question_answer3) The current gain a of a transistor is 0.9. The transistor is connected to common base configuration. What would be the change in collector current when base current changes by \[4mA\]?
question_answer6) A radioactive element A decays into B with a half-life of 2 days. A fresh prepared sample of A has a mass of \[12\text{ }g\]. What mass of A and B are there in the sample after 4 days?
question_answer7) How many \[\alpha \]-particle and \[\beta \]-particles are emitted when uranium nucleus \[_{92}^{238}U\] decays to lead nucleus \[_{82}^{206}Pb\]?
question_answer9) If the electron in hydrogen atom jumps from the third to second orbit, the wavelength of the emitted radiation in terms of Rydberg constant R is given by
question_answer10) When a monochromatic point source of light is at a distance of \[0.2\text{ }m\]from a photocell, the cut-off voltage and the saturation current are respectively \[{{\text{V}}_{0}}=0.6\]volt and\[{{I}_{s}}=18.0\,mA\]. If the same source is placed 0.6 m away from the photocell, then
A)
stopping potential \[{{V}_{0}}\text{=}0.2\]volt and saturation current \[{{I}_{s}}=18.0\text{ }mA\]
doneclear
B)
stopping potential \[{{V}_{0}}=0.6\]volt and saturation current \[{{I}_{s}}=18.0\text{ }mA\]
doneclear
C)
stopping potential \[{{V}_{0}}=0.6\] volt and saturation current \[{{I}_{s}}=2.0\,mA\]
doneclear
D)
stopping potential \[{{V}_{0}}=2.0\] volt and saturation current \[{{I}_{s}}=2.0\,mA\]
question_answer11) When light of wavelength \[300~nm\](nanometer) falls on a photoelectric emitter, photoelectrons are just liberated. For another emitter, however, light of \[600\text{ }nm\]wavelength is sufficient for creating photoemission. What is the ratio of the work function of the two emitters?
question_answer12) In Millikan's oil drop experiment, a charged drop of mass \[1.8\times {{10}^{-14}}\text{ }kg\] is stationary between the plates. The distance between the plates \[0.9\text{ }cm\]and potential difference between the plates is\[2000\text{ }V\]. The number of electons on the oil drop is
question_answer15) In Young's double slit experiment distance between source is 1 mm and distance between the screen and source is 1 m. If the fringe width on the screen is 0.06 cm, then K is
question_answer16) Angle of minimum deviation for a prism of refractive index \[1.5\] is equal to the angle of the prism. The angle of the prism is (given \[\cos \,{{41}^{o}}-24'-36''=0.75\])
question_answer17) Two media having speeds of light \[2\times {{10}^{8}}\text{ }m/s\] and \[2.4\times {{10}^{8}}\text{ }m/s,\] are separated by a plane surface. What is the critical angle for a ray going from medium I to medium II ?
question_answer20) An electromagnetic radiation of wavelength \[\lambda ,\] frequency v and propagating in air with velocity v is incident on a glass plate and is transmitted through. Which of the following statement is true for the wave inside the glass plate?
