question_answer1) Which of the following statements is wrong?
A) Voltmeter should have high resistance done clear
B) Ammeter should have low resistance done clear
C) Ammeter is placed in parallel across the conductor in a circuit done clear
D) Voltmeter is placed in parallel across the conductor in a circuit done clear
View Answer play_arrowquestion_answer2) As the temperature of hot junction increases the thermo emf
A) always increases done clear
B) always decreases done clear
C) may increase or decrease done clear
D) always remains constant done clear
View Answer play_arrowquestion_answer3) A proton and an \[\alpha \]-particle enter a uniform magnetic field perpendicularly with the same speed. If proton takes 25\[\mu F\] to make 5 revolutions, then the periodic time for the \[\alpha \]-particle would be
A) 50\[\mu s\] done clear
B) 25 \[\mu s\] done clear
C) 10 \[\mu s\] done clear
D) 5\[\mu s\] done clear
View Answer play_arrowquestion_answer4) Two parallel conductors A and B of equal length carry currents i and 10 i, respectively, in the same direction. Then
A) A and B will repel each other with same force done clear
B) A and B will attract each other with same force done clear
C) A will attract B, but B will repel A done clear
D) A and B will attract each other with different forces done clear
View Answer play_arrowquestion_answer5) An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is termed to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is
A) 200 Hz done clear
B) 150 Hz done clear
C) 100 Hz done clear
D) 250 Hz done clear
View Answer play_arrowquestion_answer6) Two slits 4 mm apart, are illuminated by light of wavelength 6000\[\overset{0}{\mathop{A}}\,\]. What will be the fringe width on a screen placed 2 m from the slits?
A) 0.12 mm done clear
B) 0.3 mm done clear
C) 3.0 mm done clear
D) 4.0 mm done clear
View Answer play_arrowquestion_answer7) A thin prism \[{{P}_{1}}\] of angle \[4{}^\circ \] and refractive index \[1.54{}^\circ \] is combined with another thin prism \[{{P}_{2}}\] of refractive index 1.72 to produce dispersion without deviation. The angle of \[{{P}_{2}}\] is
A) \[4{}^\circ \] done clear
B) \[5.33{}^\circ \] done clear
C) \[2.6{}^\circ \] done clear
D) \[3{}^\circ \] done clear
View Answer play_arrowquestion_answer8) While viewing a distant object with a telescope suddenly a housefly sits on objective lens. The correct statement is that
A) housefly will be seen enlarged in image done clear
B) housefly will be seen reduced in image done clear
C) intensity of image will be decreased done clear
D) intensity of image will be increased done clear
View Answer play_arrowquestion_answer9) A capacitor of capacitance 5\[\mu F\] is connected as shown in the figure. The internal resistance of the cell is 0.5\[\Omega \] . The amount of charge on the capacitor plate is
A) 10 \[\Omega C\] done clear
B) 5\[\Omega C\] done clear
C) 6\[\Omega C\] done clear
D) 10.2 \[\Omega C\] done clear
View Answer play_arrowquestion_answer10) A charge of \[{{10}^{-9}}\] C is placed on each of the 64 identical drops of radius 2 cm. They are then combined to form a bigger drop. Its potential will be
A) \[7.2\times {{10}^{3}}V\] done clear
B) \[7.2\times {{10}^{2}}V\] done clear
C) \[1.44\times {{10}^{2}}V\] done clear
D) \[1.44\times {{10}^{3}}V\] done clear
View Answer play_arrowquestion_answer11) A particle moves in the xy-plane under the action of a force F such that the components of its linear momentum p at any time f are \[{{P}_{x}}=2\cos \,t,\,{{P}_{y}}=\sin \,t.\] The angle between F and p at time t is
A) \[{{90}^{\text{o}}}\] done clear
B) \[{{0}^{\text{o}}}\] done clear
C) \[{{180}^{\text{o}}}\] done clear
D) \[{{30}^{\text{o}}}\] done clear
View Answer play_arrowquestion_answer12) A fighter plane is moving in a vertical circle of radius r. Its minimum velocity at the highest point A of the circle will be
A) \[\sqrt{3gr}\] done clear
B) \[\sqrt{2gr}\] done clear
C) \[\sqrt{gr}\] done clear
D) \[\sqrt{gr/2}\] done clear
View Answer play_arrowquestion_answer13) In Millikans oil drop experiment, a charged drop of mass \[1.8\times {{10}^{-13}}\]kg is stationary between its plates. The distance between its plates is 0.9 cm and potential difference is 2000 V. The number of electrons in the drop is
A) 500 done clear
B) 50 done clear
C) 5 done clear
D) 10 done clear
View Answer play_arrowquestion_answer14) Decay constant of radium is \[\lambda \]. By a suitable process its compound radium bromide is obtained. The decay constant of radium bromide will be
A) \[\lambda \] done clear
B) more than \[\lambda \] done clear
C) less than \[\lambda \] done clear
D) zero done clear
View Answer play_arrowquestion_answer15) Rn decays into Po by emitting an \[\alpha \]-particle with half-life of 4 days. A sample contains \[6.4\times {{10}^{10}}\] atoms of Rn after 12 days, the number of atoms of Rn left in the sample will be
A) \[3.2\times {{10}^{10}}\] done clear
B) \[0.53\times {{10}^{10}}\] done clear
C) \[2.1\times {{10}^{10}}\] done clear
D) \[0.8\times {{10}^{10}}\] done clear
View Answer play_arrowquestion_answer16) The energy gap between the valence and conduction bands of an insulator is about
A) 0.1 eV done clear
B) 1.0 eV done clear
C) 5.0 eV done clear
D) zero done clear
View Answer play_arrowquestion_answer17) A conducting wire is moving towards right in a magnetic field B. The direction of induced current in the wire is shown in the figure. The direction of magnetic field will be
A) in the plane of paper pointing towards right done clear
B) in the plane of paper pointing towards left done clear
C) perpendicular to the plane of paper and downwards done clear
D) perpendicular to the plane of paper and upwards done clear
View Answer play_arrowquestion_answer18) An electron moving with velocity \[2\times {{10}^{-7}}\]m/s, describes a circle in a magnetic field of strength \[2\times {{10}^{-2}}T\,.\] If\[\frac{e}{m}\] of electron is \[1.76\times {{10}^{11}}C/kg\]. Then the diameter of the circle will be
A) 11 cm done clear
B) 1.1 cm done clear
C) 1.1 mm done clear
D) 1.1 m done clear
View Answer play_arrowquestion_answer19) In an AC circuit the potential difference and current are represented respectively by V=100 sin (100t) volt,\[I=100\sin \left( 100t+\frac{\pi }{3} \right)\]milliampere. The power in the circuit is
A) 2.5 W done clear
B) 5 W done clear
C) 10 W done clear
D) 104 W done clear
View Answer play_arrowquestion_answer20) Escape velocity from earths surface is 11 km/s. If radius of a planet is double than that of earth and density is same as that of earth, then the escape velocity from this planet will be
A) 5.5 km/s done clear
B) 11 km/s done clear
C) 16.5 km/s done clear
D) 22 km/s done clear
View Answer play_arrowquestion_answer21) The orbital angular momentum of a satellite revolving at a distance r from the centre is L. If the distance is increased to 16r, then the new angular momentum will be
A) 16 L done clear
B) 64 L done clear
C) \[\frac{L}{4}\] done clear
D) 4 L done clear
View Answer play_arrowquestion_answer22) The acceleration of a particle performing SHM is \[12cm/{{s}^{2}}\] at a distance of 3 cm from the mean position. Its time period is
A) 0.5 s done clear
B) 1.0 s done clear
C) 2.0 s done clear
D) 3.14 s done clear
View Answer play_arrowquestion_answer23) A soap bubble in vacuum has a radius of 3 cm and another soap bubble in vacuum has a radius of 4 cm. If the two bubbles coalesce under isothermal condition, then the radius of the new bubble is
A) 2.3 cm done clear
B) 4.5 cm done clear
C) 5 cm done clear
D) 7 cm done clear
View Answer play_arrowquestion_answer24) A \[10c{{m}^{3}}\] cube floats in water with a height of \[4\,c{{m}^{3}}\] remaining above the surface. The density of the material from which the cube is made is
A) 0.6 g \[c{{m}^{-3}}\] done clear
B) 1.0 g\[c{{m}^{-3}}\] done clear
C) 0.4 g \[c{{m}^{-3}}\] done clear
D) 0.24 g \[c{{m}^{-3}}\] done clear
View Answer play_arrowquestion_answer25) The heat flows through a rod of length 50 cm and area of cross-section 5 \[c{{m}^{2}}\]. Its ends are respectively at 25\[^{0}C\] and 125\[^{0}C\]. The coefficient of thermal conductivity of the material rod is \[0.092\text{ }kcal/m{}^\circ C\]. The temperature gradient of the rod is
A) \[2{}^\circ C/cm\] done clear
B) \[2{}^\circ C/m\] done clear
C) \[20{}^\circ C/cm\] done clear
D) \[{{20}^{o}}C/m\] done clear
View Answer play_arrowquestion_answer26) 5 mol of hydrogen gas is heated from 30\[^{0}C\] to 60\[^{0}C\] at constant pressure. Heat given to the gas is (given R = 2 cat/ mol deg)
A) 750 cal done clear
B) 630 cal done clear
C) 1050 cal done clear
D) 1470 cal done clear
View Answer play_arrowquestion_answer27) A fish at a depth of 12 cm in water is viewed by an observer on the bank of a lake. To what height the image of the fish is raised? (Refractive index of lake water = \[\frac{4}{3}\])
A) 9 cm done clear
B) 12 cm done clear
C) 3.8 cm done clear
D) 3 cm done clear
View Answer play_arrowquestion_answer28) The rest energy of an electron is 0.511 MeV. The electron is accelerated from rest to a velocity 0.5 c. The change in its energy will he
A) 0.026 MeV done clear
B) 0.051 MeV done clear
C) 0.079 MeV done clear
D) 0.105 MeV done clear
View Answer play_arrowquestion_answer29) In Millikans oil drop experiment, an oil drop carrying a charge Q is held stationary a potential difference 2400 V between the plates. To keep a drop of half the radius stationary, the potential difference had to be made 600V. What is the charge on the second drop?
