# 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

A)
Conservation of charge, conservation of momentum

B)
Conservation of energy, conservation of charge

C)
Conservation of momentum, conservation of charge

D)
Conservation of charge, conservation of energy

• 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${{N}_{3}}$

B)
Attract${{N}_{1}}$strongly, ${{N}_{2}}$weakly and repel${{N}_{3}}$ weakly

C)
Attract${{N}_{1}}$strongly, but repel${{N}_{2}}$and${{N}_{3}}$weakly

D)
attract all three of them

• 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

A)
1

B)
$\frac{1}{2}$

C)
$\frac{1}{4}$

D)
2

• 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

A)
helix

B)
straight line

C)
ellipse

D)
circle

• 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

B)
a translational force only in a direction normal to the direction of the field

C)
a torque as well as a translational force

D)
a torque only

• 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

A)
${{t}^{2}}$

B)
$t$

C)
${{t}^{1/2}}$

D)
${{t}^{3}}$

• 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

A)
144 J

B)
288 J

C)
192 J

D)
96 J

• 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

A)
$15\sqrt{2}m{{s}^{-1}}$

B)
$15/\sqrt{2}m{{s}^{-1}}$

C)
$15m{{s}^{-1}}$

D)
$30\,m{{s}^{-1}}$

• 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

A)
$Mg(\sqrt{2}+1)$

B)
$Mg\sqrt{2}$

C)
$\frac{Mg}{\sqrt{2}}$

D)
$Mg(\sqrt{2}-1)$

• 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

A)
$-0.5J$

B)
$-1.25\,J$

C)
1.25 J

D)
0.5 J

• 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

A)
0.01s

B)
10s

C)
0.1s

D)
100s

• 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

A)
$\frac{1}{6}s$

B)
$\frac{1}{4}s$

C)
$\frac{1}{3}s$

D)
$\frac{1}{12}s$

• 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.

A)
$4\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}$

B)
$\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}$

C)
$r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/4\pi {{r}^{2}}$

D)
${{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}$ where, ${{r}_{0}}$ is the radius of the earth and a is Stefan's constant.

• 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

A)
$Wb/{{m}^{2}}$

B)
henry (H)

C)
$H/{{m}^{2}}$

D)
Weber (Wb)

• 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

A)
4N

B)
16N

C)
20N

D)
22N

• 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

A)
105 Hz

B)
1.05 Hz

C)
1050 Hz

D)
10.5 Hz

• 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

A)
$\frac{{{m}_{2}}}{{{m}_{1}}}d$

B)
$\frac{{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}d$

C)
$\frac{{{m}_{1}}}{{{m}_{2}}}d$

D)
$d$

• 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

A)
150N

B)
3N

C)
30N

D)
300N

• 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

A)
49

B)
50

C)
51

D)
48

• 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

B)
flow from Bismuth to Antimony at the cold junction

C)
not flow through the thermocouple

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

A)
ultraviolet region

B)
infrared region

C)
visible region

D)
X-ray region

• 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

A)
${{v}^{2}}$

B)
$1/m$

C)
$1/{{v}^{4}}$

D)
$1/Ze$

• question_answer23) The time taken by a photoelectron to come out after the photon strikes is approximately     AIEEE  Solved  Paper-2006

A)
${{10}^{-4}}s$

B)
${{10}^{-10}}s$

C)
${{10}^{-16}}s$

D)
${{10}^{-1}}s$

• 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

A)
alpha particles

B)
beta particles

C)
gamma photons

D)
neutrons

• question_answer25) The current I drawn from the 5 V source will be   AIEEE  Solved  Paper-2006

A)
0.33 A

B)
0.5 A

C)
0.67 A

D)
0.17 A

• 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

A)

B)

C)

D)

• 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

A)
$2.5\times {{10}^{-2}}V$

B)
$40\,V$

C)
$250\,V$

D)
$4\times {{10}^{-3}}\,V$

• 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

A)
$300{}^\circ C$

B)
$400{}^\circ C$

C)
$500{}^\circ C$

D)
$200{}^\circ C$

• 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

A)
$2.65\times {{10}^{6}}\text{ }m/s$

B)
$7.02\times {{10}^{12}}\text{ }m/s$

C)
$1.87\times {{10}^{6}}m/s$

D)
$32\times {{10}^{-19}}m/s$

• 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

A)
$NABR\,\omega$

B)
$NAB$

C)
$NABR$

D)
$NAB\,\omega$

• question_answer31) A solid which is not transparent to visible light and whose conductivity increases with temperature is formed by     AIEEE  Solved  Paper-2006

