Solved papers for JEE Main & Advanced AIEEE Solved Paper-2006
done AIEEE Solved Paper-2006 Total Questions - 150
question_answer1) The Kirchhoff's first law\[(\Sigma i=0)\]and second law\[(\Sigma iR=\Sigma E)\], where the symbols have their usual meanings, are respectively based on
AIEEE Solved Paper-2006
question_answer2) Needles\[{{N}_{1}},{{N}_{2}}\]and\[{{N}_{3}}\]are made of a ferromagnetic, a paramagnetic and a diamagnetic substance, respectively. A magnet when brought close to them will
AIEEE Solved Paper-2006
A)
Attract\[{{N}_{1}}\]and\[{{N}_{2}}\]strongly but repel\[{{N}_{3}}\]
doneclear
B)
Attract\[{{N}_{1}}\]strongly, \[{{N}_{2}}\]weakly and repel\[{{N}_{3}}\] weakly
doneclear
C)
Attract\[{{N}_{1}}\]strongly, but repel\[{{N}_{2}}\]and\[{{N}_{3}}\]weakly
question_answer3) A material B has twice the specific resistance of A. A circular wire made of B has twice the diameter of a wire made of Then, for the two wires to have the same resistance, the ratio \[{{l}_{B}}/{{l}_{A}}\] respective lengths must be
AIEEE Solved Paper-2006
question_answer4) In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a
AIEEE Solved Paper-2006
question_answer5) An electric dipole is placed at an angle of \[30{}^\circ \]to a non-uniform electric field. The dipole will experience
AIEEE Solved Paper-2006
A)
a translational force only in the direction of the field
doneclear
B)
a translational force only in a direction normal to the direction of the field
question_answer6) A particle located at\[x=0\]at time\[t=0\], starts moving along the positive x-direction with a velocity v that varies as \[v=\alpha \sqrt{x}\]. The displacement of the particle varies with time as
AIEEE Solved Paper-2006
question_answer7) A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is\[4\text{ }m{{s}^{-1}}\]. The kinetic energy of the other mass is
AIEEE Solved Paper-2006
question_answer8) A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed\[v\text{ }m{{s}^{-1}}\]. The velocity of sound in air is \[300\,m{{s}^{-1}}\]. If the person can hear frequencies up to a maximum of 10000 Hz, the maximum value of v up to which he can hear the whistle is
AIEEE Solved Paper-2006
question_answer9) A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of \[45{}^\circ \]with the initial vertical direction is
AIEEE Solved Paper-2006
question_answer10) A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time the particle goes up is
AIEEE Solved Paper-2006
question_answer11) The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is
AIEEE Solved Paper-2006
question_answer12) Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy?
AIEEE Solved Paper-2006
question_answer13) Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on earth, at a distance r from the sun.
question_answer14) Which of the following units denote the dimensions\[[M{{L}^{2}}/{{Q}^{2}}],\]where 0 denotes the electric charge?
AIEEE Solved Paper-2006
question_answer15) A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes up to 2 m height further, find the magnitude of the force. Consider\[g=10\text{ }m/{{s}^{2}}\].
AIEEE Solved Paper-2006
question_answer16) A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
AIEEE Solved Paper-2006
question_answer17) Consider a two particle system with particles having masses\[{{m}_{1}}\]and\[{{m}_{2}}\]. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?
