Solved papers for JEE Main & Advanced AIEEE Solved Paper-2005
done AIEEE Solved Paper-2005 Total Questions - 225
question_answer1) A projectile can have the same range R for two angles of projection. If\[{{t}_{1}}\]and\[{{t}_{2}}\]are the times of flights in the two cases, then the product of the two times of flights is proportional to
AIEEE Solved Paper-2005
question_answer2) An annular ring with inner and outer radii\[{{R}_{1}}\]and\[{{R}_{2}}\]is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring,\[\frac{{{F}_{1}}}{{{F}_{2}}}\]is
AIEEE Solved Paper-2005
question_answer3) A smooth block is released at rest on a\[45{}^\circ \]incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
AIEEE Solved Paper-2005
question_answer4) The upper half of an inclined plane with inclination\[\phi \]is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by
AIEEE Solved Paper-2005
question_answer5) A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?
AIEEE Solved Paper-2005
question_answer7) The relation between time t and distance\[x\]is \[t=a{{x}^{2}}+bx,\]where a and b are constants. The acceleration is
AIEEE Solved Paper-2005
question_answer8) A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance travelled is 15 S, then
AIEEE Solved Paper-2005
question_answer9) A particle is moving eastwards with a velocity of\[5m{{s}^{-1}}\]. In 10 s, the velocity changes to\[5\text{ }m{{s}^{-1}}\]northwards. The average acceleration in this time is
AIEEE Solved Paper-2005
question_answer10) A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at\[2m/{{s}^{2}}\]. He peaches the ground with a speed of 3 m/s. At what height, did he bail out?
AIEEE Solved Paper-2005
question_answer11) A block is kept on a frictionless inclined surface with angle of inclination \[\alpha \]. The incline is given an acceleration a to keep the block stationary. Then, a is equal to
AIEEE Solved Paper-2005
question_answer12) A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is
AIEEE Solved Paper-2005
question_answer13) A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass\[\frac{1}{3}\]M and a body C of mass\[\frac{2}{3}\]M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards
AIEEE Solved Paper-2005
question_answer14) The moment of inertia of uniform semi-circular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is
AIEEE Solved Paper-2005
question_answer15) A particle of mass 0.3 kg is subjected to a force \[F=-\text{ }kx\]with\[k=15\text{ }N/m.\]What will be its initial acceleration, if it is released from a point 20 cm away from the origin?
AIEEE Solved Paper-2005
question_answer16) The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is
AIEEE Solved Paper-2005
question_answer17) A mass m moves with a velocity v and collides inelastically with another identical mass. After collision the 1st mass moves with velocity\[\frac{v}{\sqrt{3}}\]in a direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision.
AIEEE Solved Paper-2005
question_answer18) A 20 cm long capillary tube is dipped, in water. The water rises upto 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
AIEEE Solved Paper-2005
question_answer19) If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is
AIEEE Solved Paper-2005
question_answer21) A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time, is given by
AIEEE Solved Paper-2005
question_answer22) Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped, is\[[{{\mu }_{k}}=0.5]\]
AIEEE Solved Paper-2005
question_answer24) AT shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.
AIEEE Solved Paper-2005
question_answer25) The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?