A)
ionic bonding

B)
covalent bonding

C)
van der Waals' bonding

D)
metallic bonding

• 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)
${{D}_{1}}<{{D}_{2}}$

B)
${{D}_{1}}={{D}_{2}}$

C)
${{D}_{1}}$can be less than or greater than${{D}_{2}}$ depending upon. The angle of prism

D)
${{D}_{1}}>{{D}_{2}}$

• 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

A)
$\frac{5}{8}$

B)
$\frac{4}{5}$

C)
$\frac{5}{4}$

D)
$\frac{4}{7}$

• 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

A)
$\frac{P}{Q}=\frac{2R}{{{S}_{1}}+{{S}_{2}}}$

B)
$\frac{P}{Q}=\frac{R({{S}_{1}}+{{S}_{2}})}{{{S}_{1}}{{S}_{2}}}$

C)
$\frac{P}{Q}=\frac{R({{S}_{1}}+{{S}_{2}})}{2{{S}_{1}}{{S}_{2}}}$

D)
$\frac{P}{Q}=\frac{R}{{{S}_{1}}+{{S}_{2}}}$

• 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

A)
$-190V$

B)
$-10V$

C)
$10V$

D)
$190V$

• 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

A)
$1.05\times {{10}^{-2}}Wb/{{m}^{2}}$

B)
$1.05\times {{10}^{-5}}Wb/{{m}^{2}}$

C)
$1.05\times {{10}^{-3}}Wb/{{m}^{2}}$

D)
$1.05\times {{10}^{-4}}Wb/{{m}^{2}}$

• question_answer37) The circuit has two oppositely connected ideal diodes in parallel. What is the current flowing in the circuit?     AIEEE  Solved  Paper-2006

A)
1.71 A

B)
2.00 A

C)
2.31 A

D)
1.33A

• question_answer38) In the following, which one of the diodes is reverse biased?     AIEEE  Solved  Paper-2006

A)

B)

C)

D)

• 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

A)

B)

C)

D)

• 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

A)
28.24 MeV

B)
17.28 MeV

C)
1.46 MeV

D)
39.2 MeV

• 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

A)
75 W

B)
40 W

C)
25 W

D)
50 W

• question_answer42) The 'rad' is the correct unit used to report the measurement of     AIEEE  Solved  Paper-2006

A)
the ability of a beam of gamma ray photons to produce ions in a target

B)
the energy delivered by radiation to a target

C)

D)
the rate of decay of a radioactive source

• 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

A)
at the mean position of the platform

B)
for an amplitude of $g/{{\omega }^{2}}$

C)
for an amplitude of${{g}^{2}}/{{\omega }^{2}}$

D)
at the highest position of the platform

• 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

A)
$2m{{l}^{2}}$

B)
$\sqrt{3}\,m{{l}^{2}}$

C)
$3\,m{{l}^{2}}$

D)
$\,m{{l}^{2}}$

• 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

A)
$F(\hat{i}-\hat{j})$

B)
$-F(\hat{i}+\hat{j})$

C)
$F(\hat{i}+\hat{j})$

D)
$-F(\hat{i}-\hat{j})$

• 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

A)
$3/\sqrt{2}$

B)
$\sqrt{2}$

C)
$1/\sqrt{2}$

D)
2

• 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

A)
$\frac{\omega (m+2M)}{m}$

B)
$\frac{\omega (m-2M)}{(m-2M)}$

C)
$\frac{\omega m}{(m+M)}$

D)
$\frac{\omega m}{(m+2M)}$

• 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

A)
$l$

B)
$2l$

C)
zero

D)
$l/2$

• 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

A)
$1/e\,A$

B)
$e\text{ }A$

C)
$0.1A$

D)
$1\,A$

• 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

A)
4 : 1

B)
1 : 2

C)
2 : 1

D)
1 : 4

• 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

A)
${{T}_{f}}=\frac{3}{7}{{T}_{0}}$

B)
${{T}_{f}}=\frac{7}{3}{{T}_{0}}$

C)
${{T}_{f}}=\frac{3}{2}{{T}_{0}}$

D)
${{T}_{f}}=\frac{5}{2}{{T}_{0}}$

• 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

A)
diatomic

B)
triatomic

C)
a mixture of monatomic and diatomic

D)
monatomic

• question_answer53) If the lattice constant of this semiconductor is decreased, then which of the following is correct?     AIEEE  Solved  Paper-2006