AIEEE Solved Paper-2006
question_answer18) A player caught a cricket ball of mass 150 g moving at a rate of 20 m/s. If the catching process is completed in 0.1 s, the force of the blow exerted by the ball on the hand of the player is equal to
AIEEE Solved Paper-2006
question_answer19) In a common-base mode of a transistor, the collector current is 5.488 mA for an emitter current of 5.60 mA. The value of the base current amplification factor (P) will be
AIEEE Solved Paper-2006
question_answer20) A thermocouple is made of two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is kept cold, then an electric current will
AIEEE Solved Paper-2006
A)
flow from Antimony to Bismuth at the hot junction
doneclear
B)
flow from Bismuth to Antimony at the cold junction
doneclear
C)
not flow through the thermocouple
doneclear
D)
flow from Antimony to Bismuth at the cold junction
question_answer21) The threshold frequency for a metallic surface corresponds to an energy of 6.2 eV and the stopping potential for a radiation incident on this surface is 5V. The incident radiation lies in
AIEEE Solved Paper-2006
question_answer22) An alpha nucleus of energy \[\frac{1}{2}m{{v}^{2}}\]bombards a heavy nuclear target of charge \[Ze\]. Then, the distance of closest approach for the alpha nucleus will be proportional to
AIEEE Solved Paper-2006
question_answer24) When\[_{3}L{{i}^{7}}\]nuclei are bombarded by protons and the resultant nuclei are\[_{4}B{{e}^{8}},\] the emitted particles will be
AIEEE Solved Paper-2006
question_answer26) The energy spectrum of \[\beta \]-particles [number N(E) as a function of \[\beta \]-energy E] emitted from a radioactive source is
AIEEE Solved Paper-2006
question_answer27) In a series resonant LCR circuit, .the voltage across R is 100 V and\[R=1k\,\Omega \]. With\[C=2\mu F\]. The resonant frequency\[\omega \] is 200 rad/s. At resonance, the voltage across L is
AIEEE Solved Paper-2006
question_answer28) The resistance of a bulb filament is\[100\text{ }\Omega \].at a temperature of\[100{}^\circ C\]. If its temperature coefficient of resistance is\[0.005/{}^\circ C,\]its resistance will become\[200\,\Omega \]. at a temperature of
AIEEE Solved Paper-2006
question_answer29) Two insulating plates are both uniformly charged in such a way that the potential difference between them is\[{{V}_{2}}-{{V}_{1}}=20\,V\] (i.e., plate 2 is at a higher potential). The plates are separated by\[d=0.1\text{ }m\]and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2? \[(e=1.6\times {{10}^{-19}}C,{{m}_{0}}=9.11\times {{10}^{-31}}kg)\]
AIEEE Solved Paper-2006
question_answer30) In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency \[\omega \] in a magnetic field B. The maximum value of emf generated in the coil is
AIEEE Solved Paper-2006
question_answer31) A solid which is not transparent to visible light and whose conductivity increases with temperature is formed by
AIEEE Solved Paper-2006
question_answer32) The refractive index of glass is 1.520 for red light and 1.525 for bin l light. Let\[{{D}_{1}}\]and\[{{D}_{2}}\]be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then,
AIEEE Solved Paper-2006
A)
\[{{D}_{1}}<{{D}_{2}}\]
doneclear
B)
\[{{D}_{1}}={{D}_{2}}\]
doneclear
C)
\[{{D}_{1}}\]can be less than or greater than\[{{D}_{2}}\] depending upon. The angle of prism
question_answer33) If the ratio of the concentration of electrons to that of holes in a semiconductor is\[\frac{7}{5}\]and the ratio of currents is \[\frac{7}{4}\], then what is the ratio of their drift velocities?
AIEEE Solved Paper-2006
question_answer34) In a Wheatstone?s bridge, three resistances P, Q and R are connected in the three arms and the fourth arm is formed by two resistances\[{{S}_{1}}\]and\[{{S}_{2}}\]connected in parallel. The condition for the bridge to be balanced will be
AIEEE Solved Paper-2006
question_answer35) The flux linked with a coil at any instant t is given by \[\phi =10{{t}^{2}}-50t+250\] The induced emf at\[t=3\text{ }s\]is
AIEEE Solved Paper-2006
question_answer36) A long solenoid has 200 turns/cm and carries a current i. The magnetic field at its centre is \[6.28\,\times {{10}^{-2}}\,Wb/{{m}^{2}}\]. Another long solenoid has 100 turns/cm and it carries a current\[i/3\]. The value of the magnetic field at its centre is
AIEEE Solved Paper-2006
question_answer37) The circuit has two oppositely connected ideal diodes in parallel. What is the current flowing in the circuit?
