Solved papers for JEE Main & Advanced AIEEE Solved Paper-2003
done AIEEE Solved Paper-2003 Total Questions - 224
question_answer1) A particle of mass M and charge Q moving with velocity v describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circle is
AIEEE Solved Paper-2003
question_answer2) A particle of charge \[-16\times {{10}^{-18}}C\] moving with velocity \[10m{{s}^{-1}}\] along the x-axis enters a region where a magnetic field of induction B is along the y-axis and an electric field of magnitude \[{{10}^{4}}\] V/m is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is
AIEEE Solved Paper-2003
question_answer3) A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now, it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T', the ratio T'/T is
AIEEE Solved Paper-2003
question_answer4) A magnetic needle lying parallel to a magnetic field requires W unit of work to turn it through \[{{60}^{o}}\]. The torque needed to maintain the needle in this position will be
AIEEE Solved Paper-2003
question_answer7) A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of \[5\,m/{{s}^{2}}\], the reading of the spring balance will be
AIEEE Solved Paper-2003
question_answer8) The length of a wire of a potentiometer is 100 cm and the emf of its stand and cell is. E volt. It is employed to measure the emf of a battery whose internal resistance is \[0.5\,\,\Omega \]. If the balance point is obtained at \[1=30\] cm from the positive end, the emf of the battery is
AIEEE Solved Paper-2003
A)
\[\frac{30\,E}{100.5}\]
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B)
\[\frac{30\,E}{100-05}\]
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C)
\[\frac{30\,(E-0.5i)}{100}\], where \[i\] is the current in the potentiometer wire
question_answer11) The thermo-emf of a thermocouple is \[25\mu V{{/}^{o}}C\] at room temperature. A galvanometer of \[40\,\Omega \]. resistance, capable of detecting current as low as \[{{10}^{-5}}\] A, is connected with the thermocouple. The smallest temperature difference that can be detected by this system is
AIEEE Solved Paper-2003
question_answer12) The negative Zn-pole of Daniell cell, sending a constant current through a circuit, decreases in mass by \[0.13\]g in 30 min. If the electrochemical equivalent of Zn and Cu are \[32.5\] and \[31.5\] respectively, the increase in the mass of the positive Cu-pole in this time is
AIEEE Solved Paper-2003
question_answer14) A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then, the relation between the moment of inertia \[{{I}_{X}}\] and \[{{I}_{Y}}\] is
question_answer15) The time period of a satellite of earth is 5 h. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become
AIEEE Solved Paper-2003
question_answer16) A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is
AIEEE Solved Paper-2003
question_answer18) When \[{{U}^{238}}\] nucleus originally at rest, decays by emitting an alpha particle having a speed u, the recoil speed of the residual nucleus is
AIEEE Solved Paper-2003
question_answer19) Two spherical bodies of mass M and 5 M and radii R and 2 R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
question_answer20) The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the
AIEEE Solved Paper-2003
A)
crystal structure
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B)
variation of the number of charge carriers with temperature
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C)
type of bonding
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D)
variation of scattering mechanism with temperature
question_answer21) A car moving with a speed of 50 km/h, can be stopped by brakes after atleast 6 m. If the same car is moving at a speed of 100 km/h, the minimum stopping distance is
AIEEE Solved Paper-2003
question_answer22) A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of \[{{30}^{o}}\] with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? \[[g=10\,m/{{s}^{2}},\sin {{30}^{o}}=1/2,\cos {{30}^{o}}=\sqrt{3}/2]\]
question_answer23) An ammeter reads upto 1 A. Its internal resistance is \[0.81\,\,\Omega \]. To increase the range to 10 A, the value of the required shunt is
AIEEE Solved Paper-2003
question_answer25) Three forces start acting C simultaneously on a particle moving with velocity v. These forces are represented in magnitude and direction by the three sides of a \[\Delta ABC\] (as shown). The particle will now move with velocity
AIEEE Solved Paper-2003
A)
less than v
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B)
greater than v
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C)
\[\left| v \right|\] in the direction of largest force BC
question_answer26) Resultant force is zero, as three forces acting on the particle can be represented in magnitude and direction by three sides of a triangle in same order. Hence, by Newton's 2nd law \[\left( F=m\frac{d\,\,v}{dt} \right)\], particle velocity (v) will be same. (\[\because \] if F = 0, v = constant) If the electric flux entering and leaving an enclosed surface respectively is \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\], the electric charge inside the surface will be
AIEEE Solved Paper-2003
