question_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
question_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
question_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\[(g=10\,\,m/{{s}^{2}})\]
question_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
question_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,\[X=\frac{\pi p{{R}^{4}}}{8\eta L})\]
question_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
question_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
question_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
question_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
question_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
question_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
question_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
question_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
question_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\[m{{s}^{-1}})\]
question_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?
question_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
question_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
question_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
question_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?\[(G=6.67\times {{10}^{-11}}N-{{m}^{2}}/k{{g}^{2}})\]
question_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
question_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\[340\,\,m/s)\]
question_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
question_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?
question_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
question_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
question_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
question_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
question_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
question_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
question_answer39) A \[36\Omega \] galvanometer is shunted by resistance of\[4\Omega \]. The percentage of the total current, which passes through the galvanometer is
question_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
question_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\[(1,\,\,1,\,\,1)?\]
question_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
question_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
question_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
question_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
question_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
question_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
question_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
question_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\[(A{{u}^{3+}}/Au)=+1.5\,\,V]\]
question_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
question_answer71) If the radius of \[{{K}^{+}}\]and\[{{F}^{-}}\] are \[133\,\,pm\] and \[136\,\,pm\] respectively, the distance between \[{{K}^{+}}\]and \[{{F}^{-}}\]in \[KF\] is
question_answer73) A reversible chemical reaction is having two reactants, in equilibrium. If the concentration of the reactants are doubled then the equilibrium constant will
question_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
question_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\[=1.86\,\,K\,\,mo{{l}^{-1}})\]
question_answer90) Identify \[Z\] in the sequence\[C{{H}_{3}}COON{{H}_{4}}\xrightarrow{\Delta }X\xrightarrow[\Delta ]{{{P}_{2}}{{O}_{5}}}Y\xrightarrow{{{H}_{2}}O/{{H}^{+}}}Z\]
question_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
question_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
question_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
question_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
question_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?
question_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
question_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
question_answer125) For what values of\[k\in R\], the expression \[2{{x}^{2}}+kxy+3{{y}^{2}}-5y-2\] can be expressed as\[({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}})\cdot ({{a}_{2}}x+{{b}_{2}}y+{{c}_{2}})\]?
question_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
question_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
question_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
question_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
question_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
question_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
question_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
question_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
question_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