AIEEE Solved Paper-2006
question_answer39) The anode voltage of a photocell is kept fixed. The wavelength \[\lambda \] of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows
AIEEE Solved Paper-2006
question_answer40) If the binding energy per nucleon in\[_{3}^{7}Li\]and\[_{2}^{4}He\]nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction \[P+_{3}^{7}Li\to 2_{2}^{4}He\] energy of proton must be
AIEEE Solved Paper-2006
question_answer41) An electric bulb is rated\[220\text{ }V-100\text{ }W\]The power consumed by it when operated on 110 V will be
AIEEE Solved Paper-2006
question_answer43) A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency\[\omega \]. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
AIEEE Solved Paper-2006
question_answer44) Four point masses, each of value m, are placed at the corners of a square ABCD of side \[l\]. The moment of inertia of this system about an axis passing through A and parallel to BD is
AIEEE Solved Paper-2006
question_answer45) A force of \[-F\hat{k}\] acts on O, the origin of the coordinate system. The torque about the point \[(1,-1)\]is
AIEEE Solved Paper-2006
question_answer46) The potential energy of a 1 kg particle free to move along the x-axis is given by \[V(x)=\left( \frac{{{x}^{4}}}{4}-\frac{{{x}^{2}}}{2} \right)J\] The total mechanical energy of the particle is 2 J. Then, the maximum speed (in m/s) is
AIEEE Solved Paper-2006
question_answer47) A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity\[\omega \]. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity\[\omega '\]is equal to
AIEEE Solved Paper-2006
question_answer48) A wire elongates by\[l\,mm\] when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm)
AIEEE Solved Paper-2006
question_answer49) An inductor\[(L=100mH)\], a resistor\[(R=100\,\Omega )\] and a battery\[(E=100\,V)\]are initially connected in series as shown in the figure. After a long time, the battery is disconnected after short circuiting the points A and B. The current in the circuit 1 ms after the short circuit is
AIEEE Solved Paper-2006
question_answer50) Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire, the in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B is
AIEEE Solved Paper-2006
question_answer51) Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature \[{{T}_{0}},\] while box B contains one mole of helium at temperature (7/3)\[{{T}_{0}}\]. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases,\[{{T}_{f}}\]in terms of\[{{T}_{0}}\]is
AIEEE Solved Paper-2006
question_answer52) The work of 146 kJ is performed in order to compress one kilo mole of a gas adiabatically and in this process, the temperature of the gas increases by\[7{}^\circ C\]. The gas is \[(R=8.3\,J\,mo{{l}^{-1}}{{K}^{-1}})\]
AIEEE Solved Paper-2006
question_answer54) The \[rms\] value of the electric field of the light coming from the sun is 720 N/C. The average total energy density of the electromagnetic wave is
AIEEE Solved Paper-2006
question_answer55) If the terminal speed of a sphere of gold (density\[=19.5\text{ }kg/{{m}^{3}}\]) is 0.2 m/s in a viscous liquid (density\[=1.5\text{ }kg/{{m}^{3}}\]), find the terminal speed of a sphere of silver (density =10.5\[kg/{{m}^{3}}\]) of the same size in the same liquid.
AIEEE Solved Paper-2006
question_answer58) The increasing order of the rate of\[HCN\] addition to compounds I-IV is (A)\[HCHO\] (B)\[C{{H}_{3}}COC{{H}_{3}}\] (C)\[PhCOC{{H}_{3}}\] (D)\[PhCOPh\]
AIEEE Solved Paper-2006
question_answer59) How many moles of magnesium phosphate, \[M{{g}_{3}}{{(P{{O}_{4}})}_{2}}\]will contain 0.25 mole of oxygen atoms?
AIEEE Solved Paper-2006
question_answer63) A reaction was found to be second order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will
AIEEE Solved Paper-2006
question_answer67) In the transformation of\[_{92}^{238}U\]to\[_{92}^{234}U\], if one emission is an \[\alpha \]-particle, what should be the other emission (s)?
