question_answer2) A train 100 m long travelling at 40 m/s starts overtaking another train 200 m long travelling at 30 m/s. The time taken by the first train to pass the second train completely is
question_answer3) A constant power P is applied to a particle of mass m. The distance travelled by the particle when its velocity increases from \[{{v}_{1}}\] to \[{{v}_{2}}\] is (neglect friction)
question_answer4) A spring of constant \[5\,\times {{10}^{3}}\,N/m\] is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is
question_answer5) Four spheres each having mass m and radius r are placed with their centres on the four comers of a square of side a. Then the moment of inertia of the system about an axis along one of the sides of the square is
question_answer6) If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is
question_answer7) A 2 kg copper block is heated to \[500{}^\circ C\] and then it is placed on a large block of ice at \[0{}^\circ C\]. If the specific heat capacity of copper is 400 J/kg/C and latent heat of water is \[3.5\times {{10}^{5}}J/kg\]. The amount of ice that can melt is
question_answer8) Number of waves in 8 cm of vacuum is same as number of waves in x cm of a medium. Refractive index of medium is 4/3, then the value x is
question_answer9) Consider a gas with density \[\rho \] and \[\overline{\text{c}}\] as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is
question_answer10) At 127°C radiated energy is \[2.7\,\times {{10}^{-3}}\,J/s\]. At what temperature radiated energy is \[4.32\,\times {{10}^{6}}J/s\]?
question_answer12) A rubber cord catapult has cross-sectional area \[25\,m{{m}^{2}}\] and initial length of rubber cord is 10 cm. It is stretched to 5 cm and then released to project a missile of mass 5 g. Taking \[{{Y}_{rubber}}\,=5\times {{10}^{8}}N{{m}^{-2}},\] velocity of projected missile is
question_answer13) The material of a wire has a density of \[1.4\,g/c{{m}^{3}}\]. If it is not wetted by a liquid of surface tension 44 dyne/cm, then the maximum radius of the wire which can float on the surface of liquid is
question_answer15) A current of 0.01 mA passes through the potentiometer wire of a resistivity of \[{{10}^{9}}\Omega \] and area of cross-section \[{{10}^{-2}}c{{m}^{2}}\]. The potential gradient is
question_answer16) A particle of mass m attached with a string of length l is just revolving on the vertical circle without slacking of the string. If \[{{v}_{A,}}{{v}_{B}}\] and\[{{v}_{D}}\] are speeds at positions A, B and D, then
question_answer17) A bucket of water is being revolved in vertical circle of radius 1 m. Minimum frequency required to prevent the water from getting down the path is \[(g=10m/{{s}^{2}})\]
question_answer18) A round disc of moment of inertia \[{{I}_{2}}\] about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia \[{{l}_{1}}\] rotating with an angular velocity co about the same axis. The final angular velocity of the combination of discs is
question_answer19) Two discs have same mass and thickness. Their materials are of densities \[{{\rho }_{1}}\] and \[{{\rho }_{2.}}\] The ratio of their moment of inertia about central axis will be
question_answer20) A 4 m long wire of resistance \[8\,\Omega \] is connected in series with a battery of emf 2 V and a resistor of \[7\Omega .\] The internal resistance of the battery is \[1\Omega .\] What is the potential gradient along the wire?