A)
All ${{E}_{c}},{{E}_{g}},{{E}_{v}}$ increase

B)
${{E}_{c}}$and$rms$increase, but${{E}_{g}}$decreases

C)
${{E}_{c}}$and ${{E}_{v}}$decrease, but${{E}_{g}}$increases

D)
All ${{E}_{c}},\,{{E}_{g}},\,{{E}_{v}}$ decrease

• 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

A)
$4.58\times {{10}^{-6}}J/{{m}^{3}}$

B)
$6.37\times {{10}^{-9}}J/{{m}^{3}}$

C)
$81.35\times {{10}^{-12}}J/{{m}^{3}}$

D)
$3.3\times {{10}^{-3}}J/{{m}^{3}}$

• 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

A)
0.4 m/s

B)
0.133 m/s

C)
0.1 m/s

D)
0.2 m/s

• question_answer56) $HBr$reacts with$C{{H}_{2}}=CHOC{{H}_{3}}$under anhydrous   conditions   at   room temperature to give     AIEEE  Solved  Paper-2006

A)
$C{{H}_{3}}CHO$and$C{{H}_{3}}Br$

B)
$BrC{{H}_{2}}CHO$and$C{{H}_{3}}OH$

C)
$BrC{{H}_{2}}C{{H}_{2}}OC{{H}_{3}}$

D)
${{H}_{3}}CCHBrOC{{H}_{3}}$

• question_answer57) The IUPAC name of the compound shown below is     AIEEE  Solved  Paper-2006

A)
2-bromo-6-chlorocyclohex-1-ene

B)
6-bromo-2-chlorocyclohexene

C)
3-bromo-1-chlorocyclohexene

D)
1-bromo-3-chlorocyclohexene

• 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

A)
$I<II<III<IV$

B)
$IV<II<III<I$

C)
$IV<III<II<I$

D)
$III<IV<II<I$

• 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

A)
0.02

B)
$3.125\times {{10}^{-2}}$

C)
$1.25\times {{10}^{-2}}$

D)
$2.5\times {{10}^{-2}}$

• question_answer60) According to Bohr's theory, the angular momentum of an electron in 5th orbit is

A)
$25\frac{h}{\pi }$

B)
$1.0\frac{h}{\pi }$

C)
$10\frac{h}{\pi }$

D)
$2.5\frac{h}{\pi }$

• question_answer61) Which of the following molecules/ions does not contain unpaired electrons?     AIEEE  Solved  Paper-2006

A)
$O_{2}^{2-}$

B)
${{B}_{2}}$

C)
$N_{2}^{+}$

D)
${{O}_{2}}$

• question_answer62) Total volume of atoms present in a face-centre cubic unit cell of a metal is (r is atomic radius)     AIEEE  Solved  Paper-2006

A)
$\frac{20}{3}\pi {{r}^{3}}$

B)
$\frac{24}{3}\pi {{r}^{3}}$

C)
$\frac{12}{3}\pi {{r}^{3}}$

D)
$\frac{16}{3}\pi {{r}^{3}}$

• 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

A)
remain unchanged

B)
triple

C)
increases by a factor of 4

D)
double

• question_answer64) Which of the following chemical reactions depicts the oxidizing behavior of${{H}_{2}}S{{O}_{4}}$?     AIEEE  Solved  Paper-2006

A)
$2HI+{{H}_{2}}S{{O}_{4}}\to {{I}_{2}}+S{{O}_{2}}+{{H}_{2}}O$

B)
$Ca{{(OH)}_{2}}+{{H}_{2}}S{{O}_{4}}\to CaS{{O}_{4}}+2{{H}_{2}}O$

C)
$NaCl+{{H}_{2}}S{{O}_{4}}\to NaHS{{O}_{4}}+HCl$

D)
$2PC{{l}_{5}}+{{H}_{2}}S{{O}_{4}}\to 2POC{{l}_{3}}+2HCl+S{{O}_{2}}C{{l}_{2}}$

• question_answer65) The IUPAC name for the complex $[CO(N{{O}_{2}}){{(N{{H}_{3}})}_{5}}]C{{l}_{2}}$is     AIEEE  Solved  Paper-2006

A)
nitrito-N-pentaaminecobalt (III) chloride

B)
nitrito-N-pentaaminecobalt (II) chloride

C)
pentaamine nitrito-N-cobalt (II) chloride

D)
pentaamine nitrito-N-cobalt (III) chloride

• question_answer66) The term anomers of glucose refers to     AIEEE  Solved  Paper-2006

A)
isomers of glucose that differ in configurations at carbons one and four (C-1 and C-4)

B)
a mixture of (D)-glucose and (L)-glucose

C)
enantiomers of glucose

D)
isomers of glucose that differ in configuration at carbon one (C-1)

• 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

A)
Two ${{\beta }^{-}}$

B)
Two ${{\beta }^{-}}$and one ${{\beta }^{+}}$

C)
One ${{\beta }^{-}}$ and one$\gamma$

D)
One ${{\beta }^{+}}$ and one ${{\beta }^{-}}$

• question_answer68) Phenyl magnesium bromide reacts with methanol to give     AIEEE  Solved  Paper-2006