AIEEE Solved Paper-2006
question_answer69) \[C{{H}_{3}}Br+N{{u}^{-}}\to C{{H}_{3}}-Nu+B{{r}^{-}}\] The decreasing order of the rate of the above reaction with nucleophiles \[(N{{u}^{-}})A\] to IV is \[[N{{u}^{-}}=(A)\,Ph{{O}^{-}},\,(B)\,Ac{{O}^{-}},\,(C)\,H{{O}^{-}},\,(D)\,C{{H}_{3}}{{O}^{-}}]\]
AIEEE Solved Paper-2006
question_answer73) Uncertainty in the position of an electron (mass\[=9.1\times {{10}^{-31}}kg\]) moving with a velocity\[300\text{ }m{{s}^{-1}},\] accurate upon 0.001% will be\[(h=6.63\times {{10}^{-34}}Js)\])
AIEEE Solved Paper-2006
question_answer74) Phosphorus pentachloride dissociates as follows, in a closed reaction vessel, \[PC{{l}_{5}}(g)PC{{l}_{3}}(g)+C{{l}_{2}}(g)\] If total pressure at equilibrium of the reaction mixture is p and degree of dissociation of \[PC{{l}_{5}}\] is\[x\], the partial pressure of\[PC{{l}_{3}}\]will be
AIEEE Solved Paper-2006
question_answer75) The standard enthalpy of formation \[(\Delta H_{f}^{o})\] at 298 K for methane,\[C{{H}_{4}}(g),\]is \[-74.8\text{ }kJ\text{ }mo{{l}^{-1}}\] The additional information required to determine the average energy for\[CH\] bond formation would be
AIEEE Solved Paper-2006
A)
the dissociation energy of Hg and enthalpy of sublimation of carbon
doneclear
B)
latent heat of vaporisation of methane
doneclear
C)
the first four ionisation energies of carbon and electron gain enthalpy of hydrogen
doneclear
D)
the dissociation energy of hydrogen molecule,\[{{H}_{2}}\]
question_answer78) A metal, M forms chlorides in its +2 and +4 oxidation states. Which of the following statements about these chlorides is correct?
AIEEE Solved Paper-2006
A)
\[MC{{l}_{2}}\] is more volatile than\[MC{{l}_{4}}\]
doneclear
B)
\[MC{{l}_{2}}\]is more soluble in anhydrous ethanol than\[MC{{l}_{4}}\]
doneclear
C)
\[MC{{l}_{2}}\]is more ionic than\[MC{{l}_{4}}\]
doneclear
D)
\[MC{{l}_{2}}\]is more easily hydrolysed than\[MC{{l}_{4}}\]
question_answer80) The molar conductivities \[\hat{\ }_{NaOAc}^{o}\]and \[\hat{\ }_{HCl}^{o}\]at infinite dilution in water at\[25{}^\circ C\]are 91.0 and \[426.2\text{ }S\text{ }c{{m}^{2}}/mol\]respectively. To calculate \[\hat{\ }_{HOAc'}^{o}\]the additional value required is
AIEEE Solved Paper-2006
question_answer82) The correct order of increasing acid strength of the compounds
(I) \[C{{H}_{3}}C{{O}_{2}}H\]
(II) \[MeOC{{H}_{2}}C{{O}_{2}}H\]
(III) \[C{{F}_{3}}C{{O}_{2}}H\]
(IV)
AIEEE Solved Paper-2006
question_answer85) Nickel\[(Z=28)\]combines with a uninegative monodentate ligand\[{{X}^{-}}\]to form a paramagnetic complex\[{{[Ni{{X}_{4}}]}^{2-}}\]. The number of unpaired electron (s) in the nickel and geometry of this complex ion are, respectively
AIEEE Solved Paper-2006
question_answer88) An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If\[{{T}_{i}}\]is the initial temperature and\[{{T}_{f}}\]is the final temperature, which of the following statements is correct?