question_answer27) A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is \[0.2\]. The weight of the block is
AIEEE Solved Paper-2003
question_answer28) A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10s. Then, the coefficient of friction is
AIEEE Solved Paper-2003
question_answer29) Consider the following two statements A. Linear momentum of a system of particles is zero. B. Kinetic energy of a system of particles is zero. Then,
AIEEE Solved Paper-2003
question_answer31) . A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is
AIEEE Solved Paper-2003
question_answer32) A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then, the true statement about the scale reading is
AIEEE Solved Paper-2003
A)
both the scales read M kg each
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B)
the scale of the lower one reads M kg and of the upper one zero
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C)
the reading of the two scales can be anything but the sum of the readings will be M kg
question_answer33) A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then, the elastic energy stored in the wire is
AIEEE Solved Paper-2003
question_answer34) The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of \[{{45}^{o}}\] with the vertical, the escape velocity will be
AIEEE Solved Paper-2003
question_answer35) A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes \[5T/3\], then the ratio of \[\frac{m}{M}\] is
AIEEE Solved Paper-2003
question_answer36) "Heat cannot be itself flow from a body at lower temperature to a body at higher temperature" is a statement or consequence of
AIEEE Solved Paper-2003
question_answer37) Two particles A and B of equal masses are suspended from two massless springs of spring constants \[{{k}_{1}}\] and \[{{k}_{2}}\], respectively. If the maximum velocities, during oscillations are equal, the ratio of amplitudes of A and B is
AIEEE Solved Paper-2003
question_answer38) The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is
AIEEE Solved Paper-2003
question_answer39) The displacement y of a wave travelling in the x-direction is given by \[y={{10}^{-4}}\sin \left( 600\,t-2x+\frac{\pi }{3} \right)\] metre where, \[x\] is expressed in metres and t in seconds. The speed of the wave motion, in \[m{{s}^{-1}}\] is
AIEEE Solved Paper-2003
question_answer40) When the current changes from \[+2\] A to \[-2\] A in \[0.05\] s, an emf of 8 V is induced in a coil. The coefficient of self-induction of the coil is
AIEEE Solved Paper-2003
question_answer41) In an oscillating LC circuit, the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is
AIEEE Solved Paper-2003
question_answer43) Let F be the force acting on a particle having position vector r and \[\tau \] be the torque of this force about the origin. Then,
AIEEE Solved Paper-2003
question_answer44) A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is
AIEEE Solved Paper-2003
question_answer45) A nucleus with \[Z=92\] emits the following in a sequence: \[\alpha ,\alpha ,{{\beta }^{-}},{{\beta }^{-}},\alpha ,\alpha ,\alpha ,\alpha ;{{\beta }^{-}},{{\beta }^{-}},\alpha ,{{\beta }^{+}},{{\beta }^{+}},\alpha \]. The Z of the resulting nucleus is
AIEEE Solved Paper-2003
question_answer47) A 3 V battery with negligible internal resistance is connected in a circuit as shown in the figure. The current I, in the circuit will be
AIEEE Solved Paper-2003
question_answer48) A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor
AIEEE Solved Paper-2003
question_answer49) The displacement of a particle varies according to the relation \[x=4\,(\cos \pi \,t+\sin \pi t)\]. The amplitude of the particle is
AIEEE Solved Paper-2003
question_answer50) A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point P at a distance R/2 from the centre of the shell is
AIEEE Solved Paper-2003
question_answer52) The coordinates of a moving particle at any time t are given by \[x=\alpha {{t}^{3}}\] and \[y=\beta {{t}^{3}}\]. The speed of the particle at time t is given by
AIEEE Solved Paper-2003
question_answer53) During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio, \[{{C}_{p}}/{{C}_{V}}\] for the gas is
AIEEE Solved Paper-2003
question_answer55) A Carnot engine takes \[3\times {{10}^{6}}\] cal of heat from a reservoir at \[{{627}^{o}}C\] and gives it to a sink at \[{{27}^{o}}C\]. The work done by the engine is
AIEEE Solved Paper-2003
question_answer56) A spring of spring 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
AIEEE Solved Paper-2003
question_answer57) A metal wire of linear mass density of \[9.8\] g/m is stretched with a tension of 10 kg-wt between two rigid supports 1 m apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n of the alternating source is
AIEEE Solved Paper-2003
question_answer58) A tuning fork of known frequency 256 Hz makes 5 beats/s with the vibrating string of a piano. The beat frequency decreases to 2 beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
AIEEE Solved Paper-2003
question_answer59) A body executes simple harmonic motion. The potential energy (PE), the kinetic energy (KE) and total energy (TE) are measured as function of displacement \[x\]. Which of the following statements is true?