A) \[\frac{Q}{4}\] done clear
B) \[\frac{Q}{2}\] done clear
C) Q done clear
D) \[\frac{3Q}{2}\] done clear
View Answer play_arrowquestion_answer30) Band spectrum is characteristic of the
A) atoms done clear
B) molecules done clear
C) amorphous solids done clear
D) crystalline solids done clear
View Answer play_arrowquestion_answer31) As a result of radioactive decay \[_{92}{{U}^{238}}\] is converted into \[_{91}P{{a}^{234}}\]. The particles emitted during this decay are
A) a proton and a neutron done clear
B) a proton and two \[\alpha \]-particles done clear
C) an\[\alpha -\]particle and a \[\beta \]-particle done clear
D) two p-particles and a proton done clear
View Answer play_arrowquestion_answer32) A p-type semiconductor has acceptor levels 57 meV above the valence band. The maximum wavelength of light required to create a hole
A) \[57\overset{0}{\mathop{A}}\,\] done clear
B) \[57\times {{10}^{-3}}\overset{0}{\mathop{A}}\,\] done clear
C) \[217105\overset{0}{\mathop{A}}\,\] done clear
D) \[11.61\times {{10}^{-33}}\overset{0}{\mathop{A}}\,\] done clear
View Answer play_arrowquestion_answer33) In an explosion a body breaks up into pieces of unequal masses. In this case
A) both parts will have numerically equal momentum done clear
B) lighter part will have more momentum done clear
C) heavier part will have more momentum done clear
D) both parts will have equal kinetic energy done clear
View Answer play_arrowquestion_answer34) A force of 10 N acts on a body of mass 20 kg for 10 s. Change in its momentum is
A) 5 kg m/s done clear
B) 100 kg m/s done clear
C) 200 kg m/s done clear
D) 1000 kg m/s done clear
View Answer play_arrowquestion_answer35) In which case does the potential energy decrease?
A) On compressing a spring done clear
B) On stretching a spring done clear
C) On moving a body against gravitational force done clear
D) On the rising of an air bubble in water done clear
View Answer play_arrowquestion_answer36) A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
A) when the mass is at the highest point of the circle done clear
B) when the mass is at the lowest point of the circle done clear
C) when the wire is horizontal done clear
D) at an angle of \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]from the upward Vertical done clear
View Answer play_arrowquestion_answer37) The time taken by AC of 50 Hz in reaching from zero to the maximum value is
A) \[50\times {{10}^{-3}}s\] done clear
B) \[5\times {{10}^{-3}}s\] done clear
C) \[1\times {{10}^{-3}}s\] done clear
D) \[2\times {{10}^{-3}}s\] done clear
View Answer play_arrowquestion_answer38) The molar heat capacity of rock salt at low temperature varies with temperature according to Debyes \[{{T}^{3}}\] law Thus \[C=k\frac{{{T}^{3}}}{{{\theta }^{3}}}\] where k = 1940 J mol\[Jmo{{l}^{-1}}{{k}^{-1}}\] Calculate how much heat is required to raise the temperature of 2 moles of rock salt from 10 K to 50 K
A) 800 J done clear
B) 373 J done clear
C) 273 J done clear
D) None of these done clear
View Answer play_arrowquestion_answer39) The velocity of an electron in the second orbit of sodium atom (atomic number =11) is r. The velocity of an electron in its fifth orbit will be
A) v done clear
B) \[\frac{22}{5}v\] done clear
C) \[\frac{5}{2}\] done clear
D) \[\frac{2}{5}v\] done clear
View Answer play_arrowquestion_answer40) . A charged particle enters a magnetic Held H with its initial velocity making an angle of 45? with H. The path of the particle will be
A) a straight line done clear
B) a circle done clear
C) an ellipse done clear
D) a helix done clear
View Answer play_arrowquestion_answer41) A 10\[\mu F\] capacitor is charged to a potential difference of 50V and is connected to another uncharged capacitor in parallel. Now the common potential difference becomes 20V. The capacitance of second capacitor is
A) 10\[\mu F\] done clear
B) 20\[\mu F\] done clear
C) 30\[\mu F\] done clear
D) 15\[\mu F\] done clear
View Answer play_arrowquestion_answer42) An alternating voltage \[E=200\sqrt{2}\sin (100t)V\] is connected to a \[1\,\mu F\] capacitor through an AC ammeter. The reading of ammeter is
A) 10 mA done clear
B) 20 mA done clear
C) 40 mA done clear
D) 80 mA done clear
View Answer play_arrowquestion_answer43) In a step-up transformer the turn ratio is 1 : 2. A Leclanche cell (emf 1.5 V) is connected across the primary. The voltage across the secondary is
A) 3.0 V done clear
B) 0.75 V done clear
C) zero done clear
D) 1.5 V done clear
View Answer play_arrowquestion_answer44) If 10% of the current passes through a moving coil galvanometer of resistance \[99\,\Omega \]. Then the shunt resistance will be
A) 9.9\[\Omega \] done clear
B) 11\[\Omega \] done clear
C) 10 \[\Omega \] done clear
D) 9 \[\Omega \] done clear
View Answer play_arrowquestion_answer45) How much energy will necessary for making a body of 500 kg escape from the earth? (\[g=9.8\,m/{{s}^{2}},\] radius of the earth \[=6.4\,\times {{10}^{6}}m\])
A) about \[9.8\times {{10}^{6}}\,J\] done clear
B) about \[6.4\times {{10}^{8}}\,J\] done clear
C) about \[3.1\times {{10}^{10}}\,J\] done clear
D) about \[27.4\times {{10}^{12}}\,J\] done clear
View Answer play_arrowquestion_answer46) In a neon discharge tube\[2.9\times {{10}^{18}}N{{e}^{+}}\] ions move to the right each second while \[1.2\times {{10}^{18}}\] electrons move to the left per second, electrons charge is\[1.6\times {{10}^{19}}C\]. The current in the discharge tube is
A) 1 A, towards right done clear
B) 0.66 A, towards right done clear
C) 0.66 A, towards left done clear
D) zero done clear
View Answer play_arrowquestion_answer47) Water is falling on the blades of a turbine at a rate of 100 kg/s. If the height of the fall is 100 m, the power transferred to the turbine will be approximately
A) 100 kW done clear
B) 10 kW done clear
C) 1 kW done clear
D) 100 W done clear
View Answer play_arrowquestion_answer48) A metre scale is standing vertically on the earths surface on one of its end. It now falls on earth without slipping. Find the velocity with which the free end of the scale strikes the earth. \[(g=10\,m/{{s}^{2}})\]
A) 9.8 m/s done clear
B) 5.47 m/s done clear
C) 4.5 m/s done clear
D) 1 m/s done clear
View Answer play_arrowquestion_answer49) For germanium crystal, the forbidden energy gap in joule is
A) \[1.216\times {{10}^{-19}}\] done clear
B) \[1.76\times {{10}^{-19}}\] done clear
C) \[1.6\times {{10}^{-19}}\] done clear
D) zero done clear
View Answer play_arrowquestion_answer50) An electron is accelerated through a potential difference of 200 V. If e/ m for the electron be \[1.6\times {{10}^{11}}\] C/kg, the velocity acquired by the electron will be
A) \[8\times {{10}^{6}}\]m/s done clear
B) \[8\times {{10}^{5}}\]m/s done clear
C) \[5.9\times {{10}^{6}}\] m/s done clear
D) \[5.9\times {{10}^{5}}\] m/s done clear
View Answer play_arrowquestion_answer51) At what temperature will the resistance of a copper wire become three times its value at \[0{}^\circ C\]? (temperature coefficient of resistance for copper = \[4\times {{10}^{-3}}{{/}^{0}}C\])
A) \[{{400}^{\text{o}}}C\] done clear
B) \[{{450}^{\text{o}}}C\] done clear
C) \[{{500}^{\text{o}}}C\] done clear
D) \[{{550}^{\text{o}}}C\] done clear
View Answer play_arrowquestion_answer52) A coil having an area of \[2{{m}^{2}}\] is placed in a magnetic field which changes from \[1\,Wb/{{m}^{2}}\] to \[4\,Wb/{{m}^{2}}\,\] in 2 s. The emf induced in the coil will be
A) 4 V done clear
B) 3 V done clear
C) 2 V done clear
D) 1 V done clear
View Answer play_arrowquestion_answer53) A 10 m long copper wire while remaining in the east-west horizontal direction is falling down with a speed of 5.0 m/s. If the horizontal component of the earths magnetic field \[=0.3\times {{10}^{-4}}Wb/{{m}^{2}}\]the emf developed between the ends of the wires is
A) 0.15 V done clear
B) 1.5 V done clear
C) 0.15 mV done clear
D) 1.5 mV done clear
View Answer play_arrowquestion_answer54) A current of 1.6 A is passed through a solution of\[CuS{{O}_{4}}\]. How many \[C{{u}^{++}}\] ions are liberated in one minute? (electronic charge = \[1.6\times {{10}^{-19}}C\])
A) \[3\times {{10}^{20}}\] done clear
B) \[3\times {{10}^{19}}\] done clear
C) \[6\times {{10}^{20}}\] done clear
D) \[6\times {{10}^{19}}\] done clear
View Answer play_arrowquestion_answer55) A solenoid has an inductance of 60 H and a resistance of 30\[\Omega \]. If it is connected to a 100 V battery, how long will it take for the current to reach \[\frac{e-1}{e}\]= 63.2% of its final value?
A) 1 s done clear
B) 2 s done clear
C) e second done clear
D) 2 e second done clear
View Answer play_arrowquestion_answer56) Three blocks of masses \[{{m}_{1}},\,{{m}_{2}}\] are connected by massless strings as shown on a frictionless table. They are pulled with a force \[{{T}_{3}}\]= 40 N. If \[{{m}_{1}}=10\,kg,{{m}_{2}}=6\,kg\] and \[{{m}_{3}}=4\,kg,\] the tension \[{{T}_{2}}\]will be
A) 20 N done clear
B) 40 N done clear
C) 10 N done clear
D) 32 N done clear
View Answer play_arrowquestion_answer57) The force constant of weightless spring is 16 N/m. A body of mass 1.0 kg suspended from it is pulled down through 5 cm and then released. The maximum kinetic energy of the system (spring + body) will be
A) \[2\times {{10}^{-2}}J\] done clear
B) \[4\times {{10}^{-2}}J\] done clear
C) \[8\times {{10}^{-2}}J\] done clear
D) \[16\times {{10}^{-2}}J\] done clear
View Answer play_arrowquestion_answer58) A mass M is moving with a constant velocity on a line parallel to the x-axis. Its angular momentum with respect to the origin or z-axis
A) is zero done clear
B) remains constant done clear
C) goes on increasing done clear
D) goes on decreasing done clear
View Answer play_arrowquestion_answer59) Which of the following pairs is an isobar?
