question_answer1) At what angle must the two forces \[(x+y)\] and \[(x-y)\]act so that the resultant may be
A) \[{{\cos }^{-1}}\left[ -\frac{{{x}^{2}}+{{y}^{2}}}{2({{x}^{2}}-{{y}^{2}})} \right]\] done clear
B) \[{{\cos }^{-1}}\left[ \frac{-2({{x}^{2}}-{{y}^{2}})}{{{x}^{2}}+{{y}^{2}}} \right]\] done clear
C) \[{{\cos }^{-1}}\left[ -\frac{({{x}^{2}}+{{y}^{2}})}{({{x}^{2}}-{{y}^{2}})} \right]\] done clear
D) \[{{\cos }^{-1}}\left[ -\frac{({{x}^{2}}-{{y}^{2}})}{({{x}^{2}}+{{y}^{2}})} \right]\] done clear
View Answer play_arrowquestion_answer2) A body starts from rest with uniform acceleration. If its velocity after n second is\[v\], then its displacement in the last \[2\,\,s\] is
A) \[\frac{2v(n+1)}{n}\] done clear
B) \[\frac{v(n+1)}{n}\] done clear
C) \[\frac{v(n-1)}{n}\] done clear
D) \[\frac{2v(n-1)}{n}\] done clear
View Answer play_arrowquestion_answer3) A wheel completes \[2000\] revolutions to cover the \[9.5\,\,km\] distance, then the diameter of the wheel is
A) \[1.5\,\,m\] done clear
B) \[1.5\,\,cm\] done clear
C) \[7.5\,\,cm\] done clear
D) \[7.5\,\,m\] done clear
View Answer play_arrowquestion_answer4) A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is
A) same everywhere done clear
B) lower in front side done clear
C) lower in rear side done clear
D) lower in upper side done clear
View Answer play_arrowquestion_answer5) A block \[A\] weighing \[100\,\,kg\] rests on a block \[B\] and is tied with a horizontal string to the wall at\[C\]. Block \[B\] weighs\[200\,\,kg\]. The coefficient of friction between \[A\] and \[B\] is \[0.25\] and between \[B\] and the surface is\[\frac{1}{3}\]. The horizontal force \[P\] necessary to move the block \[B\] should be\[(g=10\,\,m/{{s}^{2}})\]
A) \[1150\,\,N\] done clear
B) \[1250\,\,N\] done clear
C) \[1300\,\,N\] done clear
D) \[1420\,\,N\] done clear
View Answer play_arrowquestion_answer6) A boy and a man carry a uniform rod of length\[L\], horizontally in such a way that boy gets \[\frac{1}{4}th\] load. If the boy is at one end of the rod, the distance of the man from the other end is
A) \[\frac{L}{3}\] done clear
B) \[\frac{L}{4}\] done clear
C) \[\frac{2L}{3}\] done clear
D) \[\frac{3L}{4}\] done clear
View Answer play_arrowquestion_answer7) Two capillary of lengths \[L\] and \[2L\] and of radii \[R\] and \[2R\] are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary,\[X=\frac{\pi p{{R}^{4}}}{8\eta L})\]
A) \[\frac{8}{9}X\] done clear
B) \[\frac{9}{8}X\] done clear
C) \[\frac{5}{7}X\] done clear
D) \[\frac{7}{5}X\] done clear
View Answer play_arrowquestion_answer8) The molecules of a given mass of a gas have a \[\text{rms}\] velocity of \[200\,\,m/s\] at \[{{27}^{o}}C\] and \[1.0\times {{10}^{5}}\,\,N/{{m}^{2}}\] pressure. When the temperature is \[{{127}^{o}}C\] and pressure is \[0.5\times {{10}^{5}}N/{{m}^{2}}\], the \[\text{rms}\] velocity in \[m/s\] will
A) \[\frac{100\sqrt{2}}{3}\] done clear
B) \[100\sqrt{2}\] done clear
C) \[\frac{400}{\sqrt{3}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer9) \[3\,\,A\] of current is flowing in a linear conductor having a length of\[40\,\,cm\]. The conductor is placed in a magnetic field of strength \[500\] gauss and makes an angle of \[{{30}^{o}}\] with direction of the field. It experiences a force of magnitude
A) \[3\times {{10}^{4}}N\] done clear
B) \[3\times {{10}^{2}}N\] done clear
C) \[3\times {{10}^{-2}}N\] done clear
D) \[3\times {{10}^{-4}}N\] done clear
View Answer play_arrowquestion_answer10) A \[50\] turn?s Circular coil has a radius of\[3\,\,cm\], it is kept in a magnetic field acting normal to the area of the coil. The magnetic field \[B\] increased from \[0.10\,\,T\] to \[0.35\,\,T\] in \[2\] millisecond. The average induced \[\text{emf}\] in the coil is
A) \[1.77\,\,V\] done clear
B) \[17.7\,\,V\] done clear
C) \[177\,\,V\] done clear
D) \[0.177\,\,V\] done clear
View Answer play_arrowquestion_answer11) In the circuit .shown in figure neglecting source resistance, the voltmeter and ammeter readings will be respectively
A) \[0\,\,V,\,\,3\,\,A\] done clear
B) \[150\,\,V,\,\,3\,\,A\] done clear
C) \[150\,\,V,\,\,6\,\,A\] done clear
D) \[0\,\,V,\,\,8\,\,A\] done clear
View Answer play_arrowquestion_answer12) Photon and electron are given energy\[({{10}^{-2}}J)\]. Wavelengths associated with photon and electron are \[{{\lambda }_{ph}}\] and \[{{\lambda }_{el}}\] then, correct statement will be
A) \[{{\lambda }_{ph}}>{{\lambda }_{el}}\] done clear
B) \[{{\lambda }_{ph}}<{{\lambda }_{el}}\] done clear
C) \[{{\lambda }_{ph}}={{\lambda }_{el}}\] done clear
D) \[\frac{{{\lambda }_{el}}}{{{\lambda }_{ph}}}=c\] done clear
View Answer play_arrowquestion_answer13) The wavelength of radiation emitted is\[{{\lambda }_{0}}\]when an electron jumps from the third to the second orbit of hydrogen atom. For the electron jump from the fourth to the second orbit of hydrogen atom, the wavelength of radiation emitted will be
A) \[\frac{16}{25}{{\lambda }_{0}}\] done clear
B) \[\frac{20}{27}{{\lambda }_{0}}\] done clear
C) \[\frac{27}{20}{{\lambda }_{0}}\] done clear
D) \[\frac{25}{16}{{\lambda }_{0}}\] done clear
View Answer play_arrowquestion_answer14) Radius of \[_{2}H{{e}^{4}}\] nucleus is \[3\] fermi. The radius of \[_{82}P{{b}^{206}}\] nucleus will be
A) \[5\]fermi done clear
B) \[6\]Fermi done clear
C) \[11.16\] fermi done clear
D) \[8\] Fermi done clear
View Answer play_arrowquestion_answer15) The contribution in the total current flowing through a semiconductor due to electrons and holes are \[\frac{3}{4}\] and \[\frac{1}{4}\] respectively. If the drift velocity of electrons is \[\frac{5}{2}\] times that of holes at this temperature, then the ratio of concentration of electrons and holes is
A) \[6:5\] done clear
B) \[5:6\] done clear
C) \[3:2\] done clear
D) \[2:3\] done clear
View Answer play_arrowquestion_answer16) The attenuation in optical fibre is mainly due to
A) absorption done clear
B) scattering done clear
C) Neither absorption nor scattering done clear
D) Both [a] and [b] done clear
View Answer play_arrowquestion_answer17) An astronomical telescope has an angular magnification of magnitude \[5\] for distant objects. The separation between the objective and the eye-piece is \[36\,\,cm\] and the final image is formed at infinity. The focal length \[{{f}_{o}}\] of the objective and the focal length \[{{f}_{e}}\] of the eye-piece are
A) \[{{f}_{o}}=45\,\,cm\]and\[{{f}_{e}}=-9\,\,cm\] done clear
B) \[{{f}_{o}}=-7.2\,\,cm\]and\[{{f}_{e}}=5\,\,cm\] done clear
C) \[{{f}_{o}}=50\,\,cm\]and\[{{f}_{e}}=10\,\,cm\] done clear
D) \[{{f}_{o}}=30\,\,cm\]and\[{{f}_{e}}=6\,\,cm\] done clear
View Answer play_arrowquestion_answer18) A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of incident beam. At the first maximum of the diffraction pattern, the phase difference between the rays coming from the edges of the slit is
A) \[0\] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\pi \] done clear
D) \[2\pi \] done clear
View Answer play_arrowquestion_answer19) When the angle of incidence on a material is\[{{60}^{o}}\], the reflected light is completely polarized. The velocity of the refracted ray inside the material is (in\[m{{s}^{-1}})\]
A) \[3\times {{10}^{8}}\] done clear
B) \[\left[ \frac{3}{\sqrt{2}} \right]\times {{10}^{8}}\] done clear
C) \[\sqrt{3}\times {{10}^{8}}\] done clear
D) \[0.5\times {{10}^{8}}\] done clear
View Answer play_arrowquestion_answer20) Which of the following shows greenhouse effect?