AIEEE Solved Paper-2003
question_answer60) In the nuclear fusion reaction, \[_{1}^{2}H+_{1}^{3}H\to _{2}^{4}He+n\] given that the repulsive potential energy between the two nuclei is \[7.7\times {{10}^{-14}}\] J the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant \[k=1.38\times {{10}^{-23}}J/K\]]
AIEEE Solved Paper-2003
question_answer62) The wavelengths involved in the spectrum of deuterium \[\left( _{1}^{2}D \right)\] are slightly different from that of hydrogen spectrum, because
AIEEE Solved Paper-2003
A)
sizes of the two nuclei are different
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B)
nuclear forces are different in the two cases
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C)
masses of the two nuclei are different
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D)
attraction between the electron and the nucleus is different in the two cases
question_answer64) If the binding energy of the electron in a hydrogen atom is \[13.6\] eV, the energy required to remove the electron from the first excited state of \[L{{i}^{2+}}\] is
AIEEE Solved Paper-2003
question_answer65) A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to
AIEEE Solved Paper-2003
question_answer66) A rocket with a lift-off mass \[3.5\times {{10}^{4}}\] kg is blasted upwards with an initial acceleration of \[10\,m/{{s}^{2}}\] . Then, the initial thrust of the blast is
AIEEE Solved Paper-2003
question_answer68) Three charges \[-{{q}_{1}},+{{q}_{2}}\] and \[-{{q}_{3}}\] are placed as shown in the figure. The x-component of the force on \[-{{q}_{1}}\] is proportional to
AIEEE Solved Paper-2003
question_answer73) According to Newton's law of cooling, the rate of cooling of a body is proportional to \[{{(\Delta \theta )}^{n}}\], where \[\Delta \theta \] is the difference of the temperature of the body and the surroundings and n is equal to
AIEEE Solved Paper-2003
question_answer74) The length of a given cylindrical wire is increased by \[100%\]. Due to the consequent decrease in diameter, the change in the resistance of the wire will be
AIEEE Solved Paper-2003
question_answer75) In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inner-orbit jumps of the electron for Bohr orbits in an atom of hydrogen?
AIEEE Solved Paper-2003
question_answer76) The de-Broglie wavelength of a tennis ball of mass 60g moving with a velocity of 10 m/s is approximately (Planck's constant, \[h=6.63\times {{10}^{-34}}\] Js)
AIEEE Solved Paper-2003
question_answer77) The orbital angular momentum for an electron revolving in an orbit is given by \[\sqrt{l(l+1)}\frac{h}{2\pi }\]. This momentum for an s-electron will be given by
question_answer78) How many unit cells are present in a cube shaped ideal crystal of \[NaCl\] of mass \[1.00\]g? [At. masses Na \[=23,\,\,Cl=35.5\]]
AIEEE Solved Paper-2003
question_answer82) Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that graphite
AIEEE Solved Paper-2003
A)
is a non-crystalline substance
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B)
is an allotropic form of diamond
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C)
has molecules of variable molecular masses like polymers
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D)
has carbon atoms arranged in large plates of rings of strongly bound carbon atoms with weak interplate bonds
question_answer85) According to the kinetic theory of gases, in an ideal gas, between two successive collisions a gas molecule travels
AIEEE Solved Paper-2003
question_answer89) Among the following four structures I to IV \[{{C}_{2}}{{H}_{5}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ || \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{3}}{{H}_{7}}C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-\overset{\begin{smallmatrix} C{{H}_{3}} \\ || \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{2}}{{H}_{5}}\] (I) (II) \[H-\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{{{\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{C}}\,}^{\oplus }}}}\,\] \[{{C}_{2}}{{H}_{5}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{2}}{{H}_{5}}\] (III) (IV) it is true that
AIEEE Solved Paper-2003
question_answer94) In the anion \[HCO{{O}^{-}}\] the two carbon-oxygen bonds are found to be of equal length. What is the reason for it?