A) \[_{1}{{H}^{1\,\,}}and\,{{\,}_{1}}{{H}^{2}}\] done clear
B) \[_{1}{{H}^{2\,\,}}and\,{{\,}_{1}}{{H}^{3}}\] done clear
C) \[_{6}{{C}^{12\,\,}}and\,{{\,}_{6}}{{H}^{13}}\] done clear
D) \[_{15}{{P}^{30\,\,}}and\,{{\,}_{14}}S{{i}^{30}}\] done clear
View Answer play_arrowquestion_answer60) The half-life of the isotope \[_{11}N{{a}^{24\,\,}}\]is 15 h. How much time does it take for \[\frac{7}{8}\] th of a sample of this isotope to decay?
A) 75 h done clear
B) 65 h done clear
C) 55 h done clear
D) 45 h done clear
View Answer play_arrowquestion_answer61) The largest number of molecules is in
A) \[36\,\,g\]of water done clear
B) \[28\,\,g\]of\[C{{O}_{2}}\] done clear
C) \[46\,\,g\]of\[C{{H}_{3}}OH\] done clear
D) \[58\,\,g\]of\[{{N}_{2}}{{O}_{5}}\] done clear
View Answer play_arrowquestion_answer62) In the following reaction, which choice has value twice that of the equivalent weight of the oxidizing agent? \[S{{O}_{2}}+2{{H}_{2}}O\xrightarrow{{}}S+2{{H}_{2}}{{O}_{2}}\]
A) 16 done clear
B) 48 done clear
C) 64 done clear
D) 32 done clear
View Answer play_arrowquestion_answer63) Orbital is
A) circular path around the nucleus in which electrons are revolves done clear
B) space around the nucleus, where the probability of finding the electron is maximum done clear
C) amplitude of electrons wave done clear
D) None of the above done clear
View Answer play_arrowquestion_answer64) Which of the following sets of quantum number is not permitted?
A) \[n=3,\,\,l=3,\,\,m=0,\,\,s=+\frac{1}{2}\] done clear
B) \[n=3,\,\,l=2,\,\,m=\pm 2,\,\,s=-\frac{1}{2}\] done clear
C) \[n=3,\,\,l=2,\,\,m=-2,\,\,s=-\frac{1}{2}\] done clear
D) \[n=3,\,\,l=0,\,\,m=0,\,\,s=+\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer65) An element M has an atomic mass of 19 and atomic number 9, its ions is represented by
A) \[{{M}^{+}}\] done clear
B) \[{{M}^{2+}}\] done clear
C) \[{{M}^{-}}\] done clear
D) \[{{M}^{2-}}\] done clear
View Answer play_arrowquestion_answer66) In sq molecules, the type of hybridisation exhibited by sulphur is
A) \[s{{p}^{2}}\] done clear
B) \[s{{p}^{3}}\] done clear
C) \[sp\] done clear
D) \[s{{p}^{3}}d\] done clear
View Answer play_arrowquestion_answer67) In the oxyacids of chlorine,\[Cl-O\]bond contains
A) \[d\pi -d\pi \]bonding done clear
B) \[d\pi -p\pi \]bonding done clear
C) \[p\pi -p\pi \]bonding done clear
D) None of the above done clear
View Answer play_arrowquestion_answer68) Anhydrous\[AlC{{l}_{3}}\]fume in air due to
A) oxidation done clear
B) hydrolysis done clear
C) reduction done clear
D) hydrogenation done clear
View Answer play_arrowquestion_answer69) The nature of\[F{{e}_{2}}{{O}_{3}}\]is
A) acidic done clear
B) basic done clear
C) amphoteric done clear
D) None of these done clear
View Answer play_arrowquestion_answer70) Concentrated nitric acid \[(HN{{O}_{3}})\] oxidizes phosphorus to
A) \[{{H}_{3}}P{{O}_{4}}\] done clear
B) \[{{H}_{3}}P{{O}_{3}}\] done clear
C) \[{{H}_{4}}{{P}_{2}}{{O}_{7}}\] done clear
D) \[{{H}_{3}}P{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer71) Which of the following has the highest nucleophilicity?
A) \[{{F}^{-}}\] done clear
B) \[O{{H}^{-}}\] done clear
C) \[CH_{3}^{-}\] done clear
D) \[NH_{2}^{-}\] done clear
View Answer play_arrowquestion_answer72) Number of isomeric primary amines obtained from\[{{C}_{4}}{{H}_{11}}N\]are
A) 3 done clear
B) 4 done clear
C) 5 done clear
D) 6 done clear
View Answer play_arrowquestion_answer73) Which of the following reaction doesnt support the acidic nature of alkyne?
A) Reaction with\[HBr\] done clear
B) Reaction with Grignard reagent done clear
C) Reaction with ammoniacal silver salt done clear
D) Reaction with metallic sodium done clear
View Answer play_arrowquestion_answer74) \[C{{H}_{3}}-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{N}}\,-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-H;\] The\[IUPAC\]name of the compound is
A) N-formyl-N-methyl ethanamide done clear
B) N-ethyl-N-methyl methanamide done clear
C) N-methyl-N-oxo ethanamine done clear
D) None of the above done clear
View Answer play_arrowquestion_answer75) The product of the following reaction,\[{{C}_{6}}{{H}_{5}}COCHB{{r}_{2}}\xrightarrow{O{{H}^{-}}}?\]is
A) \[{{C}_{6}}{{H}_{5}}COCHO\] done clear
B) \[{{C}_{6}}{{H}_{5}}COCOOH\] done clear
C) \[{{C}_{6}}{{H}_{5}}CHO\] done clear
D) \[{{C}_{6}}{{H}_{5}}CHOHCOOH\] done clear
View Answer play_arrowquestion_answer76) Which of the following alkenes will react fastest withunder catalytic hydrogenation conditions?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer77) Glucose reacts with acetic anhydride to give pentaacetyl derivative. Which of the following is true about that?
A) that can reduce Fehling or Tollens reagent done clear
B) thats soluble in dil. \[NaOH\] solution done clear
C) that consumes one mole of \[HI{{O}_{4}}\] done clear
D) \[B{{r}_{2}}/{{H}_{2}}O\]can oxidize done clear
View Answer play_arrowquestion_answer78) Complete hydrolysis of cellulose gives
A) D-fructose done clear
B) D-ribose done clear
C) D-glucose done clear
D) L-glucose done clear
View Answer play_arrowquestion_answer79) The saponification value of an oil or fat is measured in terms of
A) \[N{{H}_{4}}OH\] done clear
B) \[NaOH\] done clear
C) \[{{C}_{6}}{{H}_{5}}OH\] done clear
D) \[kOH\] done clear
View Answer play_arrowquestion_answer80) \[{{N}_{2}}\]gas is liberated when\[[HCl+NaN{{O}_{2}}]\]reacts with the following compounds; \[A.C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\] \[B.\,\,urea\] \[C.C{{H}_{3}}CON{{H}_{2}}\] \[D.{{C}_{6}}{{H}_{5}}N{{H}_{2}}\] The answer is
A) A, B, C done clear
B) B, C, D done clear
C) A, C, D done clear
D) A, B, D done clear
View Answer play_arrowquestion_answer81) Benzaldehyde condenses with \[N,\,\,N\]dimethyl aniline in presence of anhydrous\[ZnC{{l}_{2}}\]to give
A) azo dye done clear
B) malachite done clear
C) michlers ketone done clear
D) buffer yellow done clear
View Answer play_arrowquestion_answer82) Which of the following reactions is given by only primary amines?
A) Reaction with\[HN{{O}_{2}}\] done clear
B) Reaction with chloroform and alcoholic\[KOH\] done clear
C) Reaction with acetyl chloride done clear
D) Reaction with Grignard reagent done clear
View Answer play_arrowquestion_answer83) \[C{{H}_{3}}COOH\xrightarrow{N{{H}_{3}}}\xrightarrow{\Delta }?\] The product of the reaction is isomeric with
A) \[\underset{\begin{smallmatrix} | \\ N{{H}_{2}} \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,-CHO\] done clear
B) \[C{{H}_{3}}CH=NOH\] done clear
C) \[HCONH-C{{H}_{3}}\] done clear
D) All of these done clear
View Answer play_arrowquestion_answer84) Which one of the following compound gives aspirin on reacting with acetic anhydride in presence of\[{{H}_{2}}S{{O}_{4}}\]?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer85) is fastest when\[Z\]is
A) \[Cl\] done clear
B) \[N{{H}_{2}}\] done clear
C) \[O{{C}_{2}}{{H}_{5}}\] done clear
D) \[OCO{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer86) Aldehyde not showing cannizzaros reaction is
A) paraldehyde done clear
B) chloral done clear
C) formaldehyde done clear
D) acetaldehyde done clear
View Answer play_arrowquestion_answer87) Both\[HCHO\]and\[C{{H}_{3}}CHO\]gives similar reactions with all the reagents except
A) Schiff reagent done clear
B) Fehling solution done clear
C) ammoniacal\[AgN{{O}_{3}}\] done clear
D) ammonia done clear
View Answer play_arrowquestion_answer88) Which of the following statements is not correct?
A) All alcohols are miscible with water done clear
B) Only lower alcohols are miscible with water done clear
C) All alcohols are not poisonous done clear
D) Methanol is poisonous done clear
View Answer play_arrowquestion_answer89) Cyclohexanol is
A) phenol done clear
B) \[1{}^\circ \]alcohol done clear
C) \[2{}^\circ \]alcohol done clear
D) \[3{}^\circ \]alcohol done clear
View Answer play_arrowquestion_answer90) In the manufacture of ethanol from sugar the enzymes are
A) diastase and zymase done clear
B) maltase and zymase done clear
C) diastase and invertase done clear
D) invertase and zymase done clear
View Answer play_arrowquestion_answer91) The action of chloral on chlorobenzene gives
A) BHC done clear
B) DDT done clear
C) gammexene done clear
D) lindane done clear
View Answer play_arrowquestion_answer92) Which halide will be least reactive in respect to hydrolysis?