A) Ultraviolet rays done clear
B) Infrared rays done clear
C) X-rays done clear
D) None of these done clear
View Answer play_arrowquestion_answer21) In Rutherford scattering experiment, what will be the correct angle for a scattering for an impact parameter\[b=0\]?
A) \[{{90}^{o}}\] done clear
B) \[{{270}^{o}}\] done clear
C) \[{{0}^{o}}\] done clear
D) \[{{180}^{o}}\] done clear
View Answer play_arrowquestion_answer22) A person sees his virtual image by holding a mirror very close to the face. When he moves the mirror away from his face, the image becomes inverted. What type of mirror he is using?
A) Plane mirror done clear
B) Convex mirror done clear
C) Concave mirror done clear
D) None of these done clear
View Answer play_arrowquestion_answer23) If a charged spherical conductor of radius \[10\,\,cm\] has potential \[V\] at a point distant \[5\,\,cm\] from its centre, then the potential at a point distant \[15\,\,cm\] from the centre will be
A) \[\frac{1}{3}V\] done clear
B) \[\frac{2}{3}V\] done clear
C) \[\frac{3}{2}V\] done clear
D) \[3V\] done clear
View Answer play_arrowquestion_answer24) The equation of state of some gases can be expressed as\[\left( p+\frac{a}{{{V}^{2}}} \right)(V-b)=RT\]where, \[p\] is the pressure, \[V\] the volume, \[T\] the absolute temperature and \[a\] and \[b\] are constants. The dimensional formula of \[a\] is
A) \[[M{{L}^{5}}{{T}^{-2}}]\] done clear
B) \[[{{M}^{-1}}{{L}^{5}}{{T}^{-2}}]\] done clear
C) \[[M{{L}^{-1}}{{T}^{-2}}]\] done clear
D) \[[M{{L}^{-5}}{{T}^{-2}}]\] done clear
View Answer play_arrowquestion_answer25) A \[16\,\,kg\] block moving on a frictionless horizontal surface with a velocity of \[4\,\,m/s\] compresses an ideal spring and comes to rest. If the force constant of the spring be \[100\,\,N/m,\] then the spring is compressed by
A) \[1.6\,\,m\] done clear
B) \[4\,\,m\] done clear
C) \[6.1\,\,m\] done clear
D) \[3.2\,\,m\] done clear
View Answer play_arrowquestion_answer26) A mass of \[6\times {{10}^{24}}kg\] is to be compressed in a sphere in such a way that the escape velocity from the sphere is\[3\times {{10}^{8}}m/s\]. What should be the radius of the sphere?\[(G=6.67\times {{10}^{-11}}N-{{m}^{2}}/k{{g}^{2}})\]
A) \[9\,\,km\] done clear
B) \[9\,\,m\] done clear
C) \[9\,\,cm\] done clear
D) \[9\,\,mm\] done clear
View Answer play_arrowquestion_answer27) A wire of length \[L\] and radius \[r\] fixed at one end and a force \[F\] applied to the other end produces an extension\[l\]. The extension produced in another wire of the same material of length \[2L\] and radius \[2r\] by a force\[2F\], is
A) \[l\] done clear
B) \[2l\] done clear
C) \[4l\] done clear
D) \[\frac{l}{2}\] done clear
View Answer play_arrowquestion_answer28) Two trains are moving towards each other with speeds of \[20\,\,m/s\] and \[15\,\,m/s\] relative to the ground. The first train, sounds a whistle of frequency\[600\,\,Hz\], the frequency of the whistle heard by a passenger in the second train before the train meets is (the speed of sound in air is\[340\,\,m/s)\]
A) \[600\,\,Hz\] done clear
B) \[585\,\,Hz\] done clear
C) \[645\,\,Hz\] done clear
D) \[666\,\,hz\] done clear
View Answer play_arrowquestion_answer29) Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is\[25\]. The intensities of the sources are in the ratio
A) \[25:1\] done clear
B) \[5:1\] done clear
C) \[9:4\] done clear
D) \[25:16\] done clear
View Answer play_arrowquestion_answer30) A microscope is focussed on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index \[1.5\] is placed over a mark. How should the microscope be moved to get the mark again in focus?