A)
a mixture of anisol and$Mg(OH)Br$

B)
a mixture of benzene and$Mg(OMe)Br$

C)
a mixture of toluene and$Mg(OH)Br$

D)
a mixture of phenol and$Mg(Me)Br$

• 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

A)
$D>C>A<B$

B)
$D>C>B>A$

C)
$A>B>C>D$

D)
$B>D>C>A$

• question_answer70) The pyrimidine bases present in DNA are     AIEEE  Solved  Paper-2006

A)

B)
cytosine and guanine

C)
cytosine and thymine

D)
cytosine and uracil

• question_answer71) Among the following the one that gives positive iodoform test upon reaction with 12 and$NaOH$is     AIEEE  Solved  Paper-2006

A)
$C{{H}_{3}}C{{H}_{2}}CH(OH)C{{H}_{2}}C{{H}_{3}}$

B)
${{C}_{6}}{{H}_{5}}C{{H}_{2}}C{{H}_{2}}OH$

C)

D)
$PhCHOHC{{H}_{3}}$

• question_answer72) The increasing order of stability of the following free radicals is     AIEEE  Solved  Paper-2006

A)
${{(C{{H}_{3}})}_{2}}\overset{\bullet }{\mathop{C}}\,H<{{(C{{H}_{3}})}_{3}}\overset{\bullet }{\mathop{C}}\,<{{({{C}_{6}}{{H}_{5}})}_{2}}\overset{\bullet }{\mathop{C}}\,H$ $<{{({{C}_{6}}{{H}_{5}})}_{3}}\overset{\bullet }{\mathop{C}}\,$

B)
${{({{C}_{6}}{{H}_{5}})}_{3}}\overset{\bullet }{\mathop{C}}\,<{{({{C}_{6}}{{H}_{5}})}_{2}}\overset{\bullet }{\mathop{C}}\,H<{{(C{{H}_{3}})}_{3}}\overset{\bullet }{\mathop{C}}\,$                                                               $<{{(C{{H}_{3}})}_{2}}\overset{\bullet }{\mathop{C}}\,H$

C)
${{({{C}_{6}}{{H}_{5}})}_{2}}\overset{\bullet }{\mathop{C}}\,H<{{({{C}_{6}}{{H}_{5}})}_{3}}\overset{\bullet }{\mathop{C}}\,<{{(C{{H}_{3}})}_{3}}\overset{\bullet }{\mathop{C}}\,$                                                               $<{{(C{{H}_{3}})}_{2}}\overset{\bullet }{\mathop{C}}\,H$

D)
${{(C{{H}_{3}})}_{2}}\overset{\bullet }{\mathop{C}}\,H<{{(C{{H}_{3}})}_{3}}\overset{\bullet }{\mathop{C}}\,<{{({{C}_{6}}{{H}_{5}})}_{3}}\overset{\bullet }{\mathop{C}}\,$                                                           $<{{({{C}_{6}}{{H}_{5}})}_{2}}\overset{\bullet }{\mathop{C}}\,H$

• 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

A)
$19.2\times {{10}^{-2}}m$

B)
$5.76\,\times {{10}^{-2}}\,m$

C)
$1.92\times {{10}^{-2}}m$

D)
$3.84\times {{10}^{-2}}m$

• 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

A)
$\left( \frac{x}{x+1} \right)P$

B)
$\left( \frac{2x}{1-x} \right)P$

C)
$\left( \frac{x}{x-1} \right)P$

D)
$\left( \frac{x}{1-x} \right)P$

• 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

B)
latent heat of vaporisation of methane

C)
the first four ionisation energies of carbon and electron gain enthalpy of hydrogen

D)
the dissociation energy of hydrogen molecule,${{H}_{2}}$

• question_answer76) Among the following mixtures, dipole-dipole as the major interaction, is present in     AIEEE  Solved  Paper-2006

A)
benzene and ethanol

B)
acetonitrile and acetone

C)
$KCl$and water

D)
benzene and carbon tetrachloride

• question_answer77) Fluorobenzene$({{C}_{6}}{{H}_{5}}F)$can be synthesized in the laboratory     AIEEE  Solved  Paper-2006

A)
by heating phenol with HF and KF

B)
from aniline by diazotisation followed by heating the diazonium salt with $HB{{F}_{4}}$

C)
by direct fluorination of benzene with ${{F}_{2}}$ gas

D)
by reacting bromobenzene with NaF solution

• 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$MC{{l}_{4}}$

B)
$MC{{l}_{2}}$is more soluble in anhydrous ethanol than$MC{{l}_{4}}$

C)
$MC{{l}_{2}}$is more ionic than$MC{{l}_{4}}$

D)
$MC{{l}_{2}}$is more easily hydrolysed than$MC{{l}_{4}}$

• question_answer79) Which of the following statement is true?     AIEEE  Solved  Paper-2006