A) vinyl chloride done clear
B) allyl chloride done clear
C) ethyl chloride done clear
D) \[t-\]butyl chloride done clear
View Answer play_arrowquestion_answer93) By Wurtz reaction, a mixture of methyl iodide and ethyl iodide gives
A) butane done clear
B) ethane done clear
C) propane done clear
D) a mixture of above three done clear
View Answer play_arrowquestion_answer94) The cyanide process is used for obtaining
A) \[Cu\] done clear
B) \[Na\] done clear
C) \[Zn\] done clear
D) \[Ag\] done clear
View Answer play_arrowquestion_answer95) Which of the following ore does not represent the ores of iron?
A) Cassiterite done clear
B) Limonite done clear
C) Haematite done clear
D) Magnetite done clear
View Answer play_arrowquestion_answer96) van-Arkel method of purification of metals involves converting the metal to a
A) volatile stable compound done clear
B) non-volatile stable compound done clear
C) volatile unstable compound done clear
D) None of the above done clear
View Answer play_arrowquestion_answer97) The first element of rare earth metal is
A) cerium done clear
B) cesium done clear
C) lanthanide done clear
D) actinide done clear
View Answer play_arrowquestion_answer98) Which of the following transitions involves maximum amount of energy?
A) \[{{M}^{-}}(g)\xrightarrow{{}}M(g)\] done clear
B) \[{{M}^{-}}(g)\xrightarrow{{}}{{M}^{+}}(g)\] done clear
C) \[{{M}^{+}}(g)\xrightarrow{{}}{{M}^{2+}}(g)\] done clear
D) \[{{M}^{2+}}(g)\xrightarrow{{}}{{M}^{3+}}(g)\] done clear
View Answer play_arrowquestion_answer99) Transition metal with low oxidation number will act as
A) an oxidizing agent done clear
B) a base done clear
C) an acid done clear
D) None of these done clear
View Answer play_arrowquestion_answer100) Chloride of which of the following element is colored?
A) \[Hg\] done clear
B) \[Ag\] done clear
C) \[Co\] done clear
D) \[Zn\] done clear
View Answer play_arrowquestion_answer101) Spiegeleisn is an alloy of
A) \[Fe,Co\]and\[Cr\] done clear
B) \[Fe,Co\] and\[Mg\] done clear
C) \[Fe,Mg\]and\[C\] done clear
D) \[Fe,C\]and\[Mn\] done clear
View Answer play_arrowquestion_answer102) Which of the following ions form most stable complex compound?
A) \[M{{n}^{2+}}\] done clear
B) \[N{{i}^{2+}}\] done clear
C) \[F{{e}^{2+}}\] done clear
D) \[C{{u}^{2+}}\] done clear
View Answer play_arrowquestion_answer103) Coordination number of\[Fe\]in the complexes \[{{[Fe{{(CN)}_{6}}]}^{4-}}\],\[{{[Fe{{(CN)}_{6}}]}^{3-}}\]and\[{{[FeC{{l}_{4}}]}^{-}}\]would be respectively
A) 6, 4, 6 done clear
B) 6, 6, 4 done clear
C) 6, 3, 3 done clear
D) 2, 3, 3 done clear
View Answer play_arrowquestion_answer104) Which of the following is a wrong statement?
A) \[Ni{{(CO)}_{4}}\]has zero oxidation number for\[Ni\] done clear
B) \[Ni{{(CO)}_{4}}\]has oxidation number\[+4\]for\[Ni\] done clear
C) \[Ni\]is metal done clear
D) \[CO\]is gas done clear
View Answer play_arrowquestion_answer105) Rusting of iron is catalyzed by which of the following?
A) \[Fe\] done clear
B) \[Zn\] done clear
C) \[{{O}_{2}}\] done clear
D) \[{{H}^{+}}\] done clear
View Answer play_arrowquestion_answer106) Standard electrode potential of\[NHE\]at\[298\,\,K\]is
A) \[0.05\,\,V\] done clear
B) \[0.10\,\,V\] done clear
C) \[0.50\,\,V\] done clear
D) \[0.00\,\,V\] done clear
View Answer play_arrowquestion_answer107) For a cell reaction involving a two electron change, the standard emf of the cell is found to be\[0.295\,\,V\]at\[{{25}^{o}}C\]. The equilibrium constant of the reaction at\[{{25}^{o}}C\]will be
A) \[10\] done clear
B) \[1\times {{10}^{10}}\] done clear
C) \[1\times {{10}^{-10}}\] done clear
D) \[10\times {{10}^{-2}}\] done clear
View Answer play_arrowquestion_answer108) The ionic conductance of\[B{{a}^{2+}}\]and\[C{{l}^{-}}\]are respectively\[127\]and\[76\,\,oh{{m}^{-1}}-c{{m}^{2}}\]at infinite dilution. The equivalent conductance\[(in\,\,oh{{m}^{-1}}\,\,c{{m}^{2}})\]of\[BaC{{l}_{2}}\]at infinite dilution will be
A) 139.5 done clear
B) 203 done clear
C) 279 done clear
D) 101.5 done clear
View Answer play_arrowquestion_answer109) Multimolecular colloids are present in
A) soap solution done clear
B) sol of proteins done clear
C) sol of gold done clear
D) All of these done clear
View Answer play_arrowquestion_answer110) In physical adsorption, the gas molecules are held by solid surfaces through
A) strong chemical forces done clear
B) van der waals forces done clear
C) metallic bonds done clear
D) gravitational forces done clear
View Answer play_arrowquestion_answer111) The osmotic pressure of a 5% (wt./vol.) solution of cane sugar at\[{{150}^{o}}C\]is
A) \[3.078\,\,atm\] done clear
B) \[4.078\,\,atm\] done clear
C) \[5.078\,\,atm\] done clear
D) \[2.45\,\,atm\] done clear
View Answer play_arrowquestion_answer112) The mole fraction of water in 20% aqueous solution of\[{{H}_{2}}{{O}_{2}}\]is
A) \[\frac{20}{80}\] done clear
B) \[\frac{80}{20}\] done clear
C) \[\frac{34}{77}\] done clear
D) \[\frac{77}{68}\] done clear
View Answer play_arrowquestion_answer113) The\[pH\]of a solution is increased from 3 to 6, its\[{{H}^{+}}\]ion concentration will be
A) reduced to half done clear
B) doubled done clear
C) reduced by 1000 times done clear
D) increased by 1000 times done clear
View Answer play_arrowquestion_answer114) Solubility product of\[BaC{{l}_{2}}\]is\[4\times {{10}^{-9}}\]. Its solubility in mol/L would be
A) \[1\times {{10}^{-3}}\] done clear
B) \[1\times {{10}^{-9}}\] done clear
C) \[4\times {{10}^{-27}}\] done clear
D) \[1\times {{10}^{-27}}\] done clear
View Answer play_arrowquestion_answer115) An example of a Lewis acid is
A) \[NaCl\] done clear
B) \[MgC{{l}_{2}}\] done clear
C) \[AlC{{l}_{3}}\] done clear
D) \[SnC{{l}_{4}}\] done clear
View Answer play_arrowquestion_answer116) Radioactive decay is a
A) first order reaction done clear
B) zero order reaction done clear
C) second order reaction done clear
D) third order reaction done clear
View Answer play_arrowquestion_answer117) The rate constant for the first order reaction is\[60{{s}^{-1}}\]. How much time will it take to reduce the concentration of the reactant to\[\frac{1}{16}th\]value?
A) \[4.6\times {{10}^{-2}}s\] done clear
B) \[4.6\times {{10}^{4}}s\] done clear
C) \[4.6\times {{10}^{2}}s\] done clear
D) \[4.6\times {{10}^{-4}}s\] done clear
View Answer play_arrowquestion_answer118) \[(\Delta H-\Delta U)\]for the formation of carbon monoxide\[(CO)\]from its elements at\[298\,\,K\]is\[(R=8.314\,\,J{{K}^{-1}}mo{{l}^{-1}})\]
A) \[-1238.78\,\,J\,\,mo{{l}^{-1}}\] done clear
B) \[1238.78\,\,J\,\,mo{{l}^{-1}}\] done clear
C) \[-2477.57\,\,J\,\,mo{{l}^{-1}}\] done clear
D) \[2477.57\,\,J\,\,mo{{l}^{-1}}\] done clear
View Answer play_arrowquestion_answer119) An ideal gas at constant temperature and pressure expands, then its
A) internal energy remains same done clear
B) internal energy decrease done clear
C) internal energy increases done clear
D) entropy first increases and then decreases done clear
View Answer play_arrowquestion_answer120) At which temperature nitrogen under \[1.00\,\,atm\] pressure has the same root mean square speed as that of\[C{{O}_{2}}\]at\[STP\]
A) \[{{0}^{o}}C\] done clear
B) \[{{27}^{o}}C\] done clear
C) \[-{{99}^{o}}C\] done clear
D) \[-{{200}^{o}}C\] done clear
View Answer play_arrowquestion_answer121) The value of\[\left| \begin{matrix} {{a}^{2}} & {{b}^{2}} & {{c}^{2}} \\ {{(a+1)}^{2}} & {{(b+1)}^{2}} & {{(c+1)}^{2}} \\ {{(a-1)}^{2}} & {{(b-1)}^{2}} & {{(c-1)}^{2}} \\ \end{matrix} \right|\]is
A) \[3\left| \begin{matrix} {{a}^{2}} & {{b}^{2}} & {{c}^{2}} \\ a & b & c \\ 1 & 1 & 1 \\ \end{matrix} \right|\] done clear
B) \[3\left| \begin{matrix} {{a}^{2}} & {{b}^{2}} & {{c}^{2}} \\ a & b & c \\ 1 & 1 & 1 \\ \end{matrix} \right|\] done clear
C) \[2\left| \begin{matrix} {{a}^{2}} & {{b}^{2}} & {{c}^{2}} \\ a & b & c \\ 1 & 1 & 1 \\ \end{matrix} \right|\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer122) If\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z=0\],\[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z=0\]\[{{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}z=0\]and\[\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|=0\], then the given system has
A) one trivial and one non-trivial solution done clear
B) no solution done clear
C) one solution done clear
D) infinite solution done clear
View Answer play_arrowquestion_answer123) Let\[A\]be a square matrix all of whose entries are integers. Then, which one of the following is true?