A)
The velocity v remains unchanged but \[\lambda \]changes
doneclear
B)
The frequency v and wavelength remain unchanged but v changes
doneclear
C)
The wavelength \[\lambda \] remains unchanged but velocity v changes
doneclear
D)
The frequency v remains unchanged but \[\lambda \]changes
question_answer22) In an AC circuit the instantaneous values of emf and current are \[e=200\text{ }sin\text{ }300\,t\text{ }volt\] and \[i=2\,\sin \left( 300t+\frac{\pi }{3} \right)amp\] the average power consumed in watts is
question_answer23) A transformer is used to light a 140 W, \[24\text{ }V\] lamp from \[240\text{ }VAC\]mains. The current in the mains cable of \[0.7\text{ }A\]. The efficiency of the transformer is
question_answer24) A solenoid has 2000 turns wound over a length of \[0.30\text{ }m\]. The area of its cross-section is \[1.2\times {{10}^{-3}}{{m}^{2}}\]. Around its central section a coil of 300 turns is wound. If an initial current of 2 A in the solenoid is reversed in \[0.25\text{ }s,\] the emf induced in the coil is
question_answer25) A copper ring is held horizontally and a bar magnet with its length along the axis of the ring is dropped through the ring. The acceleration of the falling magnet is
A)
less than that due to gravity
doneclear
B)
equal to that due to gravity
doneclear
C)
more than that due to gravity
doneclear
D)
depends on the length of the magnet and diameter of the ring
question_answer27) A particle starts from rest and experiences constant acceleration for 6 s. If it travels a distance d-^ in the first two seconds, a distance \[{{d}_{2}}\] in the next two seconds and a distance \[{{d}_{3}}\] in the last two seconds, then
question_answer28) A particle originally at rest at the highest point of a smooth circle in a vertical plane, is gently pushed and starts sliding/along the circle. It will leave the circle at a' vertical distance h. below the highest point such that
question_answer29) An inclined plane has an inclination \[\theta \] with horizontal. A body of mass m rests on it. If the coefficient of friction between the body and the plane is \[\mu ,\] then the minimum force that needs to be applied parallel to the inclined plane is
question_answer30) A \[60\text{ }kg\]man stands on a spring scale in a lift. At some instant he finds that the scale reading has changed from \[60\text{ }kg\] to \[50\text{ }kg\] for a while and then comes again to \[60\text{ }kg\] mark. What should he conclude?
A)
The lift was in constant motion upwards
doneclear
B)
The lift was in constant motion downwards
doneclear
C)
The lift while in motion suddenly stopped
doneclear
D)
The lift while in motion upwards suddenly' stopped
question_answer31) A diatomic molecule is formed by two atoms which may be treated as mass points \[{{m}_{1}}\] and \[{{m}_{2}},\] joined by a massless rod of length r. Then the moment of inertia of the molecule about an axis passing through the centre of mass and perpendicular to rod is
question_answer33) A planet revolves in an elliptical orbit around the sun. The semi-major and semi-minor axes are a and b, their the period is given by
question_answer34) In a capillary tube of which the lower end dips in a liquid, the liquid rises to a height of\[10\text{ }cm\]If a capillary of the same bore is taken, whose length is 5 cm and dipped in liquid, then
A)
a fountain of liquid will be obtain
doneclear
B)
the liquid will not rise in the tube at all
doneclear
C)
the liquid will rise upto the top and slowly ooze out of it
doneclear
D)
the liquid will rise to the top and will stay there
question_answer36) Solar radiation emitted by sun correspond to that emitted by black body at a temperature of \[6000\text{ }K\]. Maximum intensity is emitted at wavelength of\[4800\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]. If the sun was to cool down from \[6000\text{ }K\]to \[3000\text{ }K,\] then the peak intensity of emitted radiation would occur at a wavelength
question_answer37) An ideal gas heat engine operates in a Carnot cycle between \[{{227}^{o}}C\]and\[{{127}^{o}}C\]. It absorbs \[6\times {{10}^{4}}cal\] at the higher temperature. The amount of heat converted into work is
question_answer38) A certain mass of gas at NTP is expanded to three times its volume under adiabatic conditions. The resulting temperature of gas ,' will be (7 for gas is \[1.40\])
question_answer40) The velocity of a small ball of mass M and density \[{{d}_{1}}\] when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \[{{d}_{2}},\] the viscous force acting on the ball is
question_answer41) The length of an elastic spring is a meters when a force of \[4\text{ }N\]is applied, and b meters when the \[\text{5 }N\] force is applied. Then the length of the spring when the \[9N\] force is applied is
question_answer42) Moment of inertia of a uniform disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be
question_answer43) The escape velocity of a body from the surface of earth is \[11.2\text{ }km/s\]. It is thrown up with a velocity 4 times this velocity of escape. The velocity of the body when it has escaped the gravitational pull of earth (neglecting presence of all other heavenly bodies) is
question_answer44) If a planet of given density were made larger (keeping its density unchanged) its force of attraction for an object on its surface would increase because of increased mass of the planet but would decrease because of larger separation between the centre of the planet and its surface. Which effect would dominate?