A)
${{H}_{2}}P{{O}_{3}}$is a stronger acid than${{H}_{2}}S{{O}_{3}}$

B)
In aqueous medium HF is a stronger acid than$HCl$

C)
$HCl{{O}_{4}}$is a weaker acid than$HCl{{O}_{3}}$

D)
$HN{{O}_{3}}$is a stronger acid than $HN{{O}_{2}}$

• 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

A)
$\hat{\ }_{{{H}_{2}}O}^{o}$

B)
$\hat{\ }_{KCl}^{o}$

C)
$\hat{\ }_{NaOH}^{o}$

D)
$\hat{\ }_{NaCl}^{o}$

• question_answer81) Which one of the following sets of ions represents a collection of isoelectronic species?     AIEEE  Solved  Paper-2006

A)
${{K}^{+}},C{{l}^{-}},C{{a}^{2+}},S{{c}^{3+}}$

B)
$B{{a}^{2+}},S{{r}^{2+}},{{K}^{+}},{{S}^{2-}}$

C)
${{N}^{3-}},{{O}^{2-}},{{F}^{-}},{{S}^{2-}}$

D)
$L{{i}^{+}},N{{a}^{+}},M{{g}^{2+}},C{{a}^{2+}}$

• 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

A)
II < IV < I < III

B)
IV < I < III < II

C)
IV < I < II < III

D)
I < IV < III < II

• question_answer83) In which of the following molecules/ions, all the bonds are not equal?     AIEEE  Solved  Paper-2006

A)
$S{{F}_{4}}$

B)
$Si{{F}_{4}}$

C)
$Xe{{F}_{4}}$

D)
$B{{F}_{4}}$

• question_answer84) What products are expected from the disproportionation reaction of hypochlorous acid?     AIEEE  Solved  Paper-2006

A)
$HCl{{O}_{3}}$and $C{{l}_{2}}O$

B)
$HCl{{O}_{2}}$and$HCl{{O}_{4}}$

C)
$HCl$and$C{{l}_{2}}O$

D)
$HCl$and$HCl{{O}_{3}}$

• 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

A)
one, tetrahedral

B)
two, tetrahedral

C)
one, square planar

D)
two, square planar

• question_answer86) In$Fe{{(CO)}_{5}},$the$FeC$bond possesses     AIEEE  Solved  Paper-2006

A)
$\pi -$character only

B)
both$\sigma$and$\pi$characters

C)
ionic character only

D)
$\sigma -$character only

• question_answer87) The increasing order of the first ionization enthalpies of the elements B, P, S and p (lowest first) is     AIEEE  Solved  Paper-2006

A)
$F<S<P<B$

B)
$P<S<B<F$

C)
$B<P<S<F$

D)
$B<S<P<F$

• 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)
${{({{T}_{f}})}_{irrev}}>{{({{T}_{f}})}_{rev}}$

B)
${{T}_{f}}>{{T}_{i}}$for reversible process but${{T}_{f}}={{T}_{i}}$for irreversible process

C)
${{({{T}_{f}})}_{rev}}={{({{T}_{i}})}_{irrev}}$

D)
${{T}_{f}}={{T}_{i}}$for both reversible and irreversible processes

• question_answer89) In Langmuir's model of adsorption of a gas on a solid surface     AIEEE  Solved  Paper-2006

A)
the rate of dissociation of adsorbed molecules from the surface does not depend on the surface covered

B)
the adsorption at a single site on the surface may involve multiple molecules at the same time

C)
the mass of gas striking a given area of surface is proportional to the pressure of the gas

D)
the mass of gas striking a given area of surface is independent of the pressure of the gas

• 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

B)
the energy below which colliding molecules will not react

C)
the total energy of the reacting molecules at a temperature, T

D)
the fraction of molecules with energy greater than the activation energy of the reaction

• question_answer91) The structure of the major product formed in the following reaction is     AIEEE  Solved  Paper-2006

A)

B)

C)

D)

• question_answer92) Reaction of trans-2-phenyl-1- bromocyclopentane on reaction with alcoholic $KOH$produces     AIEEE  Solved  Paper-2006

A)
4-phenylcyclopentene

B)
2-phenylcyclopentene

C)
1-phenylcyclopentene

D)
3-phenylcyclopentene

• question_answer93) Increasing order of stability among the three main conformations (i.e.. Eclipse, Ami, Gauche) of 2-fluoroethanol is     AIEEE  Solved  Paper-2006