AIEEE Solved Paper-2006
A)
\[{{({{T}_{f}})}_{irrev}}>{{({{T}_{f}})}_{rev}}\]
doneclear
B)
\[{{T}_{f}}>{{T}_{i}}\]for reversible process but\[{{T}_{f}}={{T}_{i}}\]for irreversible process
doneclear
C)
\[{{({{T}_{f}})}_{rev}}={{({{T}_{i}})}_{irrev}}\]
doneclear
D)
\[{{T}_{f}}={{T}_{i}}\]for both reversible and irreversible processes
question_answer90) Rate of a reaction can be expressed by Arrhenius equation as \[k=A{{e}^{-E/RT}}\] In this equation, E represents
AIEEE Solved Paper-2006
A)
the energy above which all the. Colliding molecules will react
doneclear
B)
the energy below which colliding molecules will not react
doneclear
C)
the total energy of the reacting molecules at a temperature, T
doneclear
D)
the fraction of molecules with energy greater than the activation energy of the reaction
question_answer93) Increasing order of stability among the three main conformations (i.e.. Eclipse, Ami, Gauche) of 2-fluoroethanol is
AIEEE Solved Paper-2006
question_answer95) The decreasing values of bond angles from\[N{{H}_{3}}(107{}^\circ )\]to\[Sb{{H}_{3}}(91{}^\circ )\]down group-15 of the periodic table is due to
AIEEE Solved Paper-2006
question_answer97) The 'spin-only' magnetic moment [in units of Bohr magneton,\[({{\mu }_{\beta }})]\]of\[N{{i}^{2+}}\]in aqueous solution would be (Atomic number of\[Ni=28\])
AIEEE Solved Paper-2006
question_answer98) The equilibrium constant for the reaction \[S{{O}_{3}}(g)S{{O}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\] is\[{{K}_{c}}=4.9\times {{10}^{-2}}\]. The value of\[{{K}_{c}}\]for the reaction \[2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g)\]will be
AIEEE Solved Paper-2006
question_answer99) Following statements regarding the periodic trends of chemical reactivity of the alkali metals and the halogens are given. Which of these statements gives the correct picture?
AIEEE Solved Paper-2006
A)
The reactivity decreases in the alkali metals but increases in the halogens with increase in atomic number down the group
doneclear
B)
In both the alkali metals and the halogens, the chemical reactivity decreases with increase in atomic number down the group
doneclear
C)
Chemical reactivity increases with increase in atomic number down the group in both the alkali metals and halogens
doneclear
D)
In alkali metals, the reactivity increases but in the halogens it decreases with increase in atomic number down the group
question_answer100) Given the data at\[25{}^\circ C,\] \[Ag+{{I}^{-}}\xrightarrow{{}}AgI+{{e}^{-}};\] \[E{}^\circ =0.152\text{ }V\] \[Ag\xrightarrow{{}}A{{g}^{+}}+{{e}^{-}};\] \[E{}^\circ =-0.800\text{ }V\] What is the value of\[\log \text{ }{{K}_{sp}}\]for\[AgI\]? \[\left( 2.303\frac{RT}{F}=0.059\,V \right)\]
AIEEE Solved Paper-2006
question_answer101) The following mechanism has been proposed for the reaction of\[NO\]with\[B{{r}_{2}}\]to form\[NOBr\]. \[NO(g)+B{{r}_{2}}(g)NOB{{r}_{2}}(g)\] \[NOB{{r}_{2}}(g)+NO(g)\xrightarrow{{}}2NOBr(g)\] If the second step is the rate determining step, the order of the reaction with respect to\[NO(g)\]is
AIEEE Solved Paper-2006
question_answer103) Resistance of a conductivity cell filled with a solution of an electrolyte of concentration 0.1 M is\[100\text{ }\Omega \]. The conductivity of this solution is\[1.29\text{ }S\text{ }{{m}^{-1}}\].Resistance of the same cell when filled with 0.2 M of the same solution is\[520\,\Omega \]The molar conductivity of 0.02 M solution of the electrolyte will be
AIEEE Solved Paper-2006
question_answer105) Density of a 2.05 M solution of acetic acid in water is\[1.02\text{ }g/mL\]. The molality of the solution is
AIEEE Solved Paper-2006
question_answer106) The enthalpy changes for the following processes are listed below \[C{{l}_{2}}(g)=2Cl(g)\] \[242.3\text{ }kJ\text{ }mo{{l}^{-1}}\] \[{{I}_{2}}(g)=2I(g),\] \[151.0\text{ }kJ\text{ }mo{{l}^{-1}}\] \[ICl(g)=I(g)+Cl(g),\] \[211.3\text{ }kJ\text{ }mo{{l}^{-1}}\] \[{{I}_{2}}(s)={{I}_{2}}(g),\] \[62.76\text{ }kJ\text{ }mo{{l}^{-1}}\] Given that the standard states for iodine and chlorine are\[{{I}_{2}}(s)\]and\[C{{l}_{2}}(g)\], the standard enthalpy of formation of \[ICl\,(g)\] is
AIEEE Solved Paper-2006
question_answer107) How many EDTA (ethylenediaminetetra acetic acid) molecules are required to make an octahedral complex with a \[C{{a}^{2+}}\] ion ?