AIEEE Solved Paper-2003
A)
Electronic orbits of carbon atom are hybridized
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B)
The \[c=0\] bond is weaker than the C?O bond
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C)
The anion \[HCO{{O}^{-}}\] has two resonating structures
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D)
The anion is obtained by the removal of a proton from the acid molecule
question_answer96) The atomic numbers of vanadium (V), chromium (Cr), manganese (Mn) and iron (Fe) are respectively 23, 24, 25 and 26. Which one of these may be expected to have the highest second ionisation enthalpy?
AIEEE Solved Paper-2003
question_answer97) Consider the reaction equilibrium, \[2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g);\] \[\Delta {{H}^{o}}=-198\,k\,J\] On the basis of Le Chatelier's principle, the condition favourable for the forward reaction is
AIEEE Solved Paper-2003
A)
lowering of temperature as well as pressure
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B)
increasing temperature as well as pressure
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C)
lowering the temperature and increasing the pressure
question_answer98) What volume of hydrogen gas, at 273K and 1 atm pressure will be consumed in obtaining \[21.6\] g of elemental boron (atomic mass \[=10.8\]) from the reduction of boron trichloride by hydrogen?
AIEEE Solved Paper-2003
question_answer99) For the reaction equilibrium, \[{{N}_{2}}{{O}_{4}}(g)\overset{{}}{leftrightarrows}2NO(g)\] the concentrations of \[{{N}_{2}}{{O}_{4}}\] and \[N{{O}_{2}}\] at equilibrium are \[4.8\times {{10}^{-2}}\] and \[1.2\times {{10}^{-2}}mol\,{{L}^{-1}}\] respectively. The value of \[{{K}_{c}}\] for the reaction is
AIEEE Solved Paper-2003
question_answer100) The solubility in water of a sparingly soluble salt \[A{{B}_{2}}\] is \[1.0\times {{10}^{-5}}mol\,{{L}^{-1}}\] Its solubility product number will be
AIEEE Solved Paper-2003
question_answer101) When during electrolysis of a solution of \[AgN{{O}_{3}}\], 9650 coulombs of charge pass through the electroplating bath, the mass of silver deposited on the cathode will be
AIEEE Solved Paper-2003
question_answer102) For the redox reaction, \[Zn(s)+C{{u}^{2+}}(0.1M)\xrightarrow{{}}Z{{n}^{2+}}(1M)+Cu(s)\]taking place in a cell, \[E_{cell}^{o}\] is \[1.10\] volt. \[{{E}_{cell}}\] for the cell will be \[\left( 2.303\frac{RT}{F}=0.0591 \right)\]
AIEEE Solved Paper-2003
question_answer103) In a \[0.2\] molal aqueous solution of a weak acid HX, the degree of ionisation is \[0.3\]. Taking \[{{K}_{f}}\] for water as \[1.85\], the freezing point of the solution will be nearest to
AIEEE Solved Paper-2003
question_answer104) The rate law for a reaction between the substances A and B is given by rate \[=k\,{{[A]}^{n}}{{[B]}^{m}}\]. On doubling the concentration of A and halving the concentration of B, the ratio of the new rate to the earlier rate of the reaction will be as
AIEEE Solved Paper-2003
question_answer105) 25 mL of a solution of barium hydroxide on titration with \[0.1\] molar solution of hydrochloric acid gave a titre value of 35 mL. The molarity of barium hydroxide solution was
AIEEE Solved Paper-2003
question_answer106) The correct relationship between free energy change in a reaction and the corresponding equilibrium constant \[{{K}_{c}}\] is
AIEEE Solved Paper-2003
question_answer107) If at 298K the bond energies of \[C-H,C-C,\,C=C\] and \[H-H\] bonds are respectively 414, 347, 615 and 435 kJ \[mo{{l}^{-1}}\], the value of enthalpy change for the reaction \[{{H}_{2}}C=C{{H}_{2}}(g)+{{H}_{2}}(g)\xrightarrow{\,}\,{{H}_{3}}C-C{{H}_{3}}(g)\] at 298K will be
AIEEE Solved Paper-2003
question_answer111) For the reaction system \[2NO(g)+{{O}_{2}}(g)\xrightarrow{{}}2N{{O}_{2}}(g)\] volume is suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to \[{{O}_{2}}\] and second order with respect to NO; the rate of reaction will
AIEEE Solved Paper-2003
question_answer112) For a cell reaction involving a two-electron change, the standard emf of the cell is found to be \[0.295\] V at \[{{25}^{o}}C\]. The equilibrium constant of the reaction at \[{{25}^{o}}C\] will be
AIEEE Solved Paper-2003
question_answer113) In an irreversible process taking place at constant T and p and in which only pressure-volume work is being done, the change in Gibbs free energy (dG) and change in entropy (dS), satisfy the criteria
AIEEE Solved Paper-2003
question_answer115) In the respect of the equation \[k=A{{e}^{-{{E}_{\alpha }}/RT}}\] in chemical kinetics, which one of the following statements is correct?