AIEEE Solved Paper-2005
question_answer26) A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere. (You may take \[G=6.67\times {{10}^{-11}}N{{m}^{2}}/k{{g}^{2}}\])
AIEEE Solved Paper-2005
question_answer27) A gaseous mixture consists of 16 g of helium and 16 g of oxygen/The ratio\[\frac{{{C}_{p}}}{{{C}_{v}}}\] of the mixture is
AIEEE Solved Paper-2005
question_answer28) The intensity of gamma radiation from a given source is\[I\]. On passing through 36 mm of lead, it is reduced to \[I/8\]. The thickness of lead, which will reduce the intensity to \[I/2\] will be
AIEEE Solved Paper-2005
question_answer29) The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm, is incident on it. The bandgap for the semiconductor is
AIEEE Solved Paper-2005
question_answer30) A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 0.5m away, the number of electrons emitted by photocathode would
AIEEE Solved Paper-2005
question_answer31) Starting with a sample of pure\[^{66}Cu,\] 7/8 of it decays into Zn in 15 min. The corresponding half-life is
AIEEE Solved Paper-2005
question_answer32) If radius of the\[_{13}^{27}Al\] nucleus is estimated to be \[3.6\text{ }fm,\]then the radius of \[_{52}^{125}Te\]nucleus be nearly
AIEEE Solved Paper-2005
question_answer34) The figure shows a system of two concentric spheres of radii\[{{r}_{1}},{{r}_{2}}\]and kept at temperatures \[{{T}_{1}},{{T}_{2}},\]respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to
AIEEE Solved Paper-2005
question_answer35) A system goes from A to B via two processes and II as shown in figure. If\[\Delta {{U}_{1}}\]and\[\Delta {{U}_{2}}\]are the changes in internal energies in the processes I and II respectively, then
AIEEE Solved Paper-2005
A)
\[\Delta {{U}_{1}}=\Delta {{U}_{2}}\]
doneclear
B)
relation between\[\Delta {{U}_{1}}\]and\[\Delta {{U}_{2}}\]cannot be determined
question_answer37) A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is
AIEEE Solved Paper-2005
question_answer38) Two simple harmonic motions are represented by the equations \[{{y}_{1}}=0.1\sin \left( 100\pi t+\frac{\pi }{3} \right)\]and\[{{y}_{2}}=0.1\,\cos \pi t.\] The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is
AIEEE Solved Paper-2005
question_answer39) A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the water surface, the radius of this circle (in cm) is
AIEEE Solved Paper-2005
question_answer40) Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]
AIEEE Solved Paper-2005
question_answer41) A thin glass (refractive index 1.5) lens has optical power of - 5 D in air. Its optical power in a liquid medium with refractive index 1.6 will be
AIEEE Solved Paper-2005
question_answer42) The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?
AIEEE Solved Paper-2005
question_answer45) In a full wave rectifier, circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would be
AIEEE Solved Paper-2005
question_answer46) A nuclear transformation is denoted, by\[X(n,\text{ }\alpha )\to _{3}^{7}Li\]. Which of the following is the nucleus of element X?
AIEEE Solved Paper-2005
question_answer47) A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions per milliampere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 V, the resistance in Ohm's needed to be connected in series with the coil will be
AIEEE Solved Paper-2005
question_answer48) Two voltameters, one of copper and another of silver, are joined in parallel. When a total charge q flows through the voltameters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are\[{{z}_{1}}\]and\[{{z}_{2}}\]respectively, the charge which flows through the silver voltameter is
AIEEE Solved Paper-2005
question_answer49) In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be
AIEEE Solved Paper-2005
question_answer50) Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are\[{{R}_{1}}\]and\[{{R}_{2}}({{R}_{2}}>{{R}_{1}})\]. If the potential difference across the source having internal resistance\[{{R}_{2}}\]is zero, then
AIEEE Solved Paper-2005
question_answer51) A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by \[\Delta T,\] the potential difference V across the capacitance is
AIEEE Solved Paper-2005
question_answer52) One conducting 17-tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed v, then the emf induced in the circuit in terms of B, l and v, where l is the width of each tube, will be
AIEEE Solved Paper-2005
question_answer53) A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be
AIEEE Solved Paper-2005
question_answer54) Two thin, long, parallel wires, separated by a distance d carry a current of i ampere in the same direction. They will
AIEEE Solved Paper-2005
A)
attract each other with a force of\[\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi d)}\]
doneclear
B)
repel each other with a force of\[\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi d)}\]
doneclear
C)
attract each other with a force of\[\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi {{d}^{2}})}\]
doneclear
D)
repel each other with a force of\[\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi {{d}^{2}})}\]
question_answer55) When an unpolarised light of intensity\[{{I}_{0}}\]is incident on a polarising sheet, the intensity of the light which does not get transmitted is -
AIEEE Solved Paper-2005
question_answer56) A charged ball B hangs from a silk thread S, which makes an angle \[\theta \] with a large charged conducting sheet as shown in the figure. The surface charge density \[\sigma \] of the sheet is proportional to
AIEEE Solved Paper-2005
question_answer57) Two point charges\[+8q\]and\[-2q\]are located at\[x=0\]and\[x=L\]respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero, is
AIEEE Solved Paper-2005
question_answer58) Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are \[+\text{ }q\]and\[-\text{ }q\]. The potential difference between the centres of the two rings is
AIEEE Solved Paper-2005
question_answer59) A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is C, then the resultant capacitance is
AIEEE Solved Paper-2005
question_answer60) When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats/s are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats/s are heard. If the frequency of for k 1 is 200 Hz, then what was the original frequency of fork 2?