AIEEE Solved Paper-2006
question_answer109) 18 g of glucose\[({{C}_{6}}{{H}_{12}}{{O}_{6}})\]is added to 178.2 g of water. The vapour pressure of water for this aqueous solution at\[100{}^\circ C\]is
AIEEE Solved Paper-2006
question_answer110) \[(\Delta H-\Delta U)\]for the formation of carbon monoxide (CO) from its elements at 298 K is\[(R=8.314J{{K}^{-1}}mo{{l}^{-1}})\]
AIEEE Solved Paper-2006
question_answer111) If the roots of the quadratic equation \[{{x}^{2}}+px+q=0\]are tan\[30{}^\circ \]and tan\[15{}^\circ \] respectively, then the value of\[2+q-p\]is
AIEEE Solved Paper-2006
question_answer113) Let W denotes the words in the English dictionary. Define the relation R by \[R=\{(x,y)\in W\times W|\] the words\[x\]and y have atleast one letter in common}. Then, R is
AIEEE Solved Paper-2006
question_answer114) The number of values of\[x\]in the interval \[[0,3\pi ]\]satisfying the equation \[2\text{ }si{{n}^{2}}x+5\text{ }sin\text{ }x-3=0\]is
AIEEE Solved Paper-2006
question_answer115) If A and B are square matrices of size\[n\times n\]such that\[{{A}^{2}}-{{B}^{2}}=(A-B)(A+B),\]then which of the following will be always true?
AIEEE Solved Paper-2006
question_answer117) If \[(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c}),\] where \[\vec{a},\,\vec{b}\] and \[\vec{c}\] are any three vectors such that \[\vec{a}.\vec{b}\ne 0,\vec{b}.\vec{c}\ne 0,\] then \[\vec{a}\] and \[\vec{c}\] are
AIEEE Solved Paper-2006
A)
inclined at an angle of\[\frac{\pi }{6}\]between them b
doneclear
B)
perpendicular
doneclear
C)
parallel
doneclear
D)
inclined at an angle of\[\frac{\pi }{3}\]between them
question_answer118) All the values of m for which both roots of the equation \[{{x}^{2}}-2mx+{{m}^{2}}-1=0\]are greater than -2 but less than 4 lie in the interval
AIEEE Solved Paper-2006
question_answer119) ABC is a triangle, right singled at A. The resultant of the forces acting along \[\overrightarrow{AB},\,\overrightarrow{AC}\] with magnitudes\[\frac{1}{AB}\]and\[\frac{1}{AC}\]respectively is the force along \[\overrightarrow{AD},\] where D is the foot of the perpendicular from A to BC. The magnitude of the resultant is
AIEEE Solved Paper-2006
question_answer120) Suppose, a population A has 100 observations 101, 102,..., 200 and another population B has 100 observations 151, 152, .... 250. If\[{{V}_{A}}\]and\[{{V}_{B}}\]represent the variances of the two populations respectively, then\[\frac{{{V}_{A}}}{{{V}_{B}}}\]is
AIEEE Solved Paper-2006
question_answer123) The locus of the vertices of the family of parabolas\[y=\frac{{{a}^{3}}{{x}^{2}}}{3}+\frac{{{a}^{2}}x}{2}-2a\]is
AIEEE Solved Paper-2006
question_answer124) A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is
AIEEE Solved Paper-2006
question_answer125) The value of a, for which the points A, B, C with position vectors\[2\hat{i}-\hat{j}+\hat{k},\hat{i}-3\hat{j}-5\hat{k}\]and \[a\hat{i}-3\hat{j}+\hat{k}\] respectively are the vertices of a right angled triangle with \[C=\frac{\pi }{2}\]are
AIEEE Solved Paper-2006
question_answer128) At an election, a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for atleast one candidate, then the number of ways in which he can vote, is