A)
Eclipse, Gauche, Anti

B)
Gauche, Eclipse, Anti

C)
Eclipse, Anti, Gauche

D)
Anti, Gauche, Eclipse

• question_answer94) The structure of the compound that gives a tribromo derivative on treatment with bromine water is     AIEEE  Solved  Paper-2006

A)

B)

C)

D)

• 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

A)
increasing$bp-bp$repulsion

B)
increasing p-orbital character in$s{{p}^{3}}$

C)
decreasing $lp-bp$ repulsion

D)
decreasing electronegativity

• question_answer96)  The alkene formed as a major product in the above elimination reaction is     AIEEE  Solved  Paper-2006

A)

B)
$C{{H}_{2}}=C{{H}_{2}}$

C)

D)

• 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

A)
2.84

B)
4.90

C)
0

D)
1.73

• 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

A)
416

B)
$2.40\times {{10}^{-3}}$

C)
$9.8\times {{10}^{-2}}$

D)
$4.9\times {{10}^{-2}}$

• 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

B)
In both the alkali metals and the halogens, the chemical reactivity decreases with increase in atomic number down the group

C)
Chemical reactivity increases with increase in atomic number down the group in both the alkali metals and halogens

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

A)
$\text{ }8.12$

B)
$+\text{ }8.612$

C)
$-37.83$

D)
$-16.13$

• 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

A)
1

B)
0

C)
3

D)
2

• question_answer102) Lanthanoid contraction is caused due to     AIEEE  Solved  Paper-2006

A)
the appreciable shielding on outer electrons by$4f$electrons from the nuclear charge

B)
the appreciable shielding on outer electrons by$5d$electrons from the nuclear charge

C)
the same effective nuclear charge from$Ce$to$Lu$

D)
the imperfect shielding on outer electrons by$4f$electrons from the nuclear charge

• 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

A)
$124\times {{10}^{-4}}S\,{{m}^{2}}\text{ }mo{{l}^{-1}}$

B)
$1240\times {{10}^{-4}}S\,{{m}^{2}}mo{{l}^{-1}}$

C)
$1.24\times {{10}^{-4}}S\,{{m}^{2}}mo{{l}^{-1}}$

D)
$12.4\times {{10}^{-4}}S\,{{m}^{2}}mo{{l}^{-1}}$

• question_answer104) The ionic mobility of alkali metal ions in aqueous solution is maximum for     AIEEE  Solved  Paper-2006

A)
${{K}^{+}}$

B)
$R{{b}^{+}}$

C)
$L{{i}^{+}}$

D)
$N{{a}^{+}}$

• 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

A)
$1.14\text{ }mol\text{ }k{{g}^{-1}}$

B)
$3.28\text{ }mol\text{ }k{{g}^{-1}}$

C)
$2.28\text{ }mol\text{ }k{{g}^{-1}}$

D)
$0.44\text{ }mol\text{ }k{{g}^{-1}}$

• 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

A)
$-\text{ }14.6\text{ }kJ\text{ }mo{{l}^{-1}}$

B)
$-\text{ }16.8\text{ }kJ\text{ }mo{{l}^{-1}}$

C)
$+\text{ }16.8\text{ }kJ\text{ }mo{{l}^{-1}}$

D)
$+\text{ }244.8\text{ }kJ\text{ }mo{{l}^{-1}}$

• 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

A)
six

B)
three

C)
one

D)
two

• question_answer108)  The electrophile involved in the above reaction is     AIEEE  Solved  Paper-2006

A)
dichloromethyl cation$(\overset{\oplus }{\mathop{CH}}\,C{{l}_{2}})$

B)
dichlorocarbene$(:CC{{l}_{2}})$

C)
trichloromethyl anion$(\overset{-}{\mathop{C}}\,C{{l}_{3}})$

D)
forrnyl cation$(\overset{\oplus }{\mathop{C}}\,HO)$

• 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

A)
759.00 torr

B)
7.60 torr

C)
76.00 torr

D)
752.40 torr

• 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

A)
$-1238.78\text{ }J\text{ }mo{{l}^{-1}}$

B)
$1238.78\text{ }J\text{ }mo{{l}^{-1}}$

C)
$-\text{ }2477.57\text{ }J\text{ }mo{{l}^{-1}}$

D)
$2477.57\text{ }J\text{ }mo{{l}^{-1}}$

• 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

A)
3

B)
0

C)
1

D)
2

• question_answer112) The    value    of    the    integral$\int_{3}^{6}{\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}}}dx$is     AIEEE  Solved  Paper-2006