AIEEE Solved Paper-2005
question_answer61) If a simple harmonic motion is represented by \[\frac{{{d}^{2}}x}{d{{t}^{2}}}+\alpha x=0,\] its time period is
AIEEE Solved Paper-2005
question_answer62) The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
AIEEE Solved Paper-2005
A)
first increase and then decrease to the original value
doneclear
B)
first decrease and then increase to the original value
question_answer63) An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?
AIEEE Solved Paper-2005
question_answer64) If\[{{I}_{0}}\]is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?
AIEEE Solved Paper-2005
question_answer65) Two concentric coils each of radius equal to\[2\pi \]cm are placed at right angles to each other. 3 A and 4 A are the currents flowing in each coil respectively. The magnetic induction in \[Wb/{{m}^{2}}\]at the centre of the coils , will be \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}Wb/Am)\]
AIEEE Solved Paper-2005
question_answer66) A coil of inductance 300 mH and resistance\[2\Omega \]. are connected to a source of voltage 2V. The current reaches half of its steady state value in
AIEEE Solved Paper-2005
question_answer67) The self-inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of
AIEEE Solved Paper-2005
question_answer69) A circuit has a resistance of\[12\,\Omega \]and an impedance of\[15\,\Omega \]. The power factor of the circuit will be
AIEEE Solved Paper-2005
question_answer70) The phase difference between the alternating current and emf is\[\pi /2\]. Which of the following cannot be the constituent of the circuit?
AIEEE Solved Paper-2005
question_answer71) A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then
AIEEE Solved Paper-2005
question_answer72) A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is
AIEEE Solved Paper-2005
question_answer73) In a potentiometer experiment, the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of Q, the balancing length becomes 120 cm. The internal resistance of the cell is
AIEEE Solved Paper-2005
question_answer74) The resistance of hot tungsten filament is about 10 times the cold resistance. What will be the resistance of 100 W and 200 V lamp, when not in use?
AIEEE Solved Paper-2005
question_answer80) If\[\alpha \]is the degree of dissociation of\[N{{a}_{2}}S{{O}_{4}},\] the van't Hoff factor (i) used for calculating the molecular mass is
AIEEE Solved Paper-2005
question_answer85) An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be
AIEEE Solved Paper-2005
question_answer88) Consider an endothermic reaction\[X\to Y\]with the activation energies\[{{E}_{b}}\]and\[{{E}_{f}}\]for the backward and forward reactions respectively. In general
AIEEE Solved Paper-2005
A)
there is no definite relation between\[{{E}_{b}}\]and \[{{E}_{f}}\]
question_answer89) Aluminium oxide may be electrolysed at \[1000{}^\circ C\]to furnish aluminium metal (Atomic mass\[=27u;\] 1 Faraday = 96500. The cathode reaction is \[A{{l}^{3+}}+3{{e}^{-}}\to A{{l}^{0}}\] To prepare 5.12 kg of aluminium metal by this method would require
AIEEE Solved Paper-2005
question_answer90) The volume of a colloidal particle, \[{{V}_{C}}\] as compared to the volume of a solute particle in a true solution \[{{V}_{S}},\] could be
AIEEE Solved Paper-2005
question_answer91) Consider the reaction \[{{N}_{2}}+3{{H}_{2}}\xrightarrow{\,}2\,N{{H}_{3}}\] carried out at constant temperature and pressure. If\[\Delta H\]and\[\Delta U\]are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?
AIEEE Solved Paper-2005
question_answer92) The solubility product of a salt having general formula\[M{{X}_{2}},\]in water is\[4\times {{10}^{-12}}\]. The concentration of\[{{M}^{2+}}\]ions in the aqueous solution of the salt is
AIEEE Solved Paper-2005
question_answer93) Benzene and toluene form nearly ideal solutions. At\[20{}^\circ C,\]the vapour pressure of benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of benzene at \[20{}^\circ C,\]for a solution containing 78 g of benzene and 46 g of toluene in torr is
AIEEE Solved Paper-2005
question_answer94) Which one of the following statements is not true about the effect of an increase in temperature on the distribution, of molecular speeds in a gas?