question_answer45) Two balls each of mass m are placed on the vertices A and B of an equilateral triangle ABC of side\[1\text{ }m\]. A ball of mass \[2m\] is placed at vertex C. The centre of mass of this system from vertex A (located at origin) is
question_answer46) A particle moves along the x-axis from \[x={{x}_{1}}\] to \[x={{x}_{2}}\] under the action of a force given by\[F=2\text{ }x\]. Then the work done in the process is
question_answer47) A body of mass 5 kg strikes another body of mass \[2.5\text{ }kg\]initially at rest. The bodies after collision coalesce and begin to move as whole with a kinetic energy of\[5\text{ }J\]. The kinetic energy of the first body before collision is
question_answer49) Two projectiles are fired at different angles with the same magnitude of velocity, such that they have the same range. At what angles they might have been projected?
question_answer50) If two non-zero vectors obey the relation \[|\vec{P}+\vec{Q}|=|\vec{P}-\vec{Q}|\].then the angle between the vectors \[\vec{P},\] \[\vec{Q}\] is
question_answer51) A weightless spring which has a force constant k oscillates with a frequency r% when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2m is attached to one of the halves. The frequency of oscillation will not become
question_answer52) A particle moves so that its acceleration a is given by \[a=-bx,\] where x is displacement from equilibrium position and b is a non-negative real constant. The time period of oscillation of the particle is
question_answer53) A tuning fork of frequency \[500\text{ }cycles/s\]is sounded on a resonance tube. The first and second resonance is obtained at \[17\text{ }cm\]and\[52\text{ }cm\]. The velocity of sound in m/s is
question_answer55) A hollow charged metal sphere has a radius r. If the potential difference between its surface and a point at a distance \[3\text{ }r\]from the centre is V, then electrical intensity at distance \[3\text{ }r\]from the centre is
question_answer56) Current is flowing with a current density \[J=480\,A/c{{m}^{2}}\]in a copper wire. Assuming that each copper atom contributes one free electron and given that Avogadro number \[=6.0\times {{10}^{23}}\text{ }atoms/mol\] Density of copper \[=9.0\text{ }g/c{{m}^{3}}\] Atomic weight of copper \[=64\text{ }g/mol\] Electronic charge \[=1.6\times {{10}^{-19}}C\] The drift velocity of electrons is
question_answer57) A tap supplies water at \[{{20}^{o}}C\]. A man takes \[1\text{ }L\]of water per minute at \[{{35}^{o}}C\]from a geyser connected to the tap. The power of geyser is
question_answer58) A charge is fired through a magnetic field. The force acting on the charge is maximum when the angle between the direction of motion of charge and the magnetic field is
question_answer59) At a place the angle of dip is \[{{30}^{o}}\]. If the horizontal component of earth's magnetic field is H, then the total field intensity is
question_answer60) A particle is vibrating in simple harmonic motion with an amplitude of\[4\text{ }cm\]. At what displacement from the equilibrium position is its energy half potential and half-kinetic?
question_answer61) A tuning fork of frequency \[480\text{ }Hz\]produces 10 beats/s, when sounded with a sonometer string. A slight increase in tension in the sonometer string produces fewer beats/s than before. What was the frequency of sonometer string?
question_answer62) A hollow metal sphere of radius \[5\text{ }cm\]is charged such that potential at its surface is\[10\text{ }V\]. The potential at the centre of the sphere is
A)
zero volt
doneclear
B)
\[10\text{ }V\]
doneclear
C)
same as at point \[5\text{ }cm\]away from the surface
doneclear
D)
same as at point \[\text{10 }cm\] away from the surface
question_answer63) An electric dipole consisting of two opposite charges of \[2\times {{10}^{-6}}\text{ }C\]each, separated by a distance of \[3\text{ }cm\]is placed in an electric field of \[2\times {{10}^{5}}\text{ }N/C\]. The maximum torque on the dipole is
question_answer64) A given piece of wire of length I and radius r is having a resistance R. This wire is stretched uniformly to a wire of radius \[\frac{r}{2}\]. What is the new resistance?