A) \[1\,\,cm\]upward done clear
B) \[4.5\,\,cm\]downward done clear
C) \[1\,\,cm\]downward done clear
D) \[2\,\,cm\]upward done clear
View Answer play_arrowquestion_answer31) A thin lens made of glass of refractive index \[\mu =1.5\] has a focal length equals to \[12\,\,cm\] in air. It is now immersed in water\[\left( \mu =\frac{4}{3} \right)\]. Its new focal length is
A) \[48\,\,cm\] done clear
B) \[36\,\,cm\] done clear
C) \[24\,\,cm\] done clear
D) \[12\,\,cm\] done clear
View Answer play_arrowquestion_answer32) Air is pumped into an automobile tube upto a pressure of \[200\,\,kPa\] in the morning when the air temperature is\[{{22}^{o}}C\]. During the day, temperature rises to \[{{42}^{o}}C\] and the tube expands by\[2%\]. The pressure of the air in the tube at this temperature, will be approximately
A) \[212\,\,kPa\] done clear
B) \[209\,\,kPa\] done clear
C) \[206\,\,kPa\] done clear
D) \[200\,\,kPa\] done clear
View Answer play_arrowquestion_answer33) A radioactive material decays by simultaneous emission of two particles with half-lives \[1620\,\,yr\] and \[810\,\,yr\] respectively. The time in year after which one-fourth of the material remains, is
A) \[4860\,\,yr\] done clear
B) \[3240\,\,yr\] done clear
C) \[2340\,\,yr\] done clear
D) \[1080\,\,yr\] done clear
View Answer play_arrowquestion_answer34) A stone dropped from a balloon which is at a height\[h\], reaches the ground after \[t\] second. From the same balloon, if two stones are thrown, one upwards and the other downwards, with the same velocity u and they reach the ground after \[{{t}_{1}}\] and \[{{t}_{2}}\] second respectively, then
A) \[t={{t}_{1}}-{{t}_{2}}\] done clear
B) \[t=\frac{{{t}_{1}}+{{t}_{2}}}{2}\] done clear
C) \[t=\sqrt{{{t}_{1}}{{t}_{2}}}\] done clear
D) \[t=\sqrt{t_{1}^{2}-t_{2}^{2}}\] done clear
View Answer play_arrowquestion_answer35) A shell at rest at the origin explodes into three fragments of masses \[1\,kg,\,\,2\,kg\] and\[m\,\,kg\]. The \[2\,\,kg\]\[\text{and}\]\[1\,\,kg\] pieces fly off with speeds of \[12\,\,m/s\] along x-axis and \[16\,\,m/s\] along y-axis respectively. If the \[m\,\,kg\] piece flies off with a speed of\[40\,\,m/s\], the total mass of the shell must be
A) \[3.7\,\,kg\] done clear
B) \[4\,\,kg\] done clear
C) \[4.5\,\,kg\] done clear
D) \[5\,\,kg\] done clear
View Answer play_arrowquestion_answer36) If a sphere is rolling, then the ratio of its rotational kinetic energy to the total kinetic energy is
A) \[3.7\,\,kg\] done clear
B) \[4\,\,kg\] done clear
C) \[4.5\,\,kg\] done clear
D) \[5\,\,kg\] done clear
View Answer play_arrowquestion_answer37) A body weighs w newton at the surface of the earth. Its weight at a height equals to half the radius of the earth, will be
A) \[\frac{w}{2}\] done clear
B) \[\frac{2w}{3}\] done clear
C) \[\frac{4w}{9}\] done clear
D) \[\frac{8w}{27}\] done clear
View Answer play_arrowquestion_answer38) Apart of a long wire carrying a current \[i\] is bent into a circle of radius \[r\] as shown in figure. The net magnetic field at the centre \[O\] of the circular loop is
A) \[\frac{{{\mu }_{0}}I}{4r}\] done clear
B) \[\frac{{{\mu }_{0}}I}{2r}\] done clear
C) \[\frac{{{\mu }_{0}}I}{2\pi r}(\pi +1)\] done clear
D) \[\frac{{{\mu }_{0}}I}{2\pi r}(\pi -1)\] done clear
View Answer play_arrowquestion_answer39) A \[36\Omega \] galvanometer is shunted by resistance of\[4\Omega \]. The percentage of the total current, which passes through the galvanometer is
A) \[8%\] done clear
B) \[9%\] done clear
C) \[10%\] done clear
D) \[91%\] done clear
View Answer play_arrowquestion_answer40) A can filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. The time period for a revolution is about
A) \[2\,\,s\] done clear
B) \[4\,\,s\] done clear
C) \[8\,\,s\] done clear
D) \[10\,\,s\] done clear
View Answer play_arrowquestion_answer41) The centre of mass of three particles of masses \[1\,\,kg,\,\,2\,\,kg\] and \[3\,\,kg\] is at \[(3,\,\,3,\,\,3)\] with reference to a fixed coordinate system. Where should a fourth particle of mass \[4\,\,kg\] be placed, so that the centre of mass of the system of all particles shifts to a point\[(1,\,\,1,\,\,1)?\]
A) \[(-1,\,\,-1,\,\,-1)\] done clear
B) \[(-2,\,\,-2,\,\,-2)\] done clear
C) \[(2,\,\,2,\,\,2)\] done clear
D) \[(1,\,\,1,\,\,1)\] done clear
View Answer play_arrowquestion_answer42) A pulley fixed to the ceiling carries a string with blocks of masses \[m\] and \[3m\] attached to its ends. The masses of string and pulley are negligible. When the system is released, the acceleration of centre of mass will be
A) \[zero\] done clear
B) \[-\frac{g}{4}\] done clear
C) \[\frac{g}{2}\] done clear
D) \[-\frac{g}{2}\] done clear
View Answer play_arrowquestion_answer43) A ray \[PQ\] incident on the refracting face \[BA\] is refracted in the prism \[BAC\] as shown in the figure and emerges from the other refracting face \[AC\] as\[RS\], such that\[AQ=AR\]. If the angle of prism \[A={{60}^{o}}\] and the refractive index of the material of prism is\[\sqrt{3}\], then the angle of deviation of the ray is
A) \[{{60}^{o}}\] done clear
B) \[{{45}^{o}}\] done clear
C) \[{{30}^{o}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer44) To get an output 1 from the circuit shown in the figure, the input must be
A) \[A=0,\,\,B=1,\,\,C=0\] done clear
B) \[A=1,\,\,B=0,\,\,C=0\] done clear
C) \[A=1,\,\,B=0,\,\,C=1\] done clear
D) \[A=1,\,\,B=1,\,\,C=0\] done clear
View Answer play_arrowquestion_answer45) Minimum number of \[8\mu F\] and \[250\,\,V\] capacitors are used to make a combination of \[16\mu F\] and \[1000\,\,V\] are
A) \[4\] done clear
B) \[32\] done clear
C) \[8\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer46) Let \[{{E}_{a}}\] be the electric field due to a dipole in its axial plane distant \[l\] and let \[{{E}_{q}}\] be the field in the equatorial plane distant\[l'\], then the relation between \[{{E}_{a}}\] and \[{{E}_{q}}\] will be
A) \[{{E}_{a}}=4{{E}_{q}}\] done clear
B) \[{{E}_{q}}=2{{E}_{a}}\] done clear
C) \[{{E}_{a}}=2{{E}_{q}}\] done clear
D) \[{{E}_{q}}=3{{E}_{a}}\] done clear
View Answer play_arrowquestion_answer47) The current in the given circuit is-
A) \[0.3\,\,A\] done clear
B) \[0.4\,\,A\] done clear
C) \[0.1\,\,A\] done clear
D) \[0.2\,\,A\] done clear
View Answer play_arrowquestion_answer48) In the circuit shown below what will be the readings of the voltmeter and ammeter? (Total impedance of circuit\[Z=100\Omega )\]
A) \[200\,\,V,\,\,1\,\,A\] done clear
B) \[800\,\,V,\,\,2\,\,A\] done clear
C) \[100\,\,V,\,\,2\,\,A\] done clear
D) \[220\,\,V,\,\,2.2\,\,A\] done clear
View Answer play_arrowquestion_answer49) A ball of mass \[10\,\,kg\] is moving with a velocity of\[10\,\,m/s\]. It strikes another ball of mass\[5\,\,kg\], which is moving in the same direction with a velocity of\[4\,\,m/s\]. If the collision is elastic, then their velocities after collision will be respectively
A) \[12\,\,m/s,\,\,6\,\,m/s\] done clear
B) \[12\,\,m/s,\,\,25\,\,m/s\] done clear
C) \[6\,\,m/s,\,\,12\,\,m/s\] done clear
D) \[8\,\,m/s,\,\,20\,\,m/s\] done clear
View Answer play_arrowquestion_answer50) A hole is made at the bottom of the tank filled with water (density\[1000kg/{{m}^{3}})\]. If the total pressure at the bottom of the tank is \[3\] atmosphere (1 atmosphere\[=105N/{{m}^{2}})\], then the velocity of efflux is
A) \[\sqrt{200}m/s\] done clear
B) \[\sqrt{400}m/s\] done clear
C) \[\sqrt{500}m/s\] done clear
D) \[\sqrt{800}m/s\] done clear
View Answer play_arrowquestion_answer51) The \[As{{F}_{5}}\] molecule is trigonal bipyramidal. The hybrid orbitals used by the \[As\] atoms, for bonding are
A) \[{{d}_{{{x}^{2}}-{{y}^{2}}}},\,\,{{d}_{{{z}^{2}}}},\,\,s,\,\,{{p}_{x}},\,\,{{p}_{y}}\] done clear
B) \[{{d}_{xy}},\,\,s,\,\,{{p}_{x}},\,\,{{p}_{y}},\,\,{{p}_{z}}\] done clear
C) \[s,\,\,{{p}_{x}},\,\,{{p}_{y}},\,\,{{p}_{z}},\,\,{{d}_{{{z}^{2}}}}\] done clear
D) \[{{d}_{{{x}^{2}}-{{y}^{2}}}},\,\,s,\,\,{{p}_{x}},\,\,{{p}_{y}}\] done clear
View Answer play_arrowquestion_answer52) The low density of ice compared to water is due to
A) induced dipole-induced dipole interactions done clear
B) dipole-induced dipole interactions done clear
C) hydrogen bonding interactions done clear
D) dipole-dipole interactions done clear
View Answer play_arrowquestion_answer53) Inorganic benzene is
A) \[{{B}_{3}}{{H}_{3}}{{N}_{3}}\] done clear
B) \[B{{H}_{3}}N{{H}_{3}}\] done clear
C) \[{{B}_{3}}{{H}_{6}}{{N}_{3}}\] done clear
D) \[{{H}_{3}}{{B}_{3}}{{N}_{6}}\] done clear
View Answer play_arrowquestion_answer54) Which of the following compounds will show metamerism?