AIEEE Solved Paper-2005
A)
The area under the distribution curve remains the same as under the lower temperature
doneclear
B)
The distribution becomes broader
doneclear
C)
The fraction of the molecules with the most probable speed increases
question_answer95) For the reaction, \[2N{{O}_{2}}(g)2NO(g)+{{O}_{2}}(g)\] \[({{K}_{c}}=1.8\times {{10}^{-6}}at\text{ }184{}^\circ C)\] \[(R=0.00831\text{ }kJ/(molK))\] When \[{{K}_{p}}\] and\[{{K}_{c}}\]are compared at\[184{}^\circ C\]it is found that
AIEEE Solved Paper-2005
A)
whether \[{{K}_{p}}\] is greater than, less than or equal to\[{{K}_{C}}\]depends upon the total gas pressure
question_answer96) The exothermic formation of \[Cl{{F}_{3}}\] is represented by the equation \[C{{l}_{2}}(g)+3{{F}_{2}}(g)2Cl{{F}_{3}}(g);\] \[\Delta {{H}_{r}}=-329kJ\] Which of the following will increase the quantity of\[Cl{{F}_{3}}\] in an equilibrium mixture of \[C{{l}_{2}},{{F}_{2}}\]and\[Cl{{F}_{3}}\]?
AIEEE Solved Paper-2005
question_answer99) Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 mL of 1.5 M first solution +520 mL of 1.2 M second solution. What is the molarity of the final mixture?
AIEEE Solved Paper-2005
question_answer100) During the process of electrolytic refining of copper, some metals present as impurity settle as 'anode mud'. These are
AIEEE Solved Paper-2005
question_answer102) If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will
AIEEE Solved Paper-2005
A)
be a function of the molecular mass of the substance
question_answer103) In a multi-electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic and electric fields? (A)\[n=1,l=0,m=0\] (B)\[n=2,l=0,m=0\] (C)\[n=2,l=1,\text{ }m=1\] (D)\[n=3,l=2,m=1\] (E)\[n=3,l=2,m=0\]
AIEEE Solved Paper-2005
question_answer104) Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point?
AIEEE Solved Paper-2005
question_answer105) A schematic plot of In\[{{K}_{eq}}\]versus inverse of temperature for a reaction is shown below \[\log {{K}_{eq}}=\frac{-\Delta {{H}^{o}}}{2.303RT}+\frac{-\Delta {{S}^{o}}}{R}\] The reaction must be
AIEEE Solved Paper-2005
question_answer108) The disperse phase in colloidal iron (III) hydroxide and colloidal gold is positively and negatively charged, respectively. Which of the following statements is not correct?
AIEEE Solved Paper-2005
A)
Coagulation in both sols can be brought about by electrophoresis
doneclear
B)
Mixing the sols has no effect
doneclear
C)
Sodium sulphate solution causes coagulation in both sols
doneclear
D)
Magnesium chloride solution coagulates, the gold sol more readily than the iron (III) hydroxide sol
question_answer115) The oxidation state of chromium in the final product formed by the reaction between \[KI\] and acidified potassium dichromate solution is
AIEEE Solved Paper-2005
question_answer123) Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour? (Atomic number\[Cr=24,Mn=25,\text{ }Fe=26,\] \[Co=27\])
AIEEE Solved Paper-2005
question_answer126) Reaction of one molecule of\[HBr\]with one molecule of 1, 3-butadiene at\[40{}^\circ C\]gives predominantly
AIEEE Solved Paper-2005
A)
1-bromo-2-butene under kinetically controlled conditions
doneclear
B)
3-bromobutene under thermodynamically controlled conditions
doneclear
C)
1-bromo-2-butene under thermodynamically controlled conditions
doneclear
D)
3-bromobutene under kinetically controlled conditions
question_answer127) The decreasing order of nucleophilicity among the nucleophiles (A)\[C{{H}_{3}}\underset{\begin{smallmatrix} |\,| \\ O \end{smallmatrix}}{\mathop{C}}\,-{{O}^{-}}\] (B) \[C{{H}_{3}}{{O}^{-}}\] (C) \[C{{N}^{-}}\] (D)
AIEEE Solved Paper-2005
question_answer140) The reaction, \[R-\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,-X+N{{u}^{\text{O-}}}\] \[\xrightarrow{{}}R-\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,-Nu+{{X}^{\text{O-}}}\] is fastest when X is
AIEEE Solved Paper-2005
question_answer144) The value of the 'spin only' magnetic moment for one of the following configurations is 2.84 BM. The correct one is
AIEEE Solved Paper-2005
A)
\[{{d}^{5}}\](in strong ligand field)
doneclear
B)
\[{{d}^{3}}\](in weak as well as in strong fields)