question_answer65) Two .thin long parallel wires separated by a distance b are carrying current i ampere each. The magnitude of the force per unit length exerted by one wire on the other is
question_answer67) Two wires made up of the same material are of equal lengths but their radii are in the ratio of\[1:2\]. On stretching each of these two strings by the same tension, the ratio between the fundamental frequencies is
question_answer68) An object producing a pitch of \[400\text{ }Hz\]flies past a stationary person. The object was moving in a straight line with a velocity 200 m/s. The velocity of sound is 300 m/s. What is the change in frequency noted by the person as the object flies past him?
question_answer70) The magnitude of electric field at distance r from an infinitely thin rod having a linear charge density \[\lambda ,\]is (use Gauss's law)
question_answer71) A \[200\text{ }W\]and a \[100\text{ }W\]bulb, both. meant for operation at \[220\text{ }V\]are connected in series. When connected to a \[220\text{ }V\] supply the power consumed by the, combination is
question_answer79) \[\text{KMn}{{\text{O}}_{\text{4}}}\]reacts with oxalic acid according to the equation \[2MnO_{4}^{-}+5{{C}_{2}}O_{4}^{2-}+16{{H}^{+}}\xrightarrow{{}}2M{{n}^{2+}}\]\[+\,10C{{O}_{2}}+8{{H}_{2}}O\] Here, 20 mL of \[\text{0}\text{.1}\,\text{M}\,\text{KMn}{{\text{O}}_{\text{4}}}\] is equivalent to
question_answer82) An aqueous solution of 6.3 g oxalic acid dihydrate is made up to 250 mL. The volume of N sodium hydroxide required to completely neutralise 10 mL of this solution is
question_answer87) In the reaction \[2A+B\xrightarrow{{}}{{A}_{2}}B,\] if the concentration of A is doubled and that of B is halved, then the rate of reaction will
question_answer89) If the half-time for a particular reaction is found to be constant and independent of the initial concentration of the reactants, then the reaction is of
question_answer93) The van't Hoff factor for \[\text{0}\text{.1}\,\text{M}\,\text{Ba(N}{{\text{O}}_{\text{3}}}{{\text{)}}_{\text{2}}}\] solution is 2.74. The degree of dissociation is
question_answer94) The enthalpy of vaporisation of liquid water using the data \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l)\] \[\Delta H=-285.77\,kJ/mol\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(g);\] \[\Delta H=-241.84\,kJ/mol\]is
question_answer95) The enthalpy change for the transition of liquid water to steam is \[40.8\,kJ\,mo{{l}^{-1}}\]at \[373\,K.\] Calculate the entropy of vaporisation of water.
question_answer103) 50 mL of hydrogen diffuses through small hole from a vessel in 20 min time. Time taken for 40 mL of oxygen to diffuse out under similar conditions will be
question_answer114) Chemical A is used for water softening to remove temporary hardness. A reacts with sodium carbonate to generate caustic soda. When\[\text{C}{{\text{O}}_{\text{2}}}\] is bubbled through A, it turns cloudy. What is A?