A) If\[\det (A)=\pm 1\], then\[{{A}^{-1}}\]exists but all its entries are not necessarily integers done clear
B) If\[\det (A)\ne \pm 1\], then\[{{A}^{-1}}\].exists and all its entries are non-integers done clear
C) If\[\det (A)=\pm 1\], then\[{{A}^{-1}}\]exists and all its entries are integers done clear
D) If\[\det (A)=\pm 1\], then\[{{A}^{-1}}\]need not exist done clear
View Answer play_arrowquestion_answer124) Which of the following statements is/are correct? I. Adjoint of a unit matrix is a unit matrix. II. \[A(adj\,\,A)=(adj\,\,A)A=|A|\,\,I\] III. Adjoint of a symmetric matrix is symmetric. IV. Adjoint of a diagonal matrix is a diagonal matrix.
A) I done clear
B) II done clear
C) I or II done clear
D) All statements are correct done clear
View Answer play_arrowquestion_answer125) The value of\[\int{\frac{dx}{x\sqrt{1-{{(\log x)}^{2}}}}}\]is
A) \[{{\cos }^{-1}}(\log x+C)\] done clear
B) \[x\log (1-{{x}^{2}})+C\] done clear
C) \[\frac{1}{2}{{\cos }^{-1}}(\log x+C)\] done clear
D) \[{{\sin }^{-1}}(\log x+C)\] done clear
View Answer play_arrowquestion_answer126) \[\int{\frac{{{x}^{2}}}{({{x}^{2}}+2)({{x}^{2}}+3)}dx}\]is equal to
A) \[-\sqrt{2}{{\tan }^{-1}}\left( \frac{x}{\sqrt{2}} \right)+\sqrt{3}{{\tan }^{-1}}\left( \frac{x}{\sqrt{3}} \right)+C\] done clear
B) \[\sqrt{2}{{\tan }^{-1}}\left( \frac{x}{\sqrt{2}} \right)+\sqrt{3}{{\tan }^{-1}}\left( \frac{x}{\sqrt{3}} \right)+C\] done clear
C) \[-\sqrt{2}{{\tan }^{-1}}x+\sqrt{3}{{\tan }^{-1}}x+C\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer127) The degree and order of the differential equation of the family of all parabolas whose axis is x-axis, are respectively
A) 2, 1 done clear
B) 1, 2 done clear
C) 3, 2 done clear
D) 2, 3 done clear
View Answer play_arrowquestion_answer128) The differential equation satisfied by the family of curve\[y=ax\cos \left( \frac{1}{x}+b \right)\], where\[a,\,\,b\]are parameters, is
A) \[{{x}^{2}}{{y}_{2}}+y=0\] done clear
B) \[{{x}^{4}}+{{y}_{2}}+y=0\] done clear
C) \[x{{y}_{2}}-y=0\] done clear
D) \[{{x}^{4}}{{y}_{2}}-y=0\] done clear
View Answer play_arrowquestion_answer129) Integrating factor of equation\[({{x}^{2}}+1)\frac{dy}{dx}+2xy={{x}^{2}}-1\]is
A) \[\frac{2x}{{{x}^{2}}+1}\] done clear
B) \[\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\] done clear
C) \[{{x}^{2}}+1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer130) The value of\[\int_{0}^{\pi /2}{|\sin x-\cos x|}\,\,dx\]is
A) \[0\] done clear
B) \[2(\sqrt{2}-1)\] done clear
C) \[\sqrt{2}-1\] done clear
D) \[2(\sqrt{2}+1)\] done clear
View Answer play_arrowquestion_answer131) The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line\[y-4x+3=0\], is
A) \[{{x}^{2}}+{{y}^{2}}+4x-10y+25=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x-10y+16=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x-10y+25=0\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer132) The number of solutions of\[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\]is/ are
A) 0 done clear
B) 1 done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowquestion_answer133) If\[\alpha ,\,\,\beta \]are the roots of\[{{x}^{2}}-3x+1=0\], then the equation whose roots are\[\frac{1}{\alpha -2},\,\,\frac{1}{\beta -2}\]is
A) \[{{x}^{2}}+x+1=0\] done clear
B) \[{{x}^{2}}-x-1=0\] done clear
C) \[{{x}^{2}}+x-1=0\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer134) If\[x\]is real/then the value of\[\frac{{{x}^{2}}+34x-71}{{{x}^{2}}+2x-7}\]does not lie between
A) 8 and -5 done clear
B) -5 and 9 done clear
C) 0 and 9 done clear
D) 5 and 9 done clear
View Answer play_arrowquestion_answer135) The square root of\[\sqrt{50}+\sqrt{48}\]is
A) \[{{2}^{1/4}}(3+\sqrt{2})\] done clear
B) \[{{2}^{1/4}}(\sqrt{3}+\sqrt{2})\] done clear
C) \[{{2}^{1/4}}(2+\sqrt{2})\] done clear
D) \[{{2}^{1/4}}(\sqrt{3}+2)\] done clear
View Answer play_arrowquestion_answer136) Let\[{{I}_{1}}=\int_{\alpha }^{\pi -\alpha }{xf}(\sin x)\,\,dx,\,\,{{I}_{2}}\]\[=\int_{xf(\sin x)\,\,dx}^{\pi -\alpha }{f(\sin x)}\,\,dx\], then \[{{I}_{2}}\] is equal to
A) \[\frac{\pi }{2}{{I}_{1}}\] done clear
B) \[\pi {{I}_{1}}\] done clear
C) \[\frac{2}{\pi }{{I}_{1}}\] done clear
D) \[2{{I}_{1}}\] done clear
View Answer play_arrowquestion_answer137) The area of figure bounded by\[y={{e}^{x}},\,\,y={{e}^{-x}}\]and the straight line\[x=1\]is
A) \[\left( e+\frac{1}{e} \right)sq\,\,unit\] done clear
B) \[\left( e-\frac{1}{e} \right)sq\,\,unit\] done clear
C) \[\left( e+\frac{1}{e}-2 \right)sq\,\,unit\] done clear
D) \[\left( e+\frac{1}{e}+2 \right)sq\,\,unit\] done clear
View Answer play_arrowquestion_answer138) The domain and range of\[f(x)={{\sin }^{-1}}[x]\]are
A) \[[0,\,\,2),\,\,\left\{ -\frac{\pi }{2},\,\,\frac{\pi }{2} \right\}\] done clear
B) \[[-1,\,\,2)\left\{ -\frac{\pi }{2},\,\,0,\,\,\frac{\pi }{2} \right\}\] done clear
C) \[[-1,\,\,2)\left\{ -\pi ,\,\,\frac{-\pi }{2},\,\,0,\,\,\frac{\pi }{2},\,\,\pi \right\}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer139) If\[\mathbf{a,}\,\,\mathbf{b}\]and\[\mathbf{c}\]are non-collinear vectors such that for some scalars\[\text{x,}\,\,\text{y,}\,\,\text{z,}\,\,x\mathbf{a}+x\mathbf{b}+x\mathbf{c}=0\], then
A) \[x=0,\,\,y=0,\,\,z=0\] done clear
B) \[x\ne 0,\,\,y\ne 0,\,\,z=0\] done clear
C) \[x=0,\,\,y\ne 0,\,\,z\ne 0\] done clear
D) \[x\ne 0,\,\,y\ne 0,\,\,z\ne 0\] done clear
View Answer play_arrowquestion_answer140) Let\[\mathbf{a,}\,\,\mathbf{b,}\,\,\mathbf{c}\]be three vectors such that\[\mathbf{c}\ne 0\]and \[\mathbf{a}\cdot \mathbf{b}\]\[=2\mathbf{a}\cdot \mathbf{c},\,\,|\mathbf{a}|=|\mathbf{c}|=1,\,\,|\mathbf{b}|=4\]and\[\mathbf{|b\times c|}=\sqrt{15}\], if\[\mathbf{b}-2\mathbf{c}=\lambda \alpha \] then,\[\lambda \]equals
A) -1 done clear
B) 1 done clear
C) -4 done clear
D) 2 done clear
View Answer play_arrowquestion_answer141) The image of the point with position vector\[\mathbf{i}+3\mathbf{k}\]in the plane\[r\cdot (\mathbf{i}+\mathbf{j}+\mathbf{k})=1\]is
A) \[\mathbf{i}-2\mathbf{j}+\mathbf{k}\] done clear
B) \[\mathbf{i}+2\mathbf{j}-\mathbf{k}\] done clear
C) \[-\mathbf{i}-2\mathbf{j}+\mathbf{k}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer142) The vectors\[\mathbf{c},\,\,\mathbf{a},\,\,=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}\]and\[\mathbf{b}=\mathbf{j}\]are such that\[\mathbf{a},\,\,\mathbf{b},\,\,\mathbf{c}\]form a right handed system, then\[\mathbf{c}\]is
A) \[0\] done clear
B) \[y\,\,\mathbf{j}\] done clear
C) \[-z\,\,\mathbf{i}+x\,\,\mathbf{k}\] done clear
D) \[z\,\,\mathbf{i}-x\,\,\mathbf{k}\] done clear
View Answer play_arrowquestion_answer143) The equation of plane passing through a point \[A\](2, -1, 3) and parallel to the vectors \[\mathbf{a}=(3,\,\,0,\,\,-1)\]and\[\mathbf{b}=(-3,\,\,2,\,\,2)\]is
A) \[2x-3y+6z+25=0\] done clear
B) \[3x-2y+6z+25=0\] done clear
C) \[2x-3y+6z-25=0\] done clear
D) \[3x-2y+6z-25=0\] done clear
View Answer play_arrowquestion_answer144) \[\underset{x\to 1}{\mathop{\lim }}\,\frac{(2x-3)(\sqrt{x}-1)}{2{{x}^{2}}+x-3}\]is equal to
A) \[-1/10\] done clear
B) \[1/10\] done clear
C) \[-1/8\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer145) Which is the correct order for a given number a in increasing order?