question_answer21) A uniform wire of \[16\,\Omega \] resistance is made into the form of a square. Two opposite corners of the square are connected by a wire of resistance \[16\,\Omega .\] The effective resistance between the other two opposite comers is
question_answer22) A \[6\times {{10}^{-4}}\,F\] parallel plate air capacitor is connected to a 500 V batten. When air is replaced by another dielectric material, \[7.5\,\times {{10}^{-4}}C\] charge flows into the capacitor. The value of the dielectric constant of the material is
question_answer24) Given mass number of gold = 197, Density of gold \[=19.7\,g/c{{m}^{3}}\] Avogadros number \[=6\times {{10}^{23}}\]. The radius of the gold atom is approximately
question_answer25) In Youngs double slit experiment, two slits are separated by 1 m. The slits are illuminated by a light of wavelength 650 nm. The source of light is placed symmetrically with respect to the two slits. Interference pattern is observed on a screen at a distance of 1 m from the slits. The distance between the third dark fringe and the fifth bright fringe from the centre of the pattern will be
question_answer27) A satellite is moving in a circular orbit at a certain height above the earths surface. It takes \[5.26\,\times {{10}^{3}}\,s\] to complete one revolution with a centripetal acceleration equal to \[9.32\,\,m/{{s}^{2}}\]. The height of satellite orbiting above the earth is
(Earths radius \[=6.37\,\times {{10}^{6}}\,m\])
question_answer30) 30. A wire has a breaking stress of\[6\times {{10}^{5}}N/{{m}^{2}}\] and a density of \[3\times {{10}^{4}}kg/{{m}^{3}}\]. The length of the wire of the same material which will break under its town weight, (if \[g=10\,m/{{s}^{2}}\]) is
question_answer31) A man measures the period of simple pendulum inside a stationary lift and finds it to be T second. If the lift accelerates downwards with acceleration of \[\frac{g}{4},\] the period of oscillation will be
question_answer32) A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and temperature be doubled, the power radiated in watt would be
question_answer33) If the emissive power of black surface at same temperature is \[400\,W/{{m}^{2}},\] the emissive and absorptive powers of the surface assuming it was initially ordinary surface, are (Given, Mass of the body m = 4.2 kg, area of body \[=5\times {{10}^{-2}}{{m}^{2}},\]
rate of cooling \[\frac{d\theta }{dt}=\frac{1}{12}\times {{10}^{-2}}{{\,}^{\text{o}}}\text{C/min,}\] specific heat\[s=420J/kg{{\,}^{\text{0}}}\text{C)}\]
question_answer35) A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational KE per. oxygen molecule that per nitrogen molecule is
A)
1 : 1
doneclear
B)
1 : 2
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C)
2 : 1
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D)
depends on the moments of inertia of the two molecules
question_answer37) A ray of light is incident on glass slab making an angle of incidence sin\[^{-1}\left( \frac{\sqrt{3}}{2} \right).\] What will be the angle of refraction in glass of refractive index 1.5?
question_answer38) An electron at rest is accelerated through a potential difference of 200 V. If the electron acquires a velocity \[8.4\,\times {{10}^{6}}\,m/s,\] the value of e/m of electron is
question_answer40) What is the voltage gain in a common emitter amplifier, when input resistance is \[3\,\Omega \] and load resistance is \[24\,\Omega \] with \[\beta =60\,?\]
question_answer41) The input resistance or a common emitter transistor amplifier, if the output resistance is \[500\,k\Omega ,\], the current gain \[\alpha \] = 0.98 and the power gain is \[6.0625\,\times {{10}^{6}},\] is
question_answer43) If\[\left( \frac{0.51\times {{10}^{-10}}}{4} \right)\]m, is the radius of smallest electron orbit in hydrogen like atom, then this atom is
question_answer44) A series resonant circuit contains \[L=\frac{5}{\pi }mH,\] \[C=\frac{200}{\pi }\mu F\] and R = 100 \[\Omega \] If a source of emf It e = 200 sin 1000 \[1000\,\pi t\] is applied, then the rms current is
question_answer45) A rod of length 1.0 m is rotated in a plane perpendicular to a uniform magnetic field of induction 0.25 T with a frequency of 12 rev/s. The induced emf across the ends of the rod is