A)
$\frac{3}{2}$

B)
2

C)
1

D)
$\frac{1}{2}$

• 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

A)
reflexive, symmetric and not transitive

B)
reflexive, symmetric and transitive

C)
reflexive, not symmetric and transitive

D)
not reflexive, symmetric and transitive

• 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

A)
6

B)
1

C)
2

D)
4

• 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

A)
$AB=BA$

B)
Either of A or B is a zero matrix

C)
Either of A or B is an identity matrix

D)
$A=B$

• question_answer116) The value of$\sum\limits_{k=1}^{10}{\left( \sin \frac{2k\pi }{11}+i\cos \frac{2k\pi }{11} \right)}$is     AIEEE  Solved  Paper-2006

A)
1

B)
-1

C)
$-i$

D)
$i$

• 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

B)
perpendicular

C)
parallel

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

A)
$m>3$

B)
$-1<m<3$

C)
$1<m<4$

D)
$-2<m<0$

• 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

A)
$\frac{(AB)(AC)}{AB+AC}$

B)
$\frac{1}{AB}+\frac{1}{AC}$

C)
$\frac{1}{AD}$

D)
$\frac{A{{B}^{2}}+A{{C}^{2}}}{(A{{B}^{2}}){{(AC)}^{2}}}$

• 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

A)
$\frac{9}{4}$

B)
$\frac{4}{9}$

C)
$\frac{2}{3}$

D)
1

• question_answer121) $\int_{-3\pi /2}^{-\pi /2}{[{{(x+\pi )}^{3}}+{{\cos }^{2}}(x+3\pi )]}dx$is equal to     AIEEE  Solved  Paper-2006

A)
$\left( \frac{{{\pi }^{4}}}{32} \right)+\left( \frac{\pi }{2} \right)$

B)
$\frac{\pi }{2}$

C)
$\left( \frac{\pi }{4} \right)-1$

D)
$\frac{{{\pi }^{4}}}{32}$

• question_answer122) In an ellipse, the distances between its foci is 6 and minor axis is 8. Then. Its eccentricity is     AIEEE  Solved  Paper-2006

A)
$\frac{1}{2}$

B)
$\frac{4}{5}$

C)
$\frac{1}{\sqrt{5}}$

D)
$\frac{3}{5}$

• 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

A)
$xy=\frac{3}{4}$

B)
$xy=\frac{35}{16}$

C)
$xy=\frac{64}{105}$

D)
$xy=\frac{105}{64}$

• 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

A)
$3x-4y+7=0$

B)
$4x+3y=24$

C)
$3x+4y=25$

D)
$x+y=7$

• 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

A)
-2 and -1

B)
-2 and 1

C)
2 and -1

D)
2 and 1

• question_answer126) $\int_{0}^{\pi }{x\,f\,(\sin \,x)\,dx}$ is equal to     AIEEE  Solved  Paper-2006

A)
$\pi \int_{0}^{\pi }{f(\sin x)}dx$

B)
$\frac{\pi }{2}\int_{0}^{\pi /2}{f(\sin x)}dx$

C)
$\pi \int_{0}^{\pi /2}{f(\cos x)}dx$

D)
$\pi \int_{0}^{\pi /2}{f(\cos x)}dx$

• question_answer127) The two lines$x=ay+b,z=cy+d$and$x=a'y+b',z=c'y+d'$are perpendicular to each other, if     AIEEE  Solved  Paper-2006

A)
$aa'+cc'=1$

B)
$\frac{a}{a'}\,+\frac{c}{c'}\,=-1$

C)
$\frac{a}{a'}\,+\frac{c}{c'}\,=1$

D)
$aa'+cc'=-1$

• 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

A)
6210

B)
385

C)
1110

D)
5040

• 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

A)
$\frac{{{a}^{n}}-{{b}^{n}}}{b-a}$

B)
$\frac{{{a}^{n+1}}-{{b}^{n+1}}}{b-a}$

C)
$\frac{{{b}^{n+1}}-{{a}^{n+1}}}{b-a}$

D)
$\frac{{{b}^{n}}-{{a}^{n}}}{b-a}$

• 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

A)
(35, 20)

B)
(45, 35)

C)
(35, 45)

D)
(20, 45)

• 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

A)
$120{}^\circ$

B)
$45{}^\circ$

C)
$60{}^\circ$

D)
$90{}^\circ$

• 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

A)
$\frac{5}{6}$

B)
$\frac{6}{55}$

C)
$\frac{6}{{{e}^{5}}}$

D)
$\frac{6}{{{5}^{e}}}$

• 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

A)
900m

B)
320 m

C)
680 m

D)
720 m

• question_answer134) The set of points, where $f(x)=\frac{x}{1+|x|}$is differentiable, is     AIEEE  Solved  Paper-2006