question_answer145) Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount of an acid forms a compound. Water during the reaction is continuously removed. The compound formed is generally known as
AIEEE Solved Paper-2005
question_answer146) p-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound B. The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is
AIEEE Solved Paper-2005
question_answer147) If the bond dissociation energies of\[XY,{{X}_{2}}\]and \[{{Y}_{2}}\](all diatomic molecules) are in the ratio of 1: 1: 0.5 and\[\Delta {{H}_{f}}\]for the formation of\[XY\]is\[-200\text{ }kJ\text{ }mo{{l}^{-1}}\]. The bond dissociation energy of \[{{X}_{2}}\] will be
AIEEE Solved Paper-2005
question_answer148) An amount of solid\[N{{H}_{4}}HS\]is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm pressure. Ammonium hydrogen sulphide decomposes to yield\[N{{H}_{3}}\]and\[{{H}_{2}}S\]gases in the flask. When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to 0.84 atm? The equilibrium constant for \[N{{H}_{4}}HS\] decomposition at this temperature is
AIEEE Solved Paper-2005
question_answer149) An organic compound having molecular mass 60 is found to contain C = 20%, H = 6.67% and N = 46.67% while rest is oxygen. On heating it gives\[N{{H}_{3}}\]along with a solid residue. The solid residue give violet colour with alkaline copper sulphate solution. The compound is
AIEEE Solved Paper-2005
question_answer150) \[{{t}_{1/4}}\]can be taken as the time taken for the concentration of a reactant to drop to 3/4 of its Initial value. If the rate constant for a first order reaction is k, the \[{{t}_{1/4}}\] can be written as
AIEEE Solved Paper-2005
question_answer153) If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately
AIEEE Solved Paper-2005
question_answer154) Let\[R=\{(3,3),(6,6),(9,9),(12,12),\]\[(6,12),\]\[(3,9),(3,12),(3,6)\}\]be a relation on the set A\[=\{3,6,9,12\}\]. The relation is
AIEEE Solved Paper-2005
question_answer156) If the cube roots of unity are\[1,\omega ,{{\omega }^{2}}\]then the roots of the equation \[{{(x-1)}^{3}}+8=0,\] are
AIEEE Solved Paper-2005
question_answer158) Area of the greatest rectangle that can be inscribed in the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]is
AIEEE Solved Paper-2005
question_answer159) The differential equation representing the family of curves\[{{y}^{2}}=2c(x+\sqrt{c}),\]where\[c>0,\]is a parameter, is of order and degree as follows
AIEEE Solved Paper-2005
question_answer160) ABC is a triangle. Forces P,Q,R acting along \[I,A,IB\]and\[IC\]respectively are in equilibrium, where I is the incentre of\[\Delta ABC.\]Then, P : Q : R is
AIEEE Solved Paper-2005
question_answer161) If the coefficients of rth,\[(r+1)th\] and\[(r+2)th\]terms in the binomial expansion of\[{{(1+y)}^{m}}\]are in AP, then m and r satisfy the equation
AIEEE Solved Paper-2005
question_answer163) If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number
AIEEE Solved Paper-2005
question_answer166) If the coefficient of\[{{x}^{7}}\]in\[{{\left[ a{{x}^{2}}+\left( \frac{1}{bx} \right) \right]}^{11}}\]equals the coefficient of\[{{x}^{-7}}\]in\[{{\left[ ax-\left( \frac{1}{b{{x}^{2}}} \right) \right]}^{11}},\]then a and b satisfy the relation
AIEEE Solved Paper-2005
question_answer167) Let\[f:(-1,1)\to B\] be a function defined by\[f(x)={{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}},\] then f is both one-one and onto when B is the interval
AIEEE Solved Paper-2005
question_answer168) If\[{{z}_{1}}\]and\[{{z}_{2}}\]are two non-zero complex numbers such that\[|{{z}_{1}}+{{z}_{2}}|=|{{z}_{1}}|+|{{z}_{2}}|\]then \[\arg ({{z}_{1}})-\arg ({{z}_{2}})\]is equal to
question_answer171) The system of equations \[\alpha x+y+z=\alpha -1,x+\alpha \,y+z=\alpha -l\] \[x+y+\alpha z=\alpha -1\]has no solution, if \[\alpha \] is
AIEEE Solved Paper-2005
question_answer172) The value of a for which the sum of the squares of the roots of the equation\[{{x}^{2}}-(a-2)x-a-1=0\]assume the least value is
AIEEE Solved Paper-2005
question_answer177) If\[x\]is so small that\[{{x}^{3}}\]and higher powers of\[x\] may be neglected, then \[\frac{{{(1+x)}^{3/2}}-{{\left( 1+\frac{1}{2}x \right)}^{3}}}{{{(1-x)}^{1/2}}}\]may be approximated as