A) \[C{{H}_{3}}-CO-{{C}_{2}}{{H}_{5}}\] done clear
B) \[{{C}_{2}}{{H}_{5}}-S-{{C}_{2}}{{H}_{5}}\] done clear
C) \[C{{H}_{3}}-O-C{{H}_{3}}\] done clear
D) \[C{{H}_{3}}-O-{{C}_{2}}{{H}_{5}}\] done clear
View Answer play_arrowquestion_answer55) Benzene on treatment with a mixture of conc. \[HN{{O}_{3}}\] and conc. \[{{H}_{2}}S{{O}_{4}}\]at \[{{100}^{o}}C\] gives
A) nitrobenzene done clear
B) \[m-\]dinitrobenzene done clear
C) \[p-\]dinitrobenzene done clear
D) \[o-\]dinitrobenzene done clear
View Answer play_arrowquestion_answer56) \[0.765\,\,g\] of an acid gives \[0.535\,\,g\] of \[C{{O}_{2}}\] and \[0.138\,\,g\] of. Then, the ratio of the percentage of carbon and hydrogen is
A) \[19:2\] done clear
B) \[18:11\] done clear
C) \[20:17\] done clear
D) \[1:7\] done clear
View Answer play_arrowquestion_answer57) Ziegler-Natta catalyst is
A) \[{{(P{{h}_{3}}P)}_{3}}RhCl\] done clear
B) \[K[PtC{{l}_{3}}({{C}_{2}}{{H}_{4}})]\] done clear
C) \[[A{{l}_{2}}{{({{C}_{2}}{{H}_{6}})}_{6}}+TiC{{l}_{4}}]\] done clear
D) \[[Fe{{({{C}_{2}}{{H}_{5}})}_{2}}]\] done clear
View Answer play_arrowquestion_answer58) \[1\,\,L\] oxygen gas at \[STP\] will weigh
A) \[1.43\,\,g\] done clear
B) \[2.24\,\,g\] done clear
C) \[11.2\,\,g\] done clear
D) \[22.4\,\,g\] done clear
View Answer play_arrowquestion_answer59) The \[IUPAC\] name of the compound,\[{{C}_{2}}{{H}_{5}}-\underset{\begin{smallmatrix} || \\ C{{H}_{2}} \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}OH\]is
A) 2-ethylprop-2-en-1-ol done clear
B) 2-hydroxymethylbutan-1-ol done clear
C) 2-methylenebutan-1-pl done clear
D) 2-ethyl-3-hydroxyprop-1-ene done clear
View Answer play_arrowquestion_answer60) The chemical name of vitamin \[{{B}_{1}}\] is
A) ascorbic acid done clear
B) riboflavin done clear
C) pyridoxine done clear
D) thiamine done clear
View Answer play_arrowquestion_answer61) Glyptal polymer is obtained from glycol by reacting with
A) malonic acid done clear
B) phthalic acid done clear
C) maleic acid done clear
D) terephthalic acid done clear
View Answer play_arrowquestion_answer62) Molecular formula of Glauber's salt is
A) \[MgS{{O}_{4}}\cdot 7{{H}_{2}}O\] done clear
B) \[CuS{{O}_{4}}\cdot 5{{H}_{2}}O\] done clear
C) \[FeS{{O}_{4}}\cdot 7{{H}_{2}}O\] done clear
D) \[N{{a}_{2}}S{{O}_{4}}\cdot 10{{H}_{2}}O\] done clear
View Answer play_arrowquestion_answer63) The size of colloidal particles is in between
A) \[{{10}^{-7}}-{{10}^{-9}}cm\] done clear
B) \[{{10}^{-9}}-{{10}^{-11}}cm\] done clear
C) \[{{10}^{-5}}-{{10}^{-7}}cm\] done clear
D) \[{{10}^{-2}}-{{10}^{-3}}cm\] done clear
View Answer play_arrowquestion_answer64) In the reaction,\[S{{O}_{2}}+2{{H}_{2}}S\xrightarrow{{}}3S+2{{H}_{2}}O\] the substance oxidised is
A) \[{{H}_{2}}S\] done clear
B) \[S{{O}_{2}}\] done clear
C) \[S\] done clear
D) \[{{H}_{2}}O\] done clear
View Answer play_arrowquestion_answer65) The emf of the cell\[Ni|N{{i}^{2+}}(1.0\,\,M)||A{{u}^{3+}}(1.0\,\,M)|Au\]is\[[{{E}^{o}}(N{{i}^{2+}}/Ni)=-0.25\,\,V\]and\[(A{{u}^{3+}}/Au)=+1.5\,\,V]\]
A) \[2.00\,\,V\] done clear
B) \[1.25\,\,V\] done clear
C) \[-1.25\,\,V\] done clear
D) \[1.75\,\,V\] done clear
View Answer play_arrowquestion_answer66) The heat of neutralisation is highest for the reaction between
A) \[N{{H}_{4}}OH-C{{H}_{3}}COOH\] done clear
B) \[HN{{O}_{3}}-N{{H}_{4}}OH\] done clear
C) \[NaOH-C{{H}_{3}}COOH\] done clear
D) \[HCl-NaOH\] done clear
View Answer play_arrowquestion_answer67) An ideal gas expands in volume from \[1\times {{10}^{-3}}{{m}^{3}}\]to\[1\times {{10}^{-2}}{{m}^{3}}\]at \[300\,\,K\] against a constant pressure of\[1\times {{10}^{5}}N{{m}^{-2}}\]. The work done is
A) \[-900\,\,J\] done clear
B) \[-900\,\,kJ\] done clear
C) \[270\,\,kJ\] done clear
D) \[900\,\,kJ\] done clear
View Answer play_arrowquestion_answer68) Which one of the following is correct?