question_answer48) A charged particle of mass m and charge q is accelerated through a potential difference of V volt. It enters a region of uniform magnetic field which is directed perpendicular to the direction of motion of the particle. The particle will move on a circular path of radius given by
question_answer49) An electron moves at right angle to a magnetic field of \[1.5\times {{10}^{-2}}T\] with a speed of \[6\times {{10}^{7}}\,m/s\]. If the specific charge on the electron is \[1.7\,\times {{10}^{11}}\,C/kg,\] the radius of the circular path will be
question_answer50) In a circuit, 5 percent of total current passes through a galvanometer. If resistance of the galvanometer is G. Then the value of the shunt is
question_answer51) Given, C (diamond)\[+\,{{O}_{2}}\xrightarrow{{}}C{{O}_{2}};\Delta H =-395\,kJ\] C (graphite) \[+\,{{O}_{2}}\xrightarrow{{}}C{{O}_{2}};\Delta H =-393\,kJ\] The heat of formation of diamond from graphite is
question_answer65) If \[x\,\text{mol}\,{{\text{L}}^{-1}}\]is the solubility of \[\text{KAl(S}{{\text{O}}_{\text{4}}}{{\text{)}}_{\text{2}}}\] then \[{{\text{K}}_{\text{sp}}}\]is equal to
question_answer67) In an experiment, 20 mL of decinormal \[HCl\] solution was added to 10 mL of a decinormal \[\text{AgN}{{\text{O}}_{\text{3}}}\]solution. \[\text{AgCl}\]was precipitated out and the excess acid was titrated against a decinormal \[\text{NaOH}\] solution. Volume of \[\text{NaOH}\].required for this back titration is
question_answer81) The equilibrium constants for the reactions \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}\] and \[\frac{1}{2}{{N}_{2}}+\frac{3}{2}{{H}_{2}}N{{H}_{3}}\] are\[{{K}_{1}}\]and \[{{K}_{2}}\]respectively. Which one of the following is the correct relationship?
question_answer89) The end product C in the following sequence of chemical reactions is \[C{{H}_{3}}COOH\xrightarrow{CaC{{O}_{3}}}A\xrightarrow{Heat}B\xrightarrow{N{{H}_{2}}OH}C\]
question_answer104) The circle \[{{S}_{1}}\]with centre \[{{C}_{1}}({{a}_{1}},{{b}_{1}})\]and radius \[{{r}_{1}}\]touches externally the circle \[{{S}_{2}}\]with centre \[{{C}_{2}}({{a}_{2}},{{b}_{2}})\]and radius \[{{r}_{2}}.\] If the tangent at their common point passes through the origin, then
question_answer105) If three vectors a, b, c are such that \[a\ne 0\]and \[a\times b=2(a\times c),|a|=|c|=1,|b|=4\]and the angle between b and c is \[{{\cos }^{-1}}\left( \frac{1}{4} \right).\]Also \[b-2c=\lambda a,\]then find the value of \[\lambda \]
question_answer123) If \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x)={{a}^{3}},a\ne 0,\] then \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x/a)\] is equal to
question_answer130) AB, AC are tangents to a parabola \[{{y}^{2}}=4ax,\]If \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] are the lengths of perpendiculars from A, B, C on any tangents to the parabola, then
question_answer131) A family of lines is given by \[(1+2\lambda )x+(1-\lambda )y+\lambda =0,\,\lambda \] being the parameter. The line belonging to this family at the maximum distance from the point\[(1,4)\]is
question_answer132) If the eccentricity of the hyperbola \[{{x}^{2}}-{{y}^{2}}{{\sec }^{2}}\alpha =5\]is \[\sqrt{3}\]times the eccentricity of the ellipse \[{{x}^{2}}{{\sec }^{2}}\alpha +{{y}^{2}}=25,\]then the value of \[\alpha \] is
question_answer133) Lines of regressions of \[y\] on \[x\] and \[x\] on \[y\] are respectively \[y=ax+b\]and\[x=\alpha y+\beta ,\] If mean of \[x\]and\[y\] series is same, then its value. is
question_answer135) The relation between the time t and distance \[x\] is given by \[t=p{{x}^{2}}+qx,\]where p and q are constants. The relation between velocity v and acceleration \[f\] is
question_answer143) The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, then the probability of his shooting the target is
question_answer144) Let A and B be two events such that\[P(A)=0.3\] and \[P(A\cup B)=0.8\]If A and B. are independent events. Then, \[P(B)\] is equal to
question_answer145) The number of distinct real roots of \[\left| \begin{matrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \\ \end{matrix} \right|=0\]in the interval\[x\in \left[ \frac{-\pi }{4},\frac{\pi }{4} \right]\]is