A) \[{{\log }_{2}}\alpha ,\,\,{{\log }_{3}}\alpha ,\,\,{{\log }_{e}}\alpha ,\,\,{{\log }_{10}}\alpha \] done clear
B) \[{{\log }_{10}}\alpha ,\,\,{{\log }_{3}}\alpha ,\,\,{{\log }_{e}}\alpha ,\,\,{{\log }_{2}}\alpha \] done clear
C) \[{{\log }_{10}}\alpha ,\,\,{{\log }_{e}}\alpha ,\,\,{{\log }_{2}}\alpha ,\,\,\alpha {{\log }_{3}}\alpha \] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer146) If\[x=\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}},\,\,y=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}\]then \[3{{x}^{2}}+4xy\,-3{{y}^{2}}\] is equal to
A) \[\frac{1}{3}(56\sqrt{10}+12)\] done clear
B) \[\frac{1}{3}(56\sqrt{10}-12)\] done clear
C) \[\frac{1}{3}(56+12\sqrt{10})\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer147) If\[x+y=1\], then\[\sum\limits_{r=0}^{n}{{{r}^{2\cdot n}}}{{C}_{r}}{{x}^{r}}-{{y}^{n-r}}\]is equal to
A) \[nxy\] done clear
B) \[nx(x+yn)\] done clear
C) \[nx(n\,\,x+y)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer148) If\[Z=f(x+ay)+\phi (x-ay)\], then
A) \[{{Z}_{xx}}={{Z}_{yy}}\] done clear
B) \[{{Z}_{xx}}={{a}^{2}}{{Z}_{yy}}\] done clear
C) \[{{Z}_{yy}}={{a}^{2}}{{Z}_{xx}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer149) The existence of the unique solution of the system\[x+y+z=\lambda \],\[5x-y+\mu z=10\]\[2x+3y-z=6\]depends on
A) \[\mu \]only done clear
B) \[\lambda \]only done clear
C) \[\lambda \]and\[\mu \]both done clear
D) neither\[\lambda \]nor\[\mu \] done clear
View Answer play_arrowquestion_answer150) Let\[A=\left| \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \\ \end{matrix} \right|\]and\[10B=\left| \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \\ \end{matrix} \right|\]. If\[B\]is the inverse of matrix\[A\], then\[\alpha \]is
A) \[-1\] done clear
B) \[-2\] done clear
C) \[2\] done clear
D) \[5\] done clear
View Answer play_arrowquestion_answer151) The angle of intersection of ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and circle\[{{x}^{2}}+{{y}^{2}}=ab\]is
A) \[{{\tan }^{-1}}\left( \frac{a+b}{ab} \right)\] done clear
B) \[{{\tan }^{-1}}\left( \frac{a-b}{\sqrt{ab}} \right)\] done clear
C) \[{{\tan }^{-1}}\left( \frac{a+b}{\sqrt{ab}} \right)\] done clear
D) \[{{\tan }^{-1}}\left( \frac{a-b}{ab} \right)\] done clear
View Answer play_arrowquestion_answer152) If \[S=\sum\limits_{n=0}^{\infty }{\frac{{{(\log x)}^{2n}}}{(2n)!}}\], then\[S\]is equal to
A) \[x+{{x}^{-1}}\] done clear
B) \[x-{{x}^{-1}}\] done clear
C) \[\frac{1}{2}(x+{{x}^{-1}})\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer153) The value of\[\log \,\,2+2\left( \frac{1}{5}+\frac{1}{3}\cdot \frac{1}{{{5}^{3}}}+\frac{1}{5}\cdot \frac{1}{{{5}^{5}}}+.... \right)\], is
A) \[\log 2+\log 3\] done clear
B) \[\log 2+2\] done clear
C) \[\frac{1}{2}\log 2\] done clear
D) \[\log 3\] done clear
View Answer play_arrowquestion_answer154) The equation of parabola whose vertex and focus are (0, 4) and (0, 2) respectively, is
A) \[{{y}^{2}}-8x=32\] done clear
B) \[{{y}^{2}}+8x=32\] done clear
C) \[{{x}^{2}}+8y=32\] done clear
D) \[{{x}^{2}}-8y=32\] done clear
View Answer play_arrowquestion_answer155) The line\[x+2y=4\]is translated parallel to itself by 3 unit in the sense of increasing x and then rotated by\[{{30}^{o}}\] in the anti-clockwise direction about the point where the shifted line cuts the x-axis. The equation of the line in the new position is
A) \[y=\tan (\theta -{{30}^{o}})(x-4-3\sqrt{5})\] done clear
B) \[y=\tan ({{30}^{o}}-\theta )(x-4-3\sqrt{5})\] done clear
C) \[y=\tan (\theta +{{30}^{o}})(x+4+3\sqrt{5})\] done clear
D) \[y=\tan (\theta -{{30}^{o}})(x+4+3\sqrt{5})\] done clear
View Answer play_arrowquestion_answer156) The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is 6. The equation of the hyperbola referred to its axes as axes of coordinates are
A) \[3{{x}^{2}}-{{y}^{2}}=3\] done clear
B) \[{{x}^{2}}-3{{y}^{2}}=3\] done clear
C) \[3{{x}^{2}}-{{y}^{2}}=9\] done clear
D) \[{{x}^{2}}-3{{y}^{2}}=9\] done clear
View Answer play_arrowquestion_answer157) If the equation \[12{{x}^{2}}+7xy-p{{y}^{2}}-18x+qy+6=0\] represents a pair of perpendicular straight lines, then
A) \[p=12,\,\,q=-1\] done clear
B) \[p=-12,\,\,q=1\] done clear
C) \[p=12,\,\,q=1\] done clear
D) \[p=1,\,\,q=1\] done clear
View Answer play_arrowquestion_answer158) If the roots of the equation\[\frac{\alpha }{x-\alpha }+\frac{\beta }{x-\beta }=1\]be equal in magnitude but opposite in sign, then\[\alpha +\beta \]is equal to
A) 0 done clear
B) 1 done clear
C) 2 done clear
D) None of these done clear
View Answer play_arrowquestion_answer159) If\[2a+3b+6c=0\], then at least one root of the equation\[a{{x}^{2}}+bx+c=0\]lies in the interval
A) (1, 2) done clear
B) (0, 1) done clear
C) (2, 3) done clear
D) (3, 4) done clear
View Answer play_arrowquestion_answer160) The ratio in which the line\[3x+4y+2=0\] divides the distance between\[3x+4y+5=0\] and\[3x+4y-5=0\], is
A) \[7:3\] done clear
B) \[3:7\] done clear
C) \[2:3\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer161) If the circle\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]is touched by\[y=x\]at\[P\]such that\[OP=6\sqrt{2}\], then the value of\[c\]is
A) 36 done clear
B) 72 done clear
C) 144 done clear
D) None of these done clear
View Answer play_arrowquestion_answer162) The coefficient of\[{{x}^{4}}\]in the expansion of\[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{n}}\]
A) \[^{n}{{C}_{4}}\] done clear
B) \[^{n}{{C}_{4}}{{+}^{n}}{{C}_{2}}\] done clear
C) \[^{n}{{C}_{4}}{{+}^{n}}{{C}_{2}}{{+}^{n}}{{C}_{4}}{{\cdot }^{n}}{{C}_{2}}\] done clear
D) \[^{n}{{C}_{4}}{{+}^{n}}{{C}_{2}}{{+}^{n}}{{C}_{1}}{{\cdot }^{n}}{{C}_{2}}\] done clear
View Answer play_arrowquestion_answer163) \[1+\frac{1+x}{2!}+\frac{1+x+{{x}^{2}}}{3!}+\frac{1+x+{{x}^{2}}+{{x}^{3}}}{4!}\] is equal to
A) \[\frac{{{e}^{x}}+1}{x-1}\] done clear
B) \[\frac{{{e}^{x}}+1}{x+1}\] done clear
C) \[\frac{{{e}^{x}}-e}{x+1}\] done clear
D) \[\frac{{{e}^{x}}-e}{x-1}\] done clear
View Answer play_arrowquestion_answer164) The inequation\[n!>{{2}^{n-1}}\]is true for
A) for all\[n\in N\] done clear
B) for all\[n>1\] done clear
C) for all\[n>2\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer165) Let\[A=\{(x,\,\,y):y={{e}^{x}},\,\,x\in R\}\]and\[B=\{(x,\,\,y):y={{e}^{-x}},\,\,e\in R\}\]. Then,
A) \[A\cap B=\phi \] done clear
B) \[A\cap B\ne \phi \] done clear
C) \[A\cup B={{R}^{2}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer166) In\[\Delta \,ABC,\,\,\frac{b-c}{{{r}_{1}}}+\frac{c-a}{{{r}_{2}}}+\frac{a-b}{{{r}_{3}}}\]is equal to
A) \[0\] done clear
B) \[abc\] done clear
C) \[a+b+c\] done clear
D) \[ab+bc+ca\] done clear
View Answer play_arrowquestion_answer167) ABCD is a rectangular field. A vertical lamp post of height\[12\,\,m\]stands at the corner\[A\]. If the angle of elevation of its top from\[B\]is\[{{60}^{o}}\]and from\[C\]is \[{{45}^{o}}\], then the area of the field is
A) \[48\sqrt{2}\,\,{{m}^{2}}\] done clear
B) \[12\sqrt{2}\,\,{{m}^{2}}\] done clear
C) \[48\,\,{{m}^{2}}\] done clear
D) \[12\sqrt{3}\,\,{{m}^{2}}\] done clear
View Answer play_arrowquestion_answer168) The function\[f(x)=\max \{(1-x),\,\,(1+x),\,\,2\}\],\[x\in (-\infty ,\,\,\infty )\]is equivalent to
A) \[f(x)=\left\{ \begin{matrix} 1+x & , & x\le -1 \\ 2 & , & -1<x<1 \\ 1-x & , & x\ge 1 \\ \end{matrix} \right.\] done clear
B) \[f(x)=\left\{ \begin{matrix} 1-x & , & x\le -1 \\ 2 & , & -1<x<1 \\ 1+x & , & x\ge 1 \\ \end{matrix} \right.\] done clear
C) \[f(x)=\left\{ \begin{matrix} 1-x & , & x\le -1 \\ 1 & , & -1<x<1 \\ 1+x & , & x\ge 1 \\ \end{matrix} \right.\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer169) The number of values of\[x\]in the interval\[[0,\,\,5\pi ]\]satisfying the equation\[3{{\sin }^{2}}x-7\sin x+2=0\]is
A) 0 done clear
B) 5 done clear
C) 6 done clear
D) 10 done clear
View Answer play_arrowquestion_answer170) \[\left( 1+\cos \frac{\pi }{8} \right)\left( 1+\cos \frac{3\pi }{8} \right)\left( 1+\cos \frac{5\pi }{8} \right)\]\[\left( 1+\cos \frac{7\pi }{8} \right)\]is equal to
A) \[\frac{1}{2}\] done clear
B) \[\frac{1}{8}\] done clear
C) \[\cos \frac{\pi }{8}\] done clear
D) \[\frac{1+\sqrt{2}}{2\sqrt{2}}\] done clear
View Answer play_arrowquestion_answer171) The number of solutions of the equation\[2{{\sin }^{-1}}\sqrt{{{x}^{2}}-x-1}+{{\cos }^{-1}}\sqrt{{{x}^{2}}-x}=\frac{3\pi }{2}\]is
A) 0 done clear
B) 2 done clear
C) 4 done clear
D) \[\infty \] done clear
View Answer play_arrowquestion_answer172) Each side of a square subtends an angle of\[{{60}^{o}}\]at the top of a tower\[h\]metre high standing in the centre of the square. If a is the length of each side of the square, then
A) \[2{{a}^{2}}={{h}^{2}}\] done clear
B) \[2{{h}^{2}}={{a}^{2}}\] done clear
C) \[3{{a}^{2}}=2{{h}^{2}}\] done clear
D) \[2{{h}^{2}}=3{{a}^{2}}\] done clear