A) \[-\Delta G=\Delta H-T\Delta S\] done clear
B) \[\Delta H=\Delta G-T\Delta S\] done clear
C) \[\Delta S=\frac{1}{T}[\Delta G-\Delta H]\] done clear
D) \[\Delta S=\frac{1}{T}[\Delta H-\Delta G]\] done clear
View Answer play_arrowquestion_answer69) The electronic configuration of element with atomic number \[24\] is
A) \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}}3{{d}^{4}},\,\,4{{s}^{2}}\] done clear
B) \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}}3{{d}^{10}}\] done clear
C) \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}}3{{d}^{6}}\] done clear
D) \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}}3{{d}^{5}},\,\,4{{s}^{1}}\] done clear
View Answer play_arrowquestion_answer70) In van der Waals' equation, of state of the gas law, the constant \['b'\] is a measure of
A) intermolecular repulsions done clear
B) intermolecular attraction done clear
C) volume occupied by the molecules done clear
D) intermolecular collisions per unit volume done clear
View Answer play_arrowquestion_answer71) If the radius of \[{{K}^{+}}\]and\[{{F}^{-}}\] are \[133\,\,pm\] and \[136\,\,pm\] respectively, the distance between \[{{K}^{+}}\]and \[{{F}^{-}}\]in \[KF\] is
A) \[269\,\,pm\] done clear
B) \[134.5\,\,pm\] done clear
C) \[136\,\,pm\] done clear
D) \[3\,\,pm\] done clear
View Answer play_arrowquestion_answer72) The property of attracting electrons by the halogen atoms in a molecule is called
A) ionization potential done clear
B) electron affinity done clear
C) electronegativity done clear
D) electronic attraction done clear
View Answer play_arrowquestion_answer73) A reversible chemical reaction is having two reactants, in equilibrium. If the concentration of the reactants are doubled then the equilibrium constant will
A) be doubled done clear
B) become one fourth done clear
C) be halved done clear
D) remain the same done clear
View Answer play_arrowquestion_answer74) The strongest Bronsted base is
A) \[ClO_{3}^{-}\] done clear
B) \[ClO_{2}^{-}\] done clear
C) \[ClO_{4}^{-}\] done clear
D) \[Cl{{O}^{-}}\] done clear
View Answer play_arrowquestion_answer75) A solution contains \[10\,\,mL\] \[0.1\,\,N\,\,NaOH\] and NH\[10\,\,mL\,\,0.05\,\,N\,\,{{H}_{2}}S{{O}_{4}}\], \[pH\] of this solution is
A) less than\[7\] done clear
B) \[7\] done clear
C) zero done clear
D) greater than\[7\] done clear
View Answer play_arrowquestion_answer76) For which one of the following reactions\[{{K}_{p}}={{K}_{c}}\]?
A) \[PC{{l}_{5}}PC{{l}_{3}}+C{{l}_{2}}\] done clear
B) \[{{N}_{2}}+{{O}_{2}}2NO\] done clear
C) \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}\] done clear
D) \[2S{{O}_{3}}2S{{O}_{2}}+{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer77) What is the molarity of \[0.2\,\,N\,\,N{{a}_{2}}C{{O}_{3}}\] solution?
A) \[0.1\,\,M\] done clear
B) \[0\,\,M\] done clear
C) \[0.4\,\,M\] done clear
D) \[0.2\,\,M\] done clear
View Answer play_arrowquestion_answer78) The order of a reaction with rate equal to \[kC_{A}^{3/2}C_{B}^{-1/2}\]is
A) \[1\] done clear
B) \[-\frac{1}{2}\] done clear
C) \[-\frac{3}{2}\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer79) A simple method to remove peroxides from ethers is to treat them with an aqueous solution of
A) \[KI\] done clear
B) \[KCNS\] done clear
C) \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\] done clear
D) \[B{{r}_{2}}\] done clear
View Answer play_arrowquestion_answer80) Which of the following is the predominant product in the reaction of \[HOBr\] with propene?
A) 2-bromo-1-propanol done clear
B) 3-bromo-1-propanol done clear
C) 2-bromo-2-propanol done clear
D) 1-bromo-2-propanol done clear
View Answer play_arrowquestion_answer81) Most stable carbonium ion is
A) \[{{\overset{+}{\mathop{C}}\,}_{2}}{{H}_{5}}\] done clear
B) \[{{(C{{H}_{3}})}_{3}}\overset{+}{\mathop{C}}\,\] done clear
C) \[{{({{C}_{6}}{{H}_{5}})}_{3}}\overset{+}{\mathop{C}}\,\] done clear
D) \[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{C}}\,{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer82) In aqueous solutions, the basic strength of amines decreases in the order
A) \[C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{2}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N\] done clear
B) \[{{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}\] done clear
C) \[{{(C{{H}_{3}})}_{3}}N>{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}\] done clear
D) \[{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N\] done clear
View Answer play_arrowquestion_answer83) The most reactive compound towards formation of cyanohydrin on treatment with HCN followed by acidification is
A) benzaldehyde done clear
B) \[p-\]nitrobenzaldehyde done clear
C) phenylacetaldehyde done clear
D) \[p-\]hydroxybenzaldehyde done clear
View Answer play_arrowquestion_answer84) Producer gas is the mixture of
A) \[CO+{{N}_{2}}\] done clear
B) \[CO+{{H}_{2}}\] done clear
C) \[CO+\]water vapour done clear
D) \[{{N}_{2}}+C{{H}_{4}}\] done clear
View Answer play_arrowquestion_answer85) What is the freezing point of a solution containing \[8.1\,\,g\,\,HBr\] in \[100\,\,g\] water assuming the acid to be \[90%\] ionised? \[({{k}_{f}}\] for water\[=1.86\,\,K\,\,mo{{l}^{-1}})\]
A) \[{{0.85}^{o}}C\] done clear
B) \[-{{3.53}^{o}}C\] done clear
C) \[{{0}^{o}}C\] done clear
D) \[-{{0.35}^{o}}C\] done clear
View Answer play_arrowquestion_answer86) Number of elements presents in the fifth period of Periodic Table is
A) \[32\] done clear
B) \[10\] done clear
C) \[18\] done clear
D) \[8\] done clear
View Answer play_arrowquestion_answer87) \[{{[Sc({{H}_{2}}{{O}_{6}})]}^{3+}}\]ion is
A) colourless and diamagnetic done clear
B) coloured and octahedral done clear
C) colourless and paramagnetic done clear
D) coloured and paramagnetic done clear
View Answer play_arrowquestion_answer88) Which one has the highest boiling point?
A) \[{{H}_{2}}\] done clear
B) \[Xe\] done clear
C) \[C{{H}_{4}}\] done clear
D) \[He\] done clear
View Answer play_arrowquestion_answer89) Benzaldehyde reacts with ammonia to form
A) benzaldehyde ammonia done clear
B) urotropine done clear
C) hydrobenzamide done clear
D) ammonium chloride done clear
View Answer play_arrowquestion_answer90) Identify \[Z\] in the sequence\[C{{H}_{3}}COON{{H}_{4}}\xrightarrow{\Delta }X\xrightarrow[\Delta ]{{{P}_{2}}{{O}_{5}}}Y\xrightarrow{{{H}_{2}}O/{{H}^{+}}}Z\]
A) \[C{{H}_{3}}C{{H}_{2}}CON{{H}_{2}}\] done clear
B) \[C{{H}_{3}}CN\] done clear
C) \[C{{H}_{3}}COOH\] done clear
D) \[{{(C{{H}_{3}}CO)}_{2}}O\] done clear
View Answer play_arrowquestion_answer91) Acetic anhydride reacts with diethyl ether in the presence of anhydrous \[AlC{{l}_{3}}\] to give
A) \[C{{H}_{3}}C{{H}_{2}}COOH\] done clear
B) \[C{{H}_{3}}C{{H}_{2}}COOC{{H}_{2}}C{{H}_{3}}\] done clear
C) \[C{{H}_{3}}COOC{{H}_{3}}\] done clear
D) \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}\] done clear
View Answer play_arrowquestion_answer92) Denaturation of proteins leads to loss of its biological activity by
A) formation of amino acids done clear
B) loss of primary structure done clear
C) loss of both primary and secondary structures done clear
D) loss of both secondary and tertiary structures done clear
View Answer play_arrowquestion_answer93) The compound with highest boiling point
A) n-hexane done clear
B) n-pentane done clear
C) 2, 2-dimethylpropane done clear
D) 2-methylbutane done clear
View Answer play_arrowquestion_answer94) Which of the following statements concerning transition elements is false?
