question_answer2) A gas bubble formed from an explosion under water oscillates with a period T proportional to \[{{P}^{a}}{{d}^{b}}{{E}^{c}},\]where P is pressure, d is the density of water and E is the total energy of explosion. The value of a, b, c are
question_answer3) A particle moving with a uniform acceleration travels 24 A and 64m in the first two consecutive interval of 4s each. Its initial velocity will be
question_answer6) A body moves a distance of 10 m along a straight line under a action of 5 N force. If work done is 25 J, then angle between the force and direction of motion of the body will be
question_answer10) A body cools from \[60{{\,}^{o}}C\] to \[50{{\,}^{o}}C\] in 1 the room temperature is\[25{{\,}^{o}}C\] and assuming Newton law of cooling to hold g temperature of the body at the end of the next 10 min will be
question_answer11) At \[27{}^\circ C\] a gas suddenly compressed such that its pressure becomes \[\frac{1}{8}\text{th}\] of original pressure. The temperature of the gas will be \[(\gamma =5/3)\]
question_answer12) An ideal refrigerator has a freezer at a temperature of \[-\text{ }13{{\,}^{o}}C.\] The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) will be
question_answer13) In a capacitor of capacitance \[20\,\mu F\] the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, then the new capacitance will be
question_answer14) An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in this spring when it has been compressed by 0.2 m to the potential energy stored in a \[10\,\mu F\] capacitor at a potential difference of 10000 V will be
question_answer15) A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell having charge - Q. The radius of the sphere is a and that of the spherical shell is \[b(b>a).\]What is the electric field at a distance \[R(a<R<b)\]from the centre?
question_answer17) In a network as shown in the figure, the potential difference across the resistance 2R is (the cell has an emf of E volts and has no internal resistance)
question_answer18) The resistance of a galvanometer coil is R, then the shunt resistance required to convert it into a ammeter of range 4 times, will be
question_answer20) A meter stick is held vertically with one end on the floor and is then allowed to fall. Assuming that the end on the floor the stick does not slip, the velocity of the other end when it hits the floor, will be
question_answer21) If the coefficient of static friction between the tyres and road is 0.5, what is the shortest distance in which an automobile can be stopped when travelling at 72 km/h?
question_answer22) A bullet fired at an angle of \[{{30}^{o}}\] with the horizontal hits the ground 3 km away. By adjusting its angle of projection, can one hope to hit a target 5 km away. Assume the muzzle speed to be same and the air resistance is negligible
question_answer23) Two springs of spring constant 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in ratio
question_answer25) A soap bubble A of radius 0.03 and another bubble B of radius 0.04 m are brought together so that the combined bubble has a common interface of radius r, then the value of r is
question_answer26) An air bubble of radius \[{{10}^{-2}}\,m\] is rising up at a steady rate of \[2\times {{10}^{-3}}m/s\] through a liquid of density \[1.5\times {{10}^{3}}kg/{{m}^{3}},\] the coefficient of viscosity neglecting the density of. air, will be \[(g=10\,m/{{s}^{2}})\]
question_answer27) A Carnot reversible engine converts 1/6 of heat input into work. When the temperature of the sink is reduced by 62 K, the efficiency of Carnots cycle becomes 1/3. The temperature of the source and sink will be
question_answer28) The ratio of the coefficient of thermal conductivity of two different materials is \[5:3.\] If the thermal resistance of the rods of same thickness of these materials is same, then the ratio of the length of these rods will be
question_answer29) Compressional wave pulses are sent to the bottom of sea from a ship and the echo is heard after 2 s. If bulk modulus of elasticity of water is \[2\times {{10}^{9}}\text{ }N/{{m}^{2}}\]and mean temperature is \[4{{\,}^{o}}C,\] the depth of the sea will be
question_answer30) Sound waves of \[f=600\,Hz\]fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration will be (speed of sound = 300 m/s)
question_answer31) A pipe closed at one end produces a fundamental note of 412 Hz. It is cut into two pieces of equal length the fundamental notes produced by the two pieces are
question_answer32) The refractive index of water and glycerine are 1.33 and 1.47 respectively. What is the critical angle for a light ray going from the later to the former?