View Answer play_arrowquestion_answer173) The value of\[{{\cos }^{-1}}\left( \cos \frac{7\pi }{6} \right)\]is
A) \[\frac{7\pi }{6}\] done clear
B) \[\frac{5\pi }{6}\] done clear
C) \[\frac{5\pi }{6}\] done clear
D) \[\frac{13\pi }{6}\] done clear
View Answer play_arrowquestion_answer174) If\[n\in N\], then\[|\sin nx|\]
A) \[\le n|\sin x|\] done clear
B) \[\ge n|\sin x|\] done clear
C) \[=n|\sin x|\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer175) In\[\Delta \,ABC\], if\[a=30,\,\,b=24,\,\,=18\], then\[{{r}_{3}}\]is equal to
A) 15 done clear
B) 18 done clear
C) 36 done clear
D) 12 done clear
View Answer play_arrowquestion_answer176) The circumcentre of a triangle formed by the lines\[xy+2x+2y+4=0\]and\[x+y+2=0\], is
A) \[(0,\,\,-1)\] done clear
B) \[(-1,\,\,0)\] done clear
C) \[(1,\,\,1)\] done clear
D) \[(-1,\,\,-1)\] done clear
View Answer play_arrowquestion_answer177) One diagonal of a square is along the line\[8x-15y=0\]and one of its vertex is (1, 2). Then, the equation of the sides of the square passing through this vertex are
A) \[23x+7y=9,\,\,7x+23y=53\] done clear
B) \[23x-7y-9=0,\,\,7x+23y-53=0\] done clear
C) \[23x-7y+9=0,\,\,7x+23y+53=0\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer178) The two curves\[{{x}^{3}}-3x{{y}^{2}}+2=0\]and\[3{{x}^{2}}y-{{y}^{3}}=2\]
A) cut at right angles done clear
B) touch each other done clear
C) cut at an angle\[\pi /3\] done clear
D) cut at an angle\[\pi /4\] done clear
View Answer play_arrowquestion_answer179) If\[\frac{2x+3}{(x+1)(x-3)}=\frac{a}{x+1}+\frac{b}{x-3}\], then\[a+b\]is equal to
A) \[1\] done clear
B) \[2\] done clear
C) \[9/4\] done clear
D) \[-1/4\] done clear
View Answer play_arrowquestion_answer180) \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{n}\left[ {{\sec }^{2}}\frac{\pi }{4n}+{{\sec }^{2}}\frac{2\pi }{4n}+...+{{\sec }^{2}}\frac{n\pi }{4n} \right]\]is equal to
A) \[\frac{4}{\pi }\] done clear
B) \[\frac{2}{\pi }\] done clear
C) \[\frac{3}{\pi }\] done clear
D) \[\frac{5}{\pi }\] done clear
View Answer play_arrowquestion_answer181) If\[f(x)=|\cos x|\]and\[g(x)=[x]\], then\[gof(x)\]is equal to
A) \[|\cos [x]|\] done clear
B) \[|\cos x|\] done clear
C) \[[|\cos x|]\] done clear
D) \[|[\cos x]|\] done clear
View Answer play_arrowquestion_answer182) If\[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{a}{x}+\frac{b}{{{x}^{2}}} \right)}^{2x}}={{e}^{2}}\],then
A) \[a=1,\,\,b=2\] done clear
B) \[a=2,\,\,b=1\] done clear
C) \[a=1,\,\,b\in R\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer183) The area bounded by the curve\[{{y}^{2}}=2x+1\]and the straight line\[x-y-1=0\]is given by
A) \[\frac{9}{2}sq\,\,units\] done clear
B) \[\frac{43}{6}sq\,\,units\] done clear
C) \[\frac{35}{6}sq\,\,units\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer184) The value of\[f(0)\], so that the function\[f(x)=\frac{2-{{(256-7x)}^{1/8}}}{{{(5x+3x)}^{1/5}}-2},\,\,x\ne 0\]is continuous everywhere is given by
A) \[-1\] done clear
B) \[1\] done clear
C) \[{{2}^{6}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer185) The set of points where the function\[f(x)=x|x|\]is differentiable, is
A) \[(-\infty ,\,\,\infty )\] done clear
B) \[(-\infty ,\,\,0)\cup (0,\,\,\infty )\] done clear
C) \[(0,\,\,\infty )\] done clear
D) \[[0,\,\,\infty )\] done clear
View Answer play_arrowquestion_answer186) If\[f(x)=|x{{|}^{|\sin x|}}\], then\[f\left( -\frac{\pi }{4} \right)\]is equal to
A) \[{{\left( \frac{\pi }{4} \right)}^{1/\sqrt{2}}}\left( \frac{\sqrt{2}}{2}\log \frac{4}{\pi }-\frac{2\sqrt{2}}{\pi } \right)\] done clear
B) \[{{\left( \frac{\pi }{4} \right)}^{1/\sqrt{2}}}\left( \frac{\sqrt{2}}{2}\log \frac{4}{\pi }+\frac{2\sqrt{2}}{\pi } \right)\] done clear
C) \[{{\left( \frac{\pi }{4} \right)}^{1/\sqrt{2}}}\left( \frac{\sqrt{2}}{2}\log \frac{\pi }{4}-\frac{2\sqrt{2}}{\pi } \right)\] done clear
D) \[\left( \frac{\sqrt{2}}{2}\log \frac{\pi }{4}+\frac{2\sqrt{2}}{\pi } \right)\] done clear
View Answer play_arrowquestion_answer187) A circle touches the x-axis and also touches the circle which centre at (0, 3) and radius 2, The locus of the centre of the circle is
A) a parabola done clear
B) a circle done clear
C) an ellipse done clear
D) a hyperbola done clear
View Answer play_arrowquestion_answer188) The circle on focal radii of a parabola as diameter touches
A) the x-axis done clear
B) the tangent at the vertex done clear
C) the directrix done clear
D) None of the above done clear
View Answer play_arrowquestion_answer189) The, equation of the ellipse whose axes are parallel to the coordinate axes having its centre at the point (2, -3) and focus at (3,-3) and one vertex at (4, -3) is
A) \[\frac{{{(x-2)}^{2}}}{4}+\frac{{{(y+3)}^{2}}}{3}=1\] done clear
B) \[\frac{{{(x+2)}^{2}}}{3}+\frac{{{(y+3)}^{2}}}{4}=1\] done clear
C) \[\frac{{{(x+2)}^{2}}}{4}+\frac{{{(y+3)}^{2}}}{3}=1\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer190) The diameter of\[16{{x}^{2}}-9{{y}^{2}}=144\]which is conjugate to\[x=2y\]is
A) \[y=\frac{32x}{9}\] done clear
B) \[x=\frac{16}{9}y\] done clear
C) \[y=\frac{16}{9}x\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer191) If\[\frac{2x+3}{(x+1)(x-3)}=\frac{a}{x+1}+\frac{b}{x-3}\]then\[a+b\]is equal to
A) \[1\] done clear
B) \[2\] done clear
C) \[9/4\] done clear
D) \[-1/4\] done clear
View Answer play_arrowquestion_answer192) If\[\frac{{{e}^{x}}+2}{({{e}^{x}}-1)(2{{e}^{x}}-3)}=-\frac{3}{{{e}^{x}}-1}+\frac{B}{2{{e}^{x}}-3}\]then\[B\]is equal to
A) 1 done clear
B) 3 done clear
C) 5 done clear
D) 7 done clear
View Answer play_arrowquestion_answer193) \[\frac{3\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}\]equal to
A) \[5\sqrt{2}\] done clear
B) \[3\sqrt{2}\] done clear
C) \[2\sqrt{3}\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer194) If\[{{\log }_{3}}2,\,\,{{\log }_{3}}({{2}^{x}}-5)\]and\[{{\log }_{3}}\left( {{2}^{x}}-\frac{7}{2} \right)\]are in AP, then\[x\]is equal to
A) \[1,\,\,\frac{1}{2}\] done clear
B) \[1,\,\,\frac{1}{3}\] done clear
C) \[1,\,\,\frac{3}{2}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer195) If the roots of the cubic equation\[a{{x}^{3}}+b{{x}^{2}}+cx+d=0\]are in GP, then
A) \[{{c}^{3}}a={{b}^{3}}d\] done clear
B) \[c{{a}^{3}}=b{{d}^{3}}\] done clear
C) \[{{a}^{3}}b={{c}^{3}}d\] done clear
D) \[a{{b}^{3}}=c{{d}^{3}}\] done clear
View Answer play_arrowquestion_answer196) In the group\[G=(\{1,\,\,2,\,\,3,\,\,4\},\,\,{{\times }_{5}})\]the solution of\[{{2}^{-1}}\times (3{{\times }_{5}}x)=4\]is
A) 1 done clear
B) 2 done clear
C) 3 done clear
D) None of these done clear
View Answer play_arrowquestion_answer197) Negation of Ram is in Class X or Rashmi is in Class XII is
A) Ram is not in Class X but Rashmi is in Class XII done clear
B) Ram is not in Class X but Rashmi is in Class XII done clear
C) Either Ram is not in Class X or Rashmi is not in class XII done clear
D) None of the above done clear
View Answer play_arrowquestion_answer198) The inverse of the proportion\[(p\wedge \tilde{\ }q)\Rightarrow r\]is
A) \[\tilde{\ }r\Rightarrow \tilde{\ }p\vee q\] done clear
B) \[\tilde{\ }p\wedge q\Rightarrow \tilde{\ }r\] done clear
C) \[r\Rightarrow p\vee \tilde{\ }q\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer199) The least remainder when \[{{17}^{30}}\] is divided by 5, is
A) 2 done clear
B) 1 done clear
C) 4 done clear
D) 3 done clear
View Answer play_arrowquestion_answer200) The solution of differential equation; \[dy-\sin x\,\sin \,ydx\,=0\] is
A) \[{{e}^{\cos x}}\cdot \tan \frac{y}{2}=C\] done clear
B) \[{{e}^{\cos x}}\cdot \tan y=C\] done clear
C) \[\cos x\cdot \tan y=C\] done clear
D) \[\cos x\cdot \sin y=C\] done clear
View Answer play_arrowquestion_answer201) Directions: Choose the alternative which can be substituted for the given group of words. A person concerned with practical results and values
A) plagiarist done clear
B) realist done clear
C) pragmatist done clear
D) fundamentalist done clear
View Answer play_arrowquestion_answer202) Directions: Choose the alternative which can be substituted for the given group of words. Member of a band of robbers
A) dacoit done clear
B) brigand done clear
C) thief done clear
D) pirate done clear
View Answer play_arrowquestion_answer203) Directions: Choose the alternative which can be substituted for the given group of words. A person without manners or polish is
A) rustic done clear
B) naive done clear
C) boorish done clear
D) barbarian done clear
View Answer play_arrowquestion_answer204) Directions: Choose the alternative which can be substituted for the given group of words. A speech by an actor at the end of a play
A) epilogue done clear
B) monologue done clear
C) duologue done clear
D) prologue done clear
View Answer play_arrowquestion_answer205) Directions: Choose the most suitable alternative to fill in the blank. The teacher ordered Kamal to leave the room and ......... him to return.