A) They are all metals done clear
B) They easily form complex coordination compounds done clear
C) Compounds containing their ions are mostly coloured done clear
D) They show multiple oxidation states always differing by units of two done clear
View Answer play_arrowquestion_answer95) In the manufacture of bromine from sea water, the mother liquor containing bromide is treated with
A) carbon dioxide done clear
B) chlorine done clear
C) iodine done clear
D) sulphur dioxide done clear
View Answer play_arrowquestion_answer96) A transition element X has the configuration \[[Ar]{{d}^{4}}\] in its \[+3\] oxidation state. It?s atomic number is
A) \[25\] done clear
B) \[26\] done clear
C) \[22\] done clear
D) \[19\] done clear
View Answer play_arrowquestion_answer97) The element with the electronic configuration as \[[Ar]3{{d}^{10}}4{{s}^{2}}4{{p}^{3}}\] represents a
A) metal done clear
B) non-metal done clear
C) metalloid done clear
D) transition element done clear
View Answer play_arrowquestion_answer98) The number of moles of\[{{H}_{2}}\]in\[0.224\] hydrogen gas at\[STP\,\,(273\,\,K,\,\,1\,\,atm)\], is
A) \[0.1\] done clear
B) \[0.01\] done clear
C) \[0.001\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer99) The molecule which has zero dipole moment is
A) \[C{{H}_{3}}Cl\] done clear
B) \[N{{F}_{3}}\] done clear
C) \[B{{F}_{3}}\] done clear
D) \[Cl{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer100) Greenhouse effect is caused by
A) \[N{{O}_{2}}\] done clear
B) \[CO\] done clear
C) \[NO\] done clear
D) \[C{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer101) If\[y=\sin x\], then\[\frac{{{d}^{2}}}{d{{y}^{2}}}({{\cos }^{7}}x)\]is equal to
A) \[7{{\cos }^{5}}x+35{{\cos }^{3}}x\] done clear
B) \[7{{\cos }^{5}}x+35{{\cos }^{2}}x\] done clear
C) \[-7{{\cos }^{5}}x+35{{\cos }^{2}}x\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer102) The equation of ellipse whose axes are coincident with the coordinate axes and which touches the straight lines \[3x-2y-20=0\] and\[x+6y-20=0\], is
A) \[\frac{{{x}^{2}}}{5}+\frac{{{y}^{2}}}{8}=1\] done clear
B) \[\frac{{{x}^{2}}}{40}+\frac{{{y}^{2}}}{10}=10\] done clear
C) \[\frac{{{x}^{2}}}{40}+\frac{{{y}^{2}}}{10}=1\] done clear
D) \[\frac{{{x}^{2}}}{10}+\frac{{{y}^{2}}}{40}=1\] done clear
View Answer play_arrowquestion_answer103) The equation of the radical axis of the circles \[2{{x}^{2}}+2{{y}^{2}}+14x-18y+15=0\]and\[4{{x}^{2}}+4{{y}^{2}}-3x-y+5=0\], is
A) \[31x+35y-25=0\] done clear
B) \[31x-35y+25=0\] done clear
C) \[35x+31y-25=0\] done clear
D) \[35x-31y+25=0\] done clear
View Answer play_arrowquestion_answer104) SS\[\underset{x\to 1}{\mathop{\lim }}\,\frac{1+\log x-x}{1-2x+{{x}^{2}}}\]is equal to
A) \[1\] done clear
B) \[-1\] done clear
C) \[0\] done clear
D) \[-\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer105) \[\int_{0}^{\pi /2}{{{\cos }^{5}}\left( \frac{x}{2} \right)}\sin x\,\,dx\]is equal to
A) \[\frac{2}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)\] done clear
B) \[-\frac{4}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)\] done clear
C) \[\frac{4}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)\] done clear
D) \[-\frac{2}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)\] done clear
View Answer play_arrowquestion_answer106) The area of the region bounded by the curve \[y=\frac{{{a}^{3}}}{{{x}^{2}}+{{a}^{2}}}\]and \[x-axis\] is
A) \[\pi {{a}^{2}}sq\,\,unit\] done clear
B) \[2\pi {{a}^{2}}sq\,\,unit\] done clear
C) \[3\pi {{a}^{2}}sq\,\,unit\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer107) If the constant forces\[2\widehat{\mathbf{i}}-5\widehat{\mathbf{j}}+6\widehat{\mathbf{k}}\]and \[-\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}-\widehat{\mathbf{k}}\]act on a particle due to which it is displaced from a point\[A(4,\,\,-3,\,\,-2)\]to a point\[B(6,\,\,1,\,\,-3)\]then the work done by the force is
A) \[25\,\,unit\] done clear
B) \[-15\,\,unit\] done clear
C) \[9\,\,unit\] done clear
D) \[-9\,\,unit\] done clear
View Answer play_arrowquestion_answer108) The equation of the line which passes through the point \[(3,\,\,4)\] and the sum of its intercepts on the axes is\[14\], is
A) \[x+y=7\]and\[4x+3y=24\] done clear
B) \[x+y=24\]and\[4x+3y=7\] done clear
C) \[x-y=7\]and\[4x-3y=24\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer109) If\[{{x}^{2}}-x+1=0\], then the value of\[\sum\limits_{n=1}^{5}{{{\left( {{x}^{n}}+\frac{1}{{{x}^{n}}} \right)}^{2}}}\]is
A) \[8\] done clear
B) \[10\] done clear
C) \[12\] done clear
D) \[14\] done clear
View Answer play_arrowquestion_answer110) Minimum value of\[{{4}^{x}}-{{4}^{1-x}},\,\,x\in R\]is
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer111) If \[\alpha ,\,\,\beta \] are the roots of equation\[8{{x}^{2}}-3x+27=0\], then the value of\[{{\left( \frac{{{\alpha }^{2}}}{\beta } \right)}^{1/3}}+{{\left( \frac{{{\beta }^{2}}}{\alpha } \right)}^{1/3}}\]is
A) \[\frac{1}{3}\] done clear
B) \[\frac{1}{4}\] done clear
C) \[\frac{7}{2}\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer112) There are four candidates for the post of a lecturer in Mathematics and one is to be selected by votes of \[5\] men. The number of ways in which the votes can be given is
A) \[1048\] done clear
B) \[1072\] done clear
C) \[1024\] done clear
D) \[1064\] done clear
View Answer play_arrowquestion_answer113) The coefficient of \[{{x}^{4}}\] in the expansion of\[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{11}}\], is
A) \[990\] done clear
B) \[605\] done clear
C) \[810\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer114) If the matrix\[\left[ \begin{matrix} 0 & 2\beta & \gamma \\ \alpha & \beta & -\gamma \\ \alpha & -\beta & \gamma \\ \end{matrix} \right]\]is orthogonal, then
A) \[\alpha =\pm \frac{1}{\sqrt{2}}\] done clear
B) \[\beta =\pm \frac{1}{\sqrt{6}}\] done clear
C) \[\gamma =\pm \frac{1}{\sqrt{3}}\] done clear
D) All of these done clear
View Answer play_arrowquestion_answer115) The sum of the series \[{{\log }_{4}}2-{{\log }_{8}}2+{{\log }_{16}}2-....\infty \], is
A) \[{{e}^{2}}\] done clear
B) \[{{\log }_{e}}2+1\] done clear
C) \[{{\log }_{e}}2-1\] done clear
D) \[1-{{\log }_{e}}2\] done clear
View Answer play_arrowquestion_answer116) The range of the function\[f(x)=\frac{x-2}{2-x}\], when\[x\ne 2\]is
A) \[R\] done clear
B) \[R-\{1\}\] done clear
C) \[\{-1\}\] done clear
D) \[R-\{-1\}\] done clear
View Answer play_arrowquestion_answer117) If \[A\] and \[B\] are two independent events such that \[P(A)=\frac{1}{2}\] and \[P(B)=\frac{1}{5},\] then which of the following is/are correct?