question_answer33) Lenses of power 3 D and -5D are combined to form a compound lens. An object is placed at a distance of 50 cm from this lens. Its image will be formed at a distance from the lens, will be
question_answer34) If fringes width \[\lambda =5.89\times {{10}^{-5}}\] mm is 0.431 mm and shift of white central fringe on introducing a mica sheet in one path is 1.89 mm. Thickness of the mica sheet will be \[(\mu =1.59)\]
question_answer35) A body is orbiting around earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is
question_answer39) \[_{\text{7}}{{\text{N}}^{\text{14}}}\]is bombarded with \[_{2}H{{e}^{\text{4}}}.\] The resulting nucleus is \[_{8}{{O}^{17}}\] with the emission of
question_answer41) The time of vibration of a dip needle vibration in the vertical plane in the magnetic meridian is 3 s. When the same magnetic needle is made to vibrate in the horizontal plane, the time of vibration is 3\[\sqrt{2}\]s. Then angle of dip will be
question_answer42) The inductance of the oscillatory circuit of a radio station is 10 mH and its capacitance is 0.25 \[\mu F\].Taking the effect of resistance negligible, wavelength of the broadcasted waves will be (velocity of light \[=3.0\,\times {{10}^{8}}\,m/s,\,\pi =3.14\])
question_answer43) The \[{{K}_{\alpha }}\] line of singly ionized calcium has a wavelength of 393.3 nm as measured on earth. In the spectrum of one of the observed galaxies, the spectral line is located at 401.8 nm. The speed with which this galaxy is moving away from us, will be
question_answer44) In a common-base circuit of a transistor current amplification factor is 0.95. The base current when emitter current is 2 mA, will be
question_answer45) Cathode rays of velocity \[{{10}^{6}}\,m/s\] describe an approximate circular path of radius 1 m in an electric field 300 V/cm. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be
question_answer46) Light of wavelength \[5000\overset{\text{o}}{\mathop{\text{A}}}\,\] falling on a sensitive surface. If the surface has received \[{{10}^{-7}}J\] of energy, then the number of photons falling on the surface will be:
question_answer47) An X-ray machine is opearated at 40 kV. The short wavelength limit of continuous X-rays will be \[(h=6.63\,\times {{10}^{-34}}\,Js,\,\,c=3\times {{10}^{8}}m/s,\,e=1.6\times {{10}^{-19}}C)\]
question_answer48) The wavelength of the first spectral line of sodium is \[5896\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The first excitation potential of sodium atom will be \[(h=6.63\times {{10}^{-34}}\,Js)\]
question_answer49) If 200 MeV energy is released in the fission of a single nucleus of \[_{92}{{U}^{235}}\]. How much fission must occur per second to produce a power of 1kW?
question_answer50) The energy supplied to calculate by state electricity board during an average November day was 40 mkh. If this energy could be obtained by the conversion of matter, how much mass will be annihilated?