A) stopped done clear
B) refused done clear
C) forabade done clear
D) challenged done clear
View Answer play_arrowquestion_answer206) Directions: Choose the most suitable alternative to fill in the blank. I hope you must have ......... by now that failures are the stepping stones to success.
A) known done clear
B) felt done clear
C) decided done clear
D) realized done clear
View Answer play_arrowquestion_answer207) Directions: Choose the most suitable alternative to fill in the blank. The tyrant......... anyone whom he regarded as a rival.
A) massacred done clear
B) killed done clear
C) exterminated done clear
D) slaughtered done clear
View Answer play_arrowquestion_answer208) Directions: Choose the most suitable alternative to fill in the blank. In a little publicized deal, Pepsi Cola has ......... the entire soft drink market in Afghanistan.
A) conquered done clear
B) swallowed done clear
C) captured done clear
D) occupied done clear
View Answer play_arrowquestion_answer209) Directions: Choose the alternative which is nearest in meaning to the word given in capital letters. DILETTANTE
A) Opponent done clear
B) Specialist done clear
C) Amateur done clear
D) Expert done clear
View Answer play_arrowquestion_answer210) Directions: Choose the alternative which is nearest in meaning to the word given in capital letters. FLAK
A) Adventure done clear
B) Advice done clear
C) Criticism done clear
D) Praise done clear
View Answer play_arrowquestion_answer211) Directions: Choose the alternative which is nearest in meaning to the word given in capital letters. HOODLUM
A) Pioneer done clear
B) Criminal done clear
C) Devotee done clear
D) Scholar done clear
View Answer play_arrowquestion_answer212) Directions: Choose the alternative which is nearest in meaning to the word given in capital letters. SPASMODIC
A) Continuous done clear
B) Gradual done clear
C) Intermittent done clear
D) Spontaneous done clear
View Answer play_arrowquestion_answer213) Directions: Choose the alternative which is opposite in meaning of the word given in capital letters. SHAME
A) Glorify done clear
B) Exalt done clear
C) Dignify done clear
D) Enshrine done clear
View Answer play_arrowquestion_answer214) Directions: Choose the alternative which is opposite in meaning of the word given in capital letters. RESCUE
A) Extricate done clear
B) Waver done clear
C) Bind done clear
D) Desert done clear
View Answer play_arrowquestion_answer215) Directions: Choose the alternative which is opposite in meaning of the word given in capital letters. AGONY
A) Pleasure done clear
B) Bliss done clear
C) Ecstasy done clear
D) Fear done clear
View Answer play_arrowquestion_answer216) Directions: Choose the alternative which is opposite in meaning of the word given in capital letters. REQUISITE
A) Dispensable done clear
B) Random done clear
C) Inappropriate done clear
D) Chaotic done clear
View Answer play_arrowquestion_answer217) Old habits die hardly.
A) die much hardly done clear
B) die hard done clear
C) die too hard done clear
D) No improvement done clear
View Answer play_arrowquestion_answer218) The teacher asked, Why you are late?
A) Why you were late done clear
B) Why late you are done clear
C) Why are you late done clear
D) No improvement done clear
View Answer play_arrowquestion_answer219) It is ten years since I have begun living here.
A) begun done clear
B) had begun done clear
C) began done clear
D) No improvement done clear
View Answer play_arrowquestion_answer220) The various practices and norms for banks transactions are laid down by the Reserve Bank of India.
A) are laid up done clear
B) are led down done clear
C) are lead up done clear
D) No improvement done clear
View Answer play_arrowquestion_answer221) Knot: Watt: Fathom
A) The terms are connected with rope done clear
B) They are units of measurement done clear
C) The terms are used by sailors done clear
D) The terms are used for installing electricity done clear
View Answer play_arrowquestion_answer222) Majlis : Diet: Knesset
A) These are parliaments of countries done clear
B) These are old names of certain countries done clear
C) These are foreign languages done clear
D) These are the names of foods eaten in different countries done clear
View Answer play_arrowquestion_answer223) Kanha : Periyar : Dachigam
A) These are mountain peaks done clear
B) These are famous lagoons done clear
C) These are hill stations done clear
D) These are animal sanctuaries done clear
View Answer play_arrowquestion_answer224) Stirrup : Anvil: Drum
A) These are used by folk artists done clear
B) The items are used by riders done clear
C) They are parts of ear done clear
D) These are musical instruments done clear
View Answer play_arrowquestion_answer225) Kennedy : Indira : Palme
A) They were Prime Ministers done clear
B) They were very popular among children done clear
C) They were Presidents. done clear
D) All of them were assassinated done clear
View Answer play_arrowquestion_answer226) Chair : Door : Stick
A) Book : Pen : Notebook done clear
B) Statue : Brick : Pitcher done clear
C) Mason : Carpenter : Cobbler done clear
D) Tomato : Potato : Brinjal done clear
View Answer play_arrowquestion_answer227) Music : Guitar : Performer
A) Trick : Rope : Acrobat done clear
B) Dance : Tune : Instrument done clear
C) Food : Recipe : Cook done clear
D) Patient: Medicine : Doctor done clear
View Answer play_arrowquestion_answer228) Hair : Brush : Wig
A) Cement: Brick : Building done clear
B) Paper : Pen : Pencil done clear
C) Iron : Hammer: Axe done clear
D) Bread : Butter : Milk done clear
View Answer play_arrowquestion_answer229) Village : City : Suburb
A) Footpath : Road : Highway done clear
B) Pillow : Quilt: Bed done clear
C) Flowers : Garden : Park done clear
D) Pen : Pencil: Colour done clear
View Answer play_arrowquestion_answer230) Smile : Laugh : Cry
A) Frown : Anger : Temper done clear
B) Sit: Sleep : Play done clear
C) Touch : Catch : Release done clear
D) Morning : Night: Day done clear
View Answer play_arrowquestion_answer231) Which river of India is called Vridha Ganga?
A) Krishna done clear
B) Godavari done clear
C) Cauveri done clear
D) Narmada done clear
View Answer play_arrowquestion_answer232) The capital of Tanzania is
A) Nairobi done clear
B) Lusaka done clear
C) Kaupala done clear
D) Dar-e-Salaam done clear
View Answer play_arrowquestion_answer233) During which decade did the population of India record a negative growth rate?
A) 1921-31 done clear
B) 1911-21 done clear
C) 1941-51 done clear
D) 1931-41 done clear
View Answer play_arrowquestion_answer234) Marx belonged to
A) Germany done clear
B) Holland done clear
C) France done clear
D) Britain done clear
View Answer play_arrowquestion_answer235) Who is the author of A River Sutra?
A) VS Naipaul done clear
B) Nirad C Chaudhri done clear
C) Gita Mehta done clear
D) Vikram Seth done clear
View Answer play_arrowquestion_answer236) Who is known as the Father of Indian Missile Technology?
A) Dr UR Rao done clear
B) Dr. APJ Abdul Kalam done clear
C) Dr. Chidambaram done clear
D) Dr. Homi Bhabha done clear
View Answer play_arrowquestion_answer237) The art and science of map making is called
A) remote sensing done clear
B) cartography done clear
C) photogrammetry done clear
D) mapping done clear
View Answer play_arrowquestion_answer238) WTO basically promotes
A) financial support done clear
B) global peace done clear
C) unilateral trade done clear
D) multilateral trade done clear
View Answer play_arrowquestion_answer239) The forest in Sunderban is called
A) scrub jungle done clear
B) mangrove done clear
C) deciduous forest done clear
D) tundra done clear
View Answer play_arrowquestion_answer240) Indian Standard Time relates to
A) \[75.5{}^\circ \text{ }E\text{ }longitude\] done clear
B) \[82.5{}^\circ \text{ }E\text{ }longitude\] done clear
C) \[90.5{}^\circ \text{ }E\text{ }longitude\] done clear
D) \[0{}^\circ \text{ }longitude\] done clear
View Answer play_arrow
You need to login to perform this action.
You will be redirected in
3 sec