A) \[P(A\cup B)=\frac{5}{3}\] done clear
B) \[P\left( \frac{A}{B} \right)=\frac{1}{3}\] done clear
C) \[P\left( \frac{A}{A\cup B} \right)=\frac{5}{6}\] done clear
D) All of these done clear
View Answer play_arrowquestion_answer118) The probability of \[A\] to fail in an examination is \[\frac{1}{5}\] and that of \[B\] is\[\frac{3}{10}\], then the probability that either \[A\] or \[B\] fails is
A) \[\frac{1}{2}\] done clear
B) \[\frac{11}{25}\] done clear
C) \[\frac{19}{50}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer119) The value of \[\cos y\cos \left( \frac{\pi }{2}-x \right)-\cos \left( \frac{\pi }{2}-y \right)\cos x\] \[+\sin y\cos \left( \frac{\pi }{2}-x \right)+\cos x\sin \left( \frac{\pi }{2}-y \right)\]is zero, if
A) \[x=0\] done clear
B) \[y=0\] done clear
C) \[x=y\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer120) The value of\[\sin [{{\cot }^{-1}}\{{{\cot }^{-1}}({{\cos }^{-1}}x)\}]\]is equal to
A) \[\frac{\sqrt{1-{{x}^{2}}}}{x}\] done clear
B) \[\frac{x}{\sqrt{1-{{x}^{2}}}}\] done clear
C) \[x\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer121) . The maximum value of \[P=6x+8y\] subject to constraints\[2x+y\le 30,\,\,x+2y\le 24\]and\[x\ge 0,\,\,y\ge 0\]is
A) \[90\] done clear
B) \[120\] done clear
C) \[96\] done clear
D) \[240\] done clear
View Answer play_arrowquestion_answer122) With the help of trapezoidal rule for numerical integration and the following table.
\[x\] | \[0\] | \[0.25\] | \[0.50\] | \[0.75\] | \[1\] |
\[f(x)\] | \[0\] | \[0.625\] | \[0.2500\] | \[0.5625\] | \[1\] |
A) \[0.35342\] done clear
B) \[0.34375\] done clear
C) \[0.34457\] done clear
D) \[0.33334\] done clear
View Answer play_arrowquestion_answer123) If \[B\] is an idempotent matrix and\[A=I-B\], then
A) \[{{A}^{2}}=A\] done clear
B) \[AB=0\] done clear
C) \[BA=0\] done clear
D) All of the above done clear
View Answer play_arrowquestion_answer124) The coefficient of \[{{x}^{20}}\] in the expansion of\[{{(1+{{x}^{2}})}^{40}}{{\left( {{x}^{2}}+2+\frac{1}{{{x}^{2}}} \right)}^{-5}}\], is
A) \[^{30}{{C}_{10}}\] done clear
B) \[^{30}{{C}_{25}}\] done clear
C) \[1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer125) For what values of\[k\in R\], the expression \[2{{x}^{2}}+kxy+3{{y}^{2}}-5y-2\] can be expressed as\[({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}})\cdot ({{a}_{2}}x+{{b}_{2}}y+{{c}_{2}})\]?
A) \[-3,\,\,-4\] done clear
B) \[2,\,\,3\] done clear
C) \[3,\,\,4\] done clear
D) \[7,\,\,-7\] done clear
View Answer play_arrowquestion_answer126) If \[a,\,\,\,b,\,\,\,c\] are the sides of a \[\Delta \,\,ABC\] which are in\[AP\], then \[\cot \frac{C}{2}\] is equal to
A) \[3\tan \frac{A}{2}\] done clear
B) \[3\tan \frac{B}{2}\] done clear
C) \[3\cot \frac{A}{2}\] done clear
D) \[2\cot \frac{B}{2}\] done clear
View Answer play_arrowquestion_answer127) The continued product of the four values of \[{{\left[ \cos \left( \frac{\pi }{3} \right)+i\sin \left( \frac{\pi }{3} \right) \right]}^{3/4}}\], is
A) \[-1\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) \[-2\] done clear
View Answer play_arrowquestion_answer128) For the given line\[3x-4y=8\], the points \[(2,\,\,3)\] and \[(-4,\,\,5)\] are on the
A) same side done clear
B) opposite side done clear
C) lie on the line done clear
D) None of these done clear
View Answer play_arrowquestion_answer129) The abscissae and ordinates of the points \[A\] and \[B\] are the roots of the equations\[{{x}^{2}}+2ax+b=0\]and\[{{x}^{2}}+2cx+d=0\] respective, then the equation, of circle with \[AB\] is diameter, is
A) \[{{x}^{2}}+{{y}^{2}}+2ax+2cy+b+d=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2ax-2cy-b-d=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2ax+2cy-b-d=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-2ax-2cy+b+d=0\] done clear
View Answer play_arrowquestion_answer130) If \[2x+y+k=0\]is a normal to the parabola\[{{y}^{2}}=-8x\], then the value of \[k\] is
A) \[-16\] done clear
B) \[-8\] done clear
C) \[-24\] done clear
D) \[24\] done clear
View Answer play_arrowquestion_answer131) The equation of tangent parallel to \[y=x\] drawn to\[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\], is
A) \[x-y+1=0\] done clear
B) \[x-y+2=0\] done clear
C) \[x+y-1=0\] done clear
D) \[x+y-2=0\] done clear
View Answer play_arrowquestion_answer132) The domain of the function\[f(x)=\sqrt{3-x}+{{\cos }^{-1}}\left( \frac{3-2x}{5} \right)\], is
A) \[[-1,\,\,3]\] done clear
B) \[(-1,\,\,3]\] done clear
C) \[[-1,\,\,3)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer133) If \[f(x)\] is differentiable in the interval \[[2,\,\,5]\] where\[f(2)=\frac{1}{5}\]and\[f(5)=\frac{1}{2}\], then there exist a number \[c,\,\,2<c<5\] for which \[f'(c)\] is equal to
A) \[\frac{1}{2}\] done clear
B) \[\frac{1}{5}\] done clear
C) \[\frac{1}{10}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer134) If the line \[ax+by+c=0\]is a normal to the curve\[xy=1\], then
A) \[a>0,\,\,b>0\] done clear
B) \[a>0,\,\,b<0\] done clear
C) \[a<0,\,\,b<0\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer135) \[\int{{{\sec }^{3}}x}\,\,dx\]is equal to
A) \[\sec x\tan x+\log |\sec x+\tan x|+c\] done clear
B) \[\frac{1}{2}\sec x\tan x+\frac{1}{2}\log |\sec x+\tan x|+c\] done clear