AIEEE Solved Paper-2003
question_answer116) Standard reduction electrode potentials of three metals A, B and C are \[+1.5\] V, \[-3.0\] V and \[-1.2\] V respectively. The reducing power of these metals are
AIEEE Solved Paper-2003
question_answer119) A red solid is insoluble in water. However, it becomes soluble if some KI is added to water. Heating the red solid in a test tube results in liberation of some violet coloured fumes and droplets of a metal appear on the cooler parts of the test tube. The red solid is
AIEEE Solved Paper-2003
question_answer120) Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The explanation for it is that
AIEEE Solved Paper-2003
A)
concentrated hydrochloric acid emits strongly smelling HCI gas all the time
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B)
oxygen in air reacts with the emitted HCI gas to form a cloud of chlorine gas
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C)
strong affinity of HCI gas for moisture in air results in forming of droplets of liquid solution which appears like a cloudy smoke
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D)
due to strong affinity for water, concentrated hydrochloric acid pulls moisture of air towards itself. This moisture forms droplets of water and hence the cloud
question_answer125) Ammonia forms the complex ion \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] with copper ions in the alkaline solutions but not in acidic solutions. What is the reason for it?
AIEEE Solved Paper-2003
A)
In acidic solutions hydration protects copper ions
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B)
In acidic solutions protons coordinate with ammonia molecules forming \[NH_{4}^{+}\] ions and \[N{{H}_{3}}\] molecules are not available
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C)
In alkaline solutions insoluble \[Cu{{(OH)}_{2}}\] is precipitated which is soluble in excess of any alkali
question_answer126) One mole of the complex compound \[Co{{(N{{H}_{3}})}_{5}}C{{l}_{3}}\], gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with two moles of \[AgN{{O}_{3}}\] solution to yield two moles of \[AgCl\] (s). The structure of the complex is
AIEEE Solved Paper-2003
question_answer127) The radius of \[L{{a}^{3+}}\] (atomic number of \[La=57\]) is \[1.06\overset{o}{\mathop{A}}\,\]. Which one of the following given values will be closest to the radius of \[L{{u}^{3+}}\] (atomic number of \[Lu=71\])?
AIEEE Solved Paper-2003
question_answer128) The radionuclide \[_{90}^{234}Th\] undergoes two successive \[\beta \] -decays followed by one \[\alpha \] -decay. The atomic number and the mass number respectively of the resulting radionuclide are
AIEEE Solved Paper-2003
question_answer129) the half-life of a radioactive isotope is 3 h. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 h would be
AIEEE Solved Paper-2003
question_answer133) The correct order of increasing basic nature for the bases \[N{{H}_{3}},C{{H}_{3}}N{{H}_{2}}\] and \[{{(C{{H}_{3}})}_{2}}NH\]is
AIEEE Solved Paper-2003
question_answer136) During dehydration of alcohols to alkenes by heating with concentrated \[{{H}_{2}}S{{O}_{4}}\] the initiation step is
AIEEE Solved Paper-2003
question_answer140) For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liquid metal which does not solidify before glass. The metal used can be
AIEEE Solved Paper-2003
question_answer143) Bottles containing \[{{C}_{6}}{{H}_{5}}I\] and \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}I\] lost their original labels. They were labelled A and B for testing. A and B were separately taken in a test tube and boiled with \[NaOH\] solution. The end solution in each tube was made acidic with dilute \[HN{{O}_{3}}\] and then some \[AgN{{O}_{3}}\] solution was added. Substance B gave a yellow precipitate. Which one of the following statements is true for this experiment?