question_answer61) For the reaction, \[{{H}_{2}}+{{I}_{2}}2HI,\]the equilibrium concentration of \[{{H}_{2}},{{I}_{2}}\]and HI are 8.0, 3.0 and 28.0 mol/L respectively. The equilibrium constant is
question_answer69) The energy ratio of a photon of wavelength \[\text{3000 }\overset{\text{o}}{\mathop{\text{A}}}\,\]and \[\text{6000 }\overset{\text{o}}{\mathop{\text{A}}}\,\]is
question_answer75) An unknown compound D first oxidized to aldehyde and then acetic acid by a dilute solution of \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]and \[{{H}_{2}}S{{O}_{4}}.\]The compound D is
question_answer77) A gas expands isothermally against a constant external pressure of 1 atm from a volume of \[10\,d{{m}^{3}}\]to a volume of \[20\,d{{m}^{3}}.\] It absorbs 300 J of thermal energy from its surroundings. The \[\Delta U\]is
question_answer103) A body falls freely from the top of a tower and during the last second of its flight it falls \[\frac{\text{5}}{\text{9}}\text{th}\]of the whole distance. The height of the tower and time of motion are respectively
question_answer105) The equation of the plane passing through the mid point of the line of join of the points (1, 2, 3) and (3, 4, 5) and perpendicular to it is
question_answer106) The equation of the circle concentric to the circle \[2{{x}^{2}}+2{{y}^{2}}-3x+6y+2=0\] and having area double the area of this circle, is
question_answer108) Let \[f(x)=\left\{ \begin{matrix} \frac{\tan x-\cot x}{x-\frac{\pi }{4}}, & x\ne \frac{\pi }{4} \\ a, & x=\frac{\pi }{4} \\ \end{matrix} \right.\] the value of a so that \[f(x)\] is continuous at\[x=\frac{\pi }{4}\]
question_answer109) If e and e are the eccentricities of hyperbolas\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{^{2}}}}{{{b}^{2}}}=1\] and its conjugate hyperbola, then the value of \[\frac{1}{{{e}^{2}}}+\frac{1}{e{{}^{2}}}\]is
question_answer111) If forces of magnitude 12 kg-wt, 5 kg-wt and 13 kg-wt act at a point are in equilibrium, then the angle between the first two forces is
question_answer112) For a party 8 guests are invited by a husband and his wife. They sit in a row for dinner. The probability that the husband and his wife sit together is
question_answer115) The sum of coefficients of the expansion\[{{\left( \frac{1}{x}+2x \right)}^{n}}\]is 6561. The coefficient of term independent of \[x\] is
question_answer117) There are 12 white and 12 red balls in a bag. Balls are drawn one by one with replacement from the bag. The probability that 7th drawn ball is 4th white is
question_answer118) In an ellipse the angle between the lines joining the foci with the positive end of minor axis is a right angle, the eccentricity of the ellipse is
question_answer119) If \[|\vec{a}|=3,\,\,\,|\vec{b}|=5\]and \[|\vec{c}|=4\]then and \[\vec{a}+\vec{b}+\vec{c}=0,\] then the value of \[\vec{a}+\vec{b}+\vec{c}=0,\]then the value of \[\vec{a}.\vec{b}\,+\,\vec{b}.\vec{c}\]is equal to
question_answer125) On one bank of river there is a tree. On another bank, an observer makes an angle of elevation of \[{{60}^{o}}\] at the top of the tree. The angle of elevation of the top of the tree at a distance 20 m away from the bank is 30°. The width of the river is
question_answer133) If the second term in the expansion\[{{\left[ \sqrt[13]{a}\frac{a}{\sqrt{{{a}^{-1}}}} \right]}^{n}}\]is \[14{{a}^{5/2}},\] then the value of \[\frac{{{\,}^{n}}C{{\,}_{3}}}{{{\,}^{n}}{{C}_{2}}}\]is
question_answer135) Point D, E are taken on the side BC of the triangle ABC, such that \[BD=DE=EC.\]If \[\angle BAD=x,\angle DAE=y,\angle EAC=z,\] then the value of \[\frac{\sin (x+y)\sin (y+z)}{\sin x\sin \,z}\] is equal to
question_answer138) In a \[\Delta ABC,\,a,c,A\]are given and \[{{b}_{1}},{{b}_{2}}\]are two values, if the third side b such that \[{{b}_{2}}=2{{b}_{1}}\]then sin A is equal to
question_answer139) A variable chord is drawn through the origin to the circle \[{{x}^{2}}+{{y}^{2}}-2ax=0.\]The locus of the centre of the circle drawn on this chord as diameter is
question_answer140) If \[1,{{a}_{1}},{{a}_{2}},...,{{a}_{n-1}}\]are the n roots of unity, then the value of \[(1-{{a}_{1}})(1-{{a}_{2}})(1-{{a}_{3}})......(1-{{a}_{n-1}})\] is equal to
question_answer141) Let a, b, c be real. If \[a{{x}^{2}}+bx+c=0\]has two real roots \[\alpha \]and\[\beta ,\]where \[a<-1\]and \[\beta >1,\]then \[1+\frac{c}{a}+\left| \frac{b}{a} \right|\]is
question_answer144) Let a, b, c be positive and not all equal, the value of the determinant \[\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix} \right|\]is