_arrowquestion_answer147) The value of\[\int_{0}^{\pi }{\frac{dx}{5+3\cos x}}\]is:
A) \[\pi /4\] done clear
B) \[\pi /8\] done clear
C) \[\pi /2\] done clear
D) zero done clear
View Answer play_arrowquestion_answer148) If the vectors \[3\vec{i}+\vec{j}-2\vec{k},\vec{i}+2\vec{j}-3\vec{k},\]\[3\vec{i}+\lambda \vec{j}+5\vec{k}\] are co-planar, the value of is:
A) \[-4\] done clear
B) \[4\] done clear
C) 8 done clear
D) \[-8\] done clear
View Answer play_arrowquestion_answer149) Equation of the tangent and the normal drawn at the point (6, 0) on the ellipse\[\frac{{{x}^{2}}}{36}+\frac{{{y}^{2}}}{9}=1\]respectively are:
A) \[x=6,y=0\] done clear
B) \[y+x-6=0,y-x+6=0\] done clear
C) \[x=0,y=3\] done clear
D) \[x=-6,y=0\] done clear
View Answer play_arrowquestion_answer150) The equation to the parabola whose focus is \[(1,-1)\] and the directrix is \[x+y+7=0\]is:
A) \[{{x}^{2}}+{{y}^{2}}-2xy-18x-10y=0\] done clear
B) \[{{x}^{2}}-18x-10y-45=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-18x-10y-45=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-2xy-18x-10y-45=0\] done clear
View Answer play_arrowquestion_answer151) If\[\omega =-\frac{1}{2}+\frac{\sqrt{3i}}{2},\]the value of the determinant\[\left| \begin{matrix} 1 & \omega & {{\omega }^{2}} \\ \omega & {{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & \omega \\ \end{matrix} \right|\]is:
A) zero done clear
B) 3 done clear
C) \[-1\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer152) Two intersecting circles have their radii and 1 and\[\sqrt{3}\]meters. The distance between their centres is 2 meters. Then the overlapping area in sq. meters is:
A) \[\frac{19\pi +6\sqrt{3}}{6}\] done clear
B) \[\frac{5\pi +6\sqrt{3}}{6}\] done clear
C) \[\frac{\pi }{6}\] done clear
D) \[\frac{5\pi -6\sqrt{3}}{6}\] done clear
View Answer play_arrowquestion_answer153) Which of the statement in the following is false in respect of the conic\[{{x}^{2}}-3{{y}^{2}}-4x-6y-11=0\]
A) length of the latus rectum is \[4/\sqrt{3}\] done clear
B) asymptotes, intersect at right angles done clear
C) the eccentricity of the conic is \[2/\sqrt{3}\] done clear
D) centre of the conic is \[(2,-1)\] done clear
View Answer play_arrowquestion_answer154) Let\[{{z}_{1}}\]and\[{{z}_{2}}\]be nth roots of unity which subtend a right angle at the origin. Then \[n\]must be of the form:
A) \[4k+3\] done clear
B) \[4k\] done clear
C) \[4k+3\] done clear
D) \[4k+2\] done clear
View Answer play_arrowquestion_answer155) The height of the cylinder of maximum volume inscribed in a sphere of radius ?a? is:
A) \[\frac{3a}{2}\] done clear
B) \[\frac{\sqrt{2}a}{3}\] done clear
C) \[\frac{a}{\sqrt{3}}\] done clear
D) \[\frac{2}{\sqrt{3a}}\] done clear
View Answer play_arrowquestion_answer156) For all positive value of \[x\] and \[y,\]the value of \[\frac{(1+x+{{x}^{2}})(1+y+{{y}^{2}})}{xy}\]is:
A) \[\le 9\] done clear
B) \[<9\] done clear
C) \[\ge 9\] done clear
D) \[>9\] done clear
View Answer play_arrowquestion_answer157) How many nine digit numbers can be formed using the digits 2, 2, 3, 3, 5,5, 8, 8, 8 so that the odd digits occupy even positions:
A) 180 done clear
B) 7560 done clear
C) 60 done clear
D) 16 done clear
View Answer play_arrowquestion_answer158) There are points in a plane of which p points are collinear. How many lines can be formed from these points:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer159) If then is:
A) done clear
B) done clear
C) 1 done clear
D) zero done clear
View Answer play_arrowquestion_answer160) If for a triangle then the value ofis:
A) done clear
B) done clear
C) 1 done clear
D) done clear
View Answer play_arrowquestion_answer161) The value of is:
A) done clear
B) done clear
C) zero done clear
D) 1 done clear
View Answer play_arrowquestion_answer162) The value of is:
A) done clear
B) done clear
C) done clear
D) zero done clear
View Answer play_arrowquestion_answer163) The area of the figure bounded by the curves and and the co-ordinate and is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer164) If
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer165) Let if is continuous at the value of k is:
A) done clear
B) done clear
C) zero done clear
D) 1 done clear
View Answer play_arrowquestion_answer166) Let M be the set of allmatrices with eptries from the set of real number R. Then the function defined by for ever is:
A) one-one and onto done clear
B) neither one-one nor onto done clear
C) one-one but not onto done clear
D) onto but not one-one done clear
View Answer play_arrowquestion_answer167) For how many values of x in the closed interval the matrixis singular:
A) zero done clear
B) done clear
C) 1 done clear
D) 3 done clear
View Answer play_arrowquestion_answer168) is a group under matrix multiplication. Then which one of the following statements in respect of G is ture.
A) is the inverse of itself done clear
B) G is a finite group done clear
C) is not an element of G done clear
D) is an element of G. done clear
View Answer play_arrowquestion_answer169) If two circles and intersect in two distinct points, then:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer170) If are four distinct points on a circle, then is equal to:
A) 4 done clear
B) done clear
C) 1 done clear
D) zero done clear
View Answer play_arrowquestion_answer171) Which of the following linear congruences has no solution:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer172) The digit in the unit place of the number is:
A) 6 done clear
B) 7 done clear
C) zero done clear
D) 3 done clear
View Answer play_arrowquestion_answer173) If then at the function is:
A) continuous but not differentiable done clear
B) differentiable but not continuous done clear
C) continuous and differentiable done clear
D) not continuous done clear
View Answer play_arrowquestion_answer174) The perimeter of a sector is P. The area of the sector is maximum when its radius is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer175) Which one of the following subsets of is a subgroup of
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer176) The False statement in the following is:
A) is contradiction done clear
B) is a contradiction done clear
C) P is a tautology done clear
D) is a tautology. done clear
View Answer play_arrowquestion_answer177) In the groupunder addition modulo
A) zero done clear
B) 2 done clear
C) 3 done clear
D) 5 done clear
View Answer play_arrowquestion_answer178) The functionis:
A) an even function done clear
B) an odd function done clear
C) a periodic function done clear
D) none of these done clear
View Answer play_arrowquestion_answer179) The function is:
A) increasing on and decreasing on done clear
B) decreasing on and increasing on done clear
C) increasing on and decreasing on done clear
D) decreasing on and increasing on done clear
View Answer play_arrowquestion_answer180) The area of the circle centred at (1, 2) and passing through is:
A) done clear
B) done clear
C) done clear
D) none of these done clear
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