AIEEE Solved Paper-2003
question_answer145) The internal energy change when a system goes from state A to B is 40 kJ/mol. If the system goes from A to B by a reversible path and returns to state A by an irreversible path, what would be the net change in internal energy?
AIEEE Solved Paper-2003
question_answer148) On mixing a certain alkane with chlorine and irradiating it with Ultraviolet light, it forms only one monochloroalkane. This alkane could be
AIEEE Solved Paper-2003
question_answer150) A function \[f\] from the set of natural numbers to integers defined by \[f(n)=\left\{ \begin{align} & \frac{n-1}{n},\text{ }when\text{ }n\text{ }is\text{ }odd \\ & \frac{-n}{2},\,\,when\text{ }n\text{ }is\text{ }even \\ \end{align} \right.\] is
AIEEE Solved Paper-2003
question_answer151) Let \[{{z}_{1}}\] and \[{{z}_{2}}\] be two roots of the equation \[{{z}_{2}}+az+b=0,\,\,z\] being complex. Further, assume that the origin, \[{{z}_{1}}\] and \[{{z}_{2}}\] form an equilateral triangle. Then,
AIEEE Solved Paper-2003
question_answer152) If z and \[\omega \] are two non-zero complex numbers such that \[\left| z\,\omega \right|=1\] and arg (z) - arg \[(\omega )=\frac{\pi }{2}\], then \[\overline{z}\omega \] is equal to
AIEEE Solved Paper-2003
question_answer154) If \[\left| \begin{matrix} a & {{a}^{2}} & 1+{{a}^{3}} \\ b & {{b}^{2}} & 1+{{b}^{3}} \\ c & {{c}^{2}} & 1+{{c}^{3}} \\ \end{matrix} \right|=0\] and vectors \[(1,\,\,a,\,\,{{a}^{2}})\], \[(1,\,\,a,\,\,{{a}^{2}})\] and \[(1,\,\,c,\,\,{{c}^{2}})\] are non-coplanar, then the product abc equals
AIEEE Solved Paper-2003
question_answer155) If the system of linear equations \[x+2\] ay \[+\,az=0\] \[x+3\] by \[+\,bz=0\] and \[x+4\] cy \[+cz=0\] has a non-zero solution, then a, b, c
AIEEE Solved Paper-2003
question_answer156) If the sum of the roots of the quadratic equation \[a{{x}^{2}}+bx+c=0\] is equal to the sum of the squares f their reciprocals, then \[\frac{a}{c},\frac{b}{a}\], and \[\frac{c}{b}\] are in
AIEEE Solved Paper-2003
question_answer158) The value of a for which one root of the quadratic equation \[({{a}^{2}}-5a+3)\,{{x}^{2}}+(3a-1)\,x+2=0\] is twice as large as the other, is
AIEEE Solved Paper-2003
question_answer159) If \[A=\left| \begin{matrix} a & b \\ b & a \\ \end{matrix} \right|\] and \[{{A}^{2}}=\left| \begin{matrix} \alpha & \beta \\ \beta & \alpha \\ \end{matrix} \right|\], then
AIEEE Solved Paper-2003
question_answer160) A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is
AIEEE Solved Paper-2003
question_answer161) The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by
AIEEE Solved Paper-2003
question_answer163) If \[^{n}{{C}_{r}}\] denotes the number of combinations of n things taken r at a time, then the expression \[^{n}{{C}_{r+1}}{{+}^{n}}{{C}_{r-1}}+2{{\times }^{n}}{{C}_{r}}\] equals
AIEEE Solved Paper-2003
question_answer167) Let \[f(x)\] be a polynomial function of second degree. If \[f(1)=f(-1)\] and a, b, c are in AP, then \[f'\,(a),\,\,f'(b)\] and \[f'(c)\] are in
AIEEE Solved Paper-2003
question_answer168) If \[{{x}_{1}},{{x}_{2}},{{x}_{3}}\] and \[{{y}_{1}},{{y}_{2}},{{y}_{3}}\] are both in GP with the same common ratio, then the points \[({{x}_{1}},{{y}_{1}}),\,({{x}_{2}},{{y}_{2}})\] and \[({{x}_{3}},{{y}_{3}})\]
AIEEE Solved Paper-2003
question_answer170) If a \[\Delta ABC\], \[a{{\cos }^{2}}\left( \frac{C}{2} \right)+c{{\cos }^{2}}\left( \frac{A}{2} \right)=\frac{3b}{2}\] then the sides a, b and c
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question_answer171) In \[\Delta ABC\], medians AD and BE are drawn. If AD = 4, \[\angle DAB=\frac{\pi }{6}\] and \[\angle ABE=\frac{\pi }{3}\], then the area of the \[\Delta ABC\] is
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question_answer173) The upper 3/4th portion of a vertical pole subtends an angle \[{{\tan }^{-1}}3/5\] at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is
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question_answer175) If \[f:R\to R\] satisfies\[f(x+y)=f(x)+f(y)\], for all \[x,y\in R\] and \[f(1)=7\], then \[\sum\limits_{r=1}^{n}{f(r)}\] is
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question_answer176) If \[f(x)={{x}^{n}}\], then the value of \[f(1)-\frac{f'(1)}{1!}+\frac{f''(1)}{2!}-\frac{f'''(1)}{3!}+...+\frac{{{(-1)}^{n}}{{f}^{n}}(1)}{n!}\]