question_answer117) Amongst \[TiF_{6}^{2-},CoF_{6}^{3-},C{{u}_{2}}C{{l}_{2}}\]and \[NiCl_{4}^{2-}\]at. no.\[Ti=22,Co=27,Cu=29,Ni=28\]). The. colourless species are
question_answer130) The correct IUPAC name of the following compound is \[C{{H}_{3}}C{{H}_{2}}\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-C=\underset{{{C}_{2}}{{H}_{5}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-\underset{{{C}_{2}}{{H}_{5}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,HC{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\]
question_answer137) In the reaction of phenol with chloroform and aqueous solution of\[\text{NaOH}\]at \[\text{70}{{\,}^{o}}C,\] the electrophile attacking the ring is
question_answer147) Nitrosoamines \[({{R}_{2}}N-N=O)\] are soluble in water. On heating them with cone \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{,}\]they give secondary amines. The reaction is called
question_answer159) In an AP the sum of any two terms, such that the distance of one of them from the beginning is same as that of the other from the end, is
question_answer165) If for some real number k \[\underset{x\to 0}{\mathop{\lim }}\,kx\,\,\text{cosec (x) =}\underset{x\to 0}{\mathop{\text{lim}}}\,\,\,x\,\,\text{cosec}\,\,(kx),\] then the possible values of k are
question_answer169) If \[\omega \] is a cube root of unity, then a root of the equation \[\left| \begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix} \right|=0\] is
question_answer178) In a triangle ABC, \[C={{90}^{o}}\]. If r is the in radius and R is the circum radius of the triangle, then \[2\,(r+R)\]is equal to
question_answer181) A letter is taken out at random from the word 'ASSISTANT and another is taken-out from the word 'STATISTICS'. The chance that the two selected letters are identical, is
question_answer187) Let \[f(x)=\left\{ \begin{matrix} |x|,\,\,for\,\,0<|x|\le 2 \\ 1,\,\,\,\,\,for\,\,\,\,x=0 \\ \end{matrix} \right.\], then at \[x=0,\] \[f\] has
question_answer188) There are n different books and m copies of each in a college library. The number of ways in which a student can make a selection of one or more books is
question_answer189) Five digited numbers with distinct digits arc formed by using the digits,\[5,4,3,2,1,0\]. The number of those numbers which are multiples of 3, is
question_answer192) The number of dissimilar terms in expansion of \[{{(a+b)}^{n}}\] is \[n+1,\] therefore number of dissimilar terms of the expansion \[{{(a+b+c)}^{12}}\] is
question_answer193) If \[|x|<1,\] then \[1+n\left( \frac{2x}{1+x} \right)+\frac{n\,\,(n+1)}{2!}\]\[{{\left( \frac{2x}{1+x} \right)}^{2}}+.......\] is equal to
question_answer197) To open a lock, a key is taken out from a collection of n keys at random. If the lock is not opened with this key, it is put back into the collection and another key is tried. The process is repeated again and again. If it is given that with only one key in the collection, the lock can be opened, then the probability that the lock will open in n trials, is
question_answer203) If a, b, c are different real numbers and \[a\,\,\hat{i}+b\,\,\hat{j}+c\,\,\hat{k},\]\[b\,\,\hat{i}+c\,\,\hat{j}+a\,\,\hat{k}\] and \[c\,\,\hat{i}+a\,\,\hat{j}+b\,\,\hat{k}\]are position vectors of three non-collinear points, then
A)
centroid of \[\Delta ABC\] is s\[\frac{a+b+c}{3}\,(\hat{i}+\hat{j}+\hat{k})\]
doneclear
B)
\[(\hat{i}+\hat{j}+\hat{k})\] is not really inclined to three vectors
doneclear
C)
triangle ABC is a scalene triangle
doneclear
D)
perpendicular from the origin to the plane of the triangle does not meet it at the centroid
question_answer210) The locus of the point of intersection of the lines \[x\,cot\,\theta +y\,cosec\,\theta \text{=}2\]and \[x\,cosec\,\theta +y\,cot\,\theta =6\]is
question_answer214) If the fourth term in the expansion of \[{{\left( ax+\frac{1}{x} \right)}^{n}}\] is \[\frac{5}{2},\] then find the value of a and n.
question_answer219) Let \[{{T}_{n}}\] denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If \[{{T}_{n+1}}-{{T}_{n}}=21,\] then n equals
question_answer223) The vectors \[\overrightarrow{AB}=3\hat{i}+4\hat{k}\] and \[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\] are the sides of a triangle ABC. The length of the median through A is
question_answer224) A particle acted on by constant forces \[4\hat{i}+\hat{j}-3\hat{k}\] and \[3\hat{i}+\hat{j}-\hat{k}\] is displaced from the point \[\hat{i}+2\hat{j}+3\hat{k}\] to the point \[5\hat{i}+4\hat{j}+\hat{k}\]. The total work done by the forces is
question_answer225) If \[f(x)\] is a differentiable function, then \[\underset{x\to a}{\mathop{\lim }}\,\] \[\frac{a\,\,f(x)-x\,f(a)}{x-a}\] is equal to