C) \[{{\sec }^{3}}x\tan x+\log |{{\sec }^{3}}x+\tan x|+c\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer136) The order and. degree of the differential equation\[{{\left( 1+3\frac{dy}{dx} \right)}^{2/3}}=4\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)\]are
A) \[1,\,\,\frac{2}{3}\] done clear
B) \[3,\,\,1\] done clear
C) \[3,\,\,3\] done clear
D) \[1,\,\,2\] done clear
View Answer play_arrowquestion_answer137) If \[\sin x\] is an integrating factor of the differential equation\[\frac{dy}{dx}+Py=Q\], then \[P\] can be
A) \[\log \sin x\] done clear
B) \[\cot x\] done clear
C) \[\sin x\] done clear
D) \[\log \cos x\] done clear
View Answer play_arrowquestion_answer138) Let\[\overset{\to }{\mathop{\mathbf{a}}}\,=\widehat{\mathbf{i}}-\widehat{\mathbf{k}},\,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,=x\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+(1-x)\widehat{\mathbf{k}}\]and\[\overset{\to }{\mathop{\mathbf{c}}}\,=y\widehat{\mathbf{i}}+x\widehat{\mathbf{j}}+(1+x-y)\widehat{\mathbf{k}}\]. Then,\[[\overrightarrow{\mathbf{a}}\overrightarrow{\mathbf{b}}\overrightarrow{\mathbf{c}}]\] depends on,
A) only\[x\] done clear
B) only\[y\] done clear
C) neither\[x\]nor\[y\] done clear
D) both \[x\] and\[y\] done clear
View Answer play_arrowquestion_answer139) If the planes\[\overset{\to }{\mathop{\mathbf{r}}}\,\cdot (2\widehat{\mathbf{i}}-\lambda \widehat{\mathbf{j}}+\widehat{\mathbf{k}})=3\]and\[\overset{\to }{\mathop{\mathbf{r}}}\,\cdot (4\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\mu \widehat{\mathbf{k}})=5\]are parallel, then the value of \[\lambda \] and \[\mu \] are
A) \[\frac{1}{2},\,\,-2\] done clear
B) \[-\frac{1}{2},\,\,2\] done clear
C) \[-\frac{1}{2},\,\,-2\] done clear
D) \[\frac{1}{2},\,\,2\] done clear
View Answer play_arrowquestion_answer140) Two forces \[P\] and \[Q\] acting at a point have a resultant\[R\]. The resolved of \[R\] in the direction of \[P\] is a magnitude\[Q\]. Then, the angle between the forces and the magnitude of the resultant are
A) \[\theta ={{\cos }^{-1}}\left( \frac{P-Q}{Q} \right),\,\,R=\sqrt{{{P}^{2}}-{{Q}^{2}}+2PQ}\] done clear
B) \[\theta ={{\cos }^{-1}}\left( \frac{Q-P}{Q} \right),\,\,R=\sqrt{{{Q}^{2}}-{{P}^{2}}+2PQ}\] done clear
C) \[\theta ={{\cos }^{-1}}\left( \frac{P-Q}{P} \right),\,\,R=\sqrt{2{{P}^{2}}-{{Q}^{2}}+2PQ}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer141) A point is moving in a straight line with uniform acceleration describes \[a\] and \[b\] feet in successive intervals of \[{{t}_{1}}\] and \[{{t}_{2}}\] seconds. Then, the acceleration is
A) \[\frac{2(b{{t}_{1}}-a{{t}_{2}})}{{{t}_{1}}{{t}_{2}}({{t}_{1}}+{{t}_{2}})}\] done clear
B) \[\frac{b{{t}_{2}}-a{{t}_{1}}}{{{t}_{1}}{{t}_{2}}({{t}_{1}}+{{t}_{2}})}\] done clear
C) \[\frac{b{{t}_{2}}-a{{t}_{1}}}{2{{t}_{1}}{{t}_{2}}({{t}_{1}}+{{t}_{2}})}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer142) If\[2f(x)+3f\left( \frac{1}{x} \right)=\frac{1}{x}-2,\,\,x\ne 0\], then\[\int_{1}^{2}{f(x)}\,\,dx\]equal to
A) \[-\frac{2}{5}\log 2+\frac{1}{2}\] done clear
B) \[-\frac{2}{5}\log 2-\frac{1}{2}\] done clear
C) \[\frac{2}{5}\log 2+\frac{1}{2}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer143) The maximum value of the function \[y=x{{(x-1)}^{2}}\], is
A) \[0\] done clear
B) \[\frac{4}{27}\] done clear
C) \[-4\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer144) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{x}}{\sqrt{4-\sqrt{x}}-\sqrt{x}}\]is equal to
A) \[0\] done clear
B) \[1\] done clear
C) \[-1\] done clear
D) does not exist done clear
View Answer play_arrowquestion_answer145) If\[\frac{d}{dx}\left( \frac{1+{{x}^{4}}+{{x}^{8}}}{1+{{x}^{2}}+{{x}^{4}}} \right)=a{{x}^{3}}+bx\], then
A) \[a=4,\,\,b=2\] done clear
B) \[a=4,\,\,b=-2\] done clear
C) \[a=-2,\,\,b=4\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer146) If\[y={{x}^{n-1}}\log x\], then\[{{x}^{2}}{{y}_{2}}+(3-2n)x{{y}_{1}}\]is equal to
A) \[-{{(n-1)}^{2}}y\] done clear
B) \[{{(n-1)}^{2}}y\] done clear
C) \[-{{n}^{2}}y\] done clear
D) \[{{n}^{2}}y\] done clear
View Answer play_arrowquestion_answer147) The length of latusrectum of the ellipse\[2{{x}^{2}}+{{y}^{2}}-8x+2y+7=0\], is
A) \[\sqrt{2}\] done clear
B) \[2\] done clear
C) \[8\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer148) The angle between the pair of tangents from the point \[\left( 1,\,\,\frac{1}{2} \right)\] to the circle\[{{x}^{2}}+{{y}^{2}}+4x+2y-4=0\], is
A) \[{{\cos }^{-1}}\left( \frac{4}{5} \right)\] done clear
B) \[{{\sin }^{-1}}\left( \frac{4}{5} \right)\] done clear
C) \[{{\tan }^{-1}}\left( \frac{4}{5} \right)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer149) The value of\[\cos \left( \frac{\pi }{7} \right)\cos \left( \frac{4\pi }{7} \right)\cos \left( \frac{5\pi }{7} \right)\]is equal to
A) \[\frac{1}{2}\] done clear
B) \[\frac{1}{4}\] done clear
C) \[-\frac{1}{8}\] done clear
D) \[\frac{1}{8}\] done clear
View Answer play_arrowquestion_answer150) The vertical poles, \[AB\] of length \[2\,\,m\] and \[CD\] of length \[20\,\,m\] are erected with base \[B\] and \[D\] respectively. It is given that distance between the poles is more than \[20\,\,m\] and \[(\angle ACB)=\frac{2}{77}\], then distance between the poles is
A) \[68\,\,m\] done clear
B) \[24\,\,m\] done clear
C) \[72\,\,m\] done clear
D) None of these done clear
View Answer play_arrow
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