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question_answer180) Let f(a) = g(a) = k and their nth derivatives \[{{f}^{n}}(a),\,{{g}^{n}}(a)\] exist and are not equal for some n. Further, if \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)\,g(x)-i(a)-g(a)f(x)+g(a)}{g(x)-f(x)}=4\], then the value of k is equal to
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question_answer183) If the function \[f(x)=2{{x}^{3}}-9a{{x}^{2}}+12{{a}^{2}}x+1\], where a > 0, attains its maximum and minimum at p and q respectively such that \[{{p}^{2}}=q\], then a equals
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question_answer186) The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\int_{0}^{{{x}^{2}}}{{{\sec }^{2}}t\,dt}}{x\sin x}\] is
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question_answer189) Let \[\frac{d}{dx}F(x)=\left( \frac{{{e}^{\sin x}}}{x} \right),x>0\]. If \[\int_{1}^{4}{\,\,\,\frac{3}{x}{{e}^{\sin {{x}^{3}}}}dx=F(k)-F(1)}\]. then one of the possible value of k, is
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question_answer191) Let \[f(x)\] be a function satisfying \[f'(x)=f(x)\] with \[f(0)=1\] and \[g(x)\] be a function that satisfies \[f(x)+g(x)={{x}^{2}}\]. Then, the value of the integral \[\int_{0}^{1}{f(x)\,g(x)\,dx}\], is
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question_answer192) The degree and order of the differential equation of the family of all parabolas whose axis is X-axis, are respectively
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question_answer194) If the equation of the locus of a point equidistant from the points \[({{a}_{1}}-{{b}_{1}})\] and \[({{a}_{2}}-{{b}_{2}})\] is \[({{a}_{1}}-{{a}_{2}})x+({{b}_{1}}-{{b}_{2}})\,y+c=0\], then the value of 'c' is
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question_answer195) Locus of centroid of the triangle whose vertices are (b sin t, - b cost) and (1, 0), where t is a parameter, is
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question_answer196) If the pair of straight lines \[{{x}^{2}}-2pxy-{{y}^{2}}=0\]and \[{{x}^{2}}-2qxy-{{y}^{2}}=0\] be such that each pair bisects the angle between the other pair, then
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question_answer197) A square of side a lies above the X-axis and has one vertex at the origin. The side passing through the origin makes an angle \[\left( 0<\alpha <\frac{\pi }{4} \right)\] with the positive direction of X-axis. The equation of its diagonal not passing through the origin is
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question_answer198) If the two circles \[{{(x-1)}^{2}}+{{(y-3)}^{2}}={{r}^{2}}\] and \[{{x}^{2}}+{{y}^{2}}-8x+2y+8=0\] intersect in two distinct points, then
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question_answer199) The lines \[2x-3y=5\] and \[3x-4y=7\] are diameters of a circle having area as 154 sq units. Then, the equation of the circle is
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question_answer200) The normal at the point \[(bt_{1}^{2},b{{t}_{1}})\] on a parabola meets the parabola again in the point\[(bt_{2}^{2},2b{{t}_{2}})\], then
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question_answer201) The foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and the hyperbola \[\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25}\] coincide. Then, the value of \[{{b}^{2}}\] is
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question_answer202) A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 3), B(2, 1, 3) and C(-1, 1, 2). Then, the angle between the faces OAB and ABC will be
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question_answer203) The radius of the circle in which the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2x-2y-4z-19=0\] is cut by the plane \[x+2y+2z+7=0\], is
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question_answer204) The lines \[\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}\] and \[\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}\] are coplanar, if
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question_answer206) The shortest distance from the plane \[12x+4y+3z=327\] to the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+4x-2y-6z=155\] is