A)
$(-\infty ,-1)\cup (-1,\infty )$

B)
$(-\infty ,\infty )$

C)
$(0,\infty )$

D)
$(-\infty ,0\cup (0,\infty )$

• question_answer135) Let$A=\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} \right]$and$B=\left[ \begin{matrix} a & 0 \\ 0 & b \\ \end{matrix} \right],a,b,\in N$. Then,     AIEEE  Solved  Paper-2006

A)
there exist more than one but finite number of B's such that$AB=BA$

B)
there exists exactly one B such that$AB=BA$

C)
there exist infinitely many 8's such that$AB=BA$

D)
there cannot exist any B such that$AB=BA$

• 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

A)
$\frac{7}{2}$

B)
$\frac{2}{7}$

C)
$\frac{11}{41}$

D)
$\frac{41}{11}$

• question_answer137) The function$f(x)=\frac{x}{2}+\frac{2}{x}$has a local minimum at     AIEEE  Solved  Paper-2006

A)
$x=-2$

B)
$x=0$

C)
$x=1$

D)
$x=2$

• question_answer138) Angle between the tangents to the curve$y={{x}^{2}}-5x+6$at the points (2, 0) and (3, 0) is     AIEEE  Solved  Paper-2006

A)
$\pi /2$

B)
$\pi /6$

C)
$\pi /4$

D)
$\pi /3$

• question_answer139) If $x$is real, the maximum value of$\frac{3{{x}^{2}}+9x+17}{3{{x}^{2}}+9x+7}$is     AIEEE  Solved  Paper-2006

A)
41

B)
1

C)
17/7

D)
1/4

• 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

A)
$\sqrt{\frac{{{x}^{3}}}{8}}$

B)
$\frac{1}{2}{{x}^{2}}$

C)
$\pi {{x}^{2}}$

D)
$\frac{3}{2}{{x}^{2}}$

• 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

A)
$(3,\infty )$

B)
$\left( \frac{1}{2},3 \right)$

C)
$\left( -3,-\frac{1}{2} \right)$

D)
$\left( 0,\frac{1}{2} \right)$

• question_answer142) If${{x}^{m}}{{y}^{n}}={{(x+y)}^{m+n}},$then$\frac{dy}{dx}$is       AIEEE  Solved  Paper-2006

A)
$\frac{x+y}{xy}$

B)
$xy$

C)
$\frac{x}{y}$

D)
$\frac{y}{x}$

• 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

A)
${{x}^{2}}+{{y}^{2}}+2x-2y-62=0$

B)
${{x}^{2}}+{{y}^{2}}-2x+2y-62=0$

C)
${{x}^{2}}+{{y}^{2}}-2x+2y-47=0$

D)
${{x}^{2}}+{{y}^{2}}+2x-2y-47=0$

• question_answer144) The image of the point (-1, 3, 4) in the plane $x-2y=0$is       AIEEE  Solved  Paper-2006

A)
(15, 11, 4)

B)
$\left( -\frac{17}{3},-\frac{19}{3},1 \right)$

C)
(8, 4, 4)

D)
$\left( -\frac{17}{3},-\frac{19}{3},4 \right)$

• 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

A)
first order and second degree

B)
first order and first degree

C)
second order and first degree

D)
second order and second degree

• 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

A)
$[a]f(a)-\{f(1)+f(2)+....+f([a])\}$

B)
$[a]f([a])-\{f(1)+f(2)+....+f(a)\}$

C)
$af([a])-\{f(1)+f(2)+....+f(a)\}$

D)
$af(a)-\{f(1)+f(2)+....+f([a])\}$

• 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

A)
${{x}^{2}}+{{y}^{2}}=1$

B)
${{x}^{2}}+{{y}^{2}}=\frac{27}{4}$

C)
${{x}^{2}}+{{y}^{2}}=\frac{9}{4}$

D)
${{x}^{2}}+{{y}^{2}}=\frac{3}{2}$

• 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

A)
$(n-1)({{a}_{1}}-{{a}_{n}})$

B)
$n{{a}_{1}}{{a}_{n}}$

C)
$(n-1){{a}_{1}}{{a}_{n}}$

D)
$n({{a}_{1}}-{{a}_{n}})$

• 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

A)
54

B)
6

C)
12

D)
18

• question_answer150) If$0<x<\pi$and $\cos x+\sin x=\frac{1}{2},$then $tan\text{ }x$is       AIEEE  Solved  Paper-2006

A)
$\frac{(4-\sqrt{7})}{3}$

B)
$-\frac{(4+\sqrt{7})}{3}$

C)
$\frac{(1+\sqrt{7})}{4}$

D)
$\frac{(1-\sqrt{7})}{4}$