AIEEE Solved Paper-2006
question_answer129) If the expansion in powers of\[x\]of the function \[\frac{1}{(1-ax)(1-bx)}\]is\[{{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+{{a}_{2}}{{x}^{3}}+....,\]then\[{{a}_{n}}\]is
AIEEE Solved Paper-2006
question_answer130) For natural numbers m, n, if \[{{(1-y)}^{m}}{{(1+y)}^{n}}=1+{{a}_{1}}y+{{a}_{2}}{{y}^{2}}+.....\]and\[{{a}_{1}}={{a}_{2}}=10,\]then (m, n) is
AIEEE Solved Paper-2006
question_answer131) A particle has two velocities of equal magnitude inclined to each other at an angle \[\theta \]. If one of them is halved, the angle between the- other and the original resultant velocity is bisected by the new resultant. Then, 0 is
AIEEE Solved Paper-2006
question_answer132) At a telephone enquiry system, the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 min time intervals. The probability that there is atmost one phone call during a 10 min time period, is
AIEEE Solved Paper-2006
question_answer133) A body falling .from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4 s prior to passing through P. If \[g=10m/{{s}^{2}},\]then the height above the point P from where the body began to fall is
AIEEE Solved Paper-2006
question_answer136) Let \[{{a}_{1}},{{a}_{2}},{{a}_{3}},....\] be terms of an AP. If \[\frac{{{a}_{1}}+{{a}_{2}}+.....+{{a}_{p}}}{{{a}_{1}}+{{a}_{2}}+....{{a}_{q}}}=\frac{{{p}^{2}}}{{{q}^{2}}},\] \[p\ne q,\]then\[\frac{{{a}_{6}}}{{{a}_{21}}}\]equals
AIEEE Solved Paper-2006
question_answer140) A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length\[x\]. The maximum area enclosed by the park is
AIEEE Solved Paper-2006
question_answer141) If\[(a,\text{ }{{a}^{2}})\]falls inside the angle made by the lines \[y=\frac{x}{2},\text{ }x>0\]and\[y=3x,\text{ }x>0,\]then a belongs to
AIEEE Solved Paper-2006
question_answer143) If the lines\[3x-4y-7=0\]and\[2x-3y-5=0\]are two diameters of a circle of area\[49\,\pi \,sq\]units, the equation of the circle is
AIEEE Solved Paper-2006
question_answer145) The differential equation whose solution is \[A{{x}^{2}}+B{{y}^{2}}=1,\]where A and B are arbitrary constants, is of
AIEEE Solved Paper-2006
question_answer146) The value of \[\int_{I}^{a}{[x]\,f'\,(x)\,dx,\,\,a>1,}\] where\[[x]\] denotes the greatest integer not exceeding \[x,\]is
AIEEE Solved Paper-2006
question_answer147) Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid-points of the chords of the circle C 'that subtend an angle of\[\frac{2\pi }{3}\]at its centre, is
AIEEE Solved Paper-2006
question_answer148) If\[{{a}_{1}},{{a}_{2}},....{{a}_{n}}\]are in HP, then the expression\[{{a}_{1}}{{a}_{2}}+{{a}_{2}}{{a}_{3}}+,....+{{a}_{n-1}}{{a}_{n}}\]is equal to
AIEEE Solved Paper-2006
question_answer149) If\[{{z}^{2}}+z+1=0,\]where z is complex number, then the value of \[{{\left( z+\frac{1}{z} \right)}^{2}}+{{\left( {{z}^{2}}+\frac{1}{{{z}^{2}}} \right)}^{2}}+{{\left( {{z}^{3}}+\frac{1}{{{z}^{3}}} \right)}^{2}}\] \[+......+{{\left( {{z}^{6}}+\frac{1}{{{z}^{6}}} \right)}^{2}}\]is
AIEEE Solved Paper-2006