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question_answer207) Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b?, c from the origin, then
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question_answer208) a, b, c are three vectors, such that \[a+b+c=0,\,\,\left| a \right|=1,\,\,\left| b \right|=2,\,\,\left| c \right|=3\], then \[a\,.\,b+b\,.\,\,c+c\,.\,\,a\] is equal to
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question_answer210) Consider points A, B, C and D with position vectors \[7\hat{i}-4\hat{j}+7\hat{k}\], \[\hat{i}-6\hat{j}+10\hat{k}\], \[-\hat{i}-3\hat{j}+4\,\hat{k}\]and \[5\,\hat{i}-\hat{j}+5\,\hat{k}\], respectively. Then, ABCD is a
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A)
square
doneclear
B)
rhombus
doneclear
C)
rectangle
doneclear
D)
parallelogram but not a rhombus None of the given option is correct.
question_answer211) The vectors \[AB=3\hat{i}+4\hat{k}\] and \[AC=5\,\hat{i}-2\,\hat{j}+4\,\hat{k}\] are the sides of a \[\Delta ABC\]. The length of the median through A is
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question_answer212) 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
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question_answer213) Let \[u=\hat{i}+\hat{j},\,v=\hat{i}-\hat{j}\] and \[w=\hat{i}+2\,\hat{j}+3\,\,\hat{k}\]. If \[\hat{n}\] is a unit vector such that \[u\,.\,\,\hat{n}=0\] and \[v\,.\,\,\hat{n}=0\], then \[\left| w\,.\,\,\hat{n} \right|\] is equal to
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question_answer214) The median of a set of 9 distinct observations is 205. If each of the largest 4 observations of the set is increased by 2, then the median of the new set
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question_answer215) In an experiment with 15 observations on x, the following results were available \[\sum {{x}^{2}}=2830,\,\,\sum x=170\]. One observation that was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance is
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question_answer216) Five horses are in a race. Mr A selects two of the horses at random and bets on them. The probability that Mr A selected the winning horse, is
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question_answer217) Events A, B, C are mutually exclusive 3x +1 events such that \[P(A)=\frac{3x+1}{3},\,P(B)=\frac{1-x}{4}\] and \[P(C)=\frac{1-2x}{2}\]. The set of possible values of x are in the interval
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question_answer218) The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then \[P(X=1)\] is
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question_answer219) The resultant of forces P and Q is R. If Q is doubled, then R is doubled. If the direction of Q is reversed, then R is again doubled, then? \[{{P}^{2}}:{{Q}^{2}}:{{R}^{2}}\] is
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question_answer220) Let \[{{R}_{1}}\] and \[{{R}_{2}}\] respectively be the maximum ranges up and down an inclined plane and R be the maximum range on the horizontal plane. Then. \[{{R}_{1}},R,{{R}_{2}}\] are in
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question_answer221) A couple is of moment G and the force forming the couple is P. If P is turned through a right angle, the moment of the couple thus formed is H. If instead, the forces P is turned through an angle a, then the moment of couple becomes
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question_answer222) Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uniform acceleration f. Let \[\alpha \] be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time
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question_answer223) Two stones are projected from the top of a cliff h metres high, with the same speed u, so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle \[\theta \] to the horizontal, then tan \[\theta \] equals
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question_answer224) A body travels a distance s in t seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration f and in the second part with constant retardation r. The value of t is given by
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