AIEEE Solved Paper-2005
question_answer178) If\[x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}},y=\sum\limits_{n=0}^{\infty }{{{b}^{n}}},z=\sum\limits_{n=0}^{\infty }{{{c}^{n}}},\]where a, b, c are in AP and\[|a|<1,|b|<1,|c|<1,\]then\[x,\text{ }y,\text{ }z\]are in
AIEEE Solved Paper-2005
question_answer179) In a\[\Delta ABC,\]let \[\angle C=\pi /2,\] if r is the inradius and R is the circumradius of the\[\Delta ABC,\]then \[2(r+R)\]equals
AIEEE Solved Paper-2005
question_answer181) If in a\[\Delta ABC,\]the altitudes from the vertices A,B,C on opposite sides are in HP, then sin A, sin B, sin C are in
AIEEE Solved Paper-2005
question_answer182) The normal to the curve \[x=a(\cos \theta +\theta \sin \theta ),y=a(\sin \theta -\theta \cos \theta )\]at any point\['\theta '\]is such that
AIEEE Solved Paper-2005
question_answer183) A function is matched below against an interval, where it is supposed to be increasing. Which of the following pairs is incorrectly matched? Interval Function
AIEEE Solved Paper-2005
question_answer184) Let \[\alpha \] and \[\beta \] be the distinct roots of\[a{{x}^{2}}+bx+c=0,\]then \[\underset{x\to \alpha }{\mathop{\lim }}\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}}\]is equal to
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question_answer186) The line parallel to the X-axis and passing through the intersection of the lines \[ax+2\,by+3b=0\]and\[bx-2ay-3a=0,\]where \[(a,b)\ne (0,0)\]is
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question_answer187) A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of\[50\text{ }c{{m}^{3}}/\min \]. When the thickness of ice is 15 cm, then the rate at which the thickness of ice decreases, is
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question_answer190) Let\[f(x)\]be a non-negative continuous function such that the area bounded by the curve\[y=f(x),\]X-axis and the ordinates\[x=\pi /4\] and \[x=\beta >\pi /4\] is\[\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \right)\].Then\[f\left( \frac{\pi }{2} \right)\],is
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question_answer193) The parabolas\[{{y}^{2}}=4x\]and\[{{x}^{2}}=4y\]divide the square region bounded by the lines \[x=4,\text{ }y=4\]and the coordinate axes. If \[{{S}_{1}},{{S}_{2}},{{S}_{3}}\]are respectively the areas of these parts numbered from top to bottom, then\[{{S}_{1}}:{{S}_{2}}:{{S}_{3}}\]
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question_answer194) If the plane\[2ax-3ay+4az+6=0\]passes through the mid-point of the line joining the centres of the spheres\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+6x-8y-2z=13\] and\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-10x+4y-2z=8,\]then a equals
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question_answer195) The distance between the line\[r=2\hat{i}-2\hat{j}+3\hat{k}+\lambda (\hat{i}-\hat{j}+4\hat{k})\]and the plane\[r.(\hat{i}+5\hat{j}+\hat{k})=5\]is
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question_answer196) For any vector a, the value of\[{{(a\times \hat{i})}^{2}}+{{(a\times \hat{j})}^{2}}+{{(a\times \hat{k})}^{2}}\]is equal to
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question_answer197) If non-zero numbers a, b, c are in HP, then the straight line \[\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0\]always passes through a fixed point. That point is
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question_answer198) It a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is
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question_answer199) If the circles\[{{x}^{2}}+{{y}^{2}}+2ax+cy+a=0\]and \[{{x}^{2}}+{{y}^{2}}-3\text{ }ax+dy-1=0\]intersect in two distinct points P and 0, then the line \[5x+by-a=0\]passes through P and Q for
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question_answer200) A circle touches the X-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is
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question_answer201) If a circle passes through the point (a, b) and cuts the circle\[{{x}^{2}}+{{y}^{2}}={{p}^{2}}\]orthogonally, then the equation of the locus of its centre is
