Solved papers for JEE Main & Advanced AIEEE Solved Paper-2011
done