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question_answer202) An ellipse has OB as semi-minor axis, F and F' its foci and the angle FBF' is a right angle. Then, the eccentricity of the ellipse is
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question_answer203) The locus of a point \[P(\alpha ,\beta )\] moving under the condition that the line\[y=\alpha x+\beta \]is a tangent to the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]is
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question_answer204) If the angle\[\theta \]between the line\[\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}\]and the plane \[2x-y+\sqrt{\lambda }z+4=0\]is such that \[\sin \theta =\frac{1}{3}\]The value of\[\lambda \]is
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question_answer206) Let A and B be two events such that \[P\overline{(A\cup B)}=\frac{1}{6},P(A\cap B)=\frac{1}{4}\]and\[P(\overline{A})=\frac{1}{4},\]where \[\overline{A}\] stands for complement of event A. Then, events A and B are
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question_answer207) Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house, is
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question_answer209) Two points A and B move from rest along a straight line with constant acceleration f and f?, respectively. If A takes m second more than B and describes n unit more than B in acquiring the same speed, then
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question_answer210) A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of\[2\text{ }cm/{{s}^{2}}\]and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then, the lizard will catch the insect after
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question_answer211) The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one-third of the other force. The ratio of larger force to smaller one is
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question_answer213) Let a, b and c be distinct non-negative numbers. If the vectors\[a\hat{i}+a\hat{j}+c\hat{k},\hat{i}+\hat{k}\]and \[c\hat{i}+c\hat{j}+b\hat{k}\] lie in a plane, then c is
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question_answer214) If a, b, b are non-coplanar vectors and \[\lambda \], is a real number, then\[[\lambda (a+b){{\lambda }^{2}}\,b\,\,\lambda c]=[ab+cd]\]for
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question_answer215) A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance
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question_answer217) Let\[{{x}_{1}},{{x}_{2}},.....,{{x}_{n}}\]be n observations such that \[\Sigma x_{i}^{2}=400\]and\[\Sigma {{x}_{i}}=80\]. Then, a possible value of n among the following is
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question_answer218) A particle is projected from a point O with velocity u at an angle of\[60{}^\circ \]with the horizontal. When it is moving in a direction at right angle to its direction at O, then its velocity is given by
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question_answer219) If both the roots of the quadratic equation\[{{x}^{2}}-2kx+{{k}^{2}}+k-5=0\]are less than 5, then k lies in the interval
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question_answer221) A real valued function\[f(x)\]satisfies the functional equation \[f(x-y)=f(x)\text{ }f(y)-f(a-x)\text{ }f(a+y)\] where, a is a given constant and\[f(0)=1\]\[f(2\text{ }a-x)\]is equal to
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question_answer222) If the equation \[{{a}_{n}}{{X}^{n}}+{{a}_{n-1}}{{X}^{n-1}}+....+{{a}_{1}}x=0,\] \[{{a}_{1}}\ne 0,n\ge 2,\]has a positive root \[x=\alpha ,\] then the equation \[n{{a}_{n}}{{x}^{n-1}}+(n-1){{a}_{n-1}}{{X}^{n-2}}+....+{{a}_{1}}=0\] has a positive root, which is
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question_answer225) If the pair of linesa\[{{x}^{2}}+2(a+b)xy+b{{y}^{2}}=0\] lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sector is thrice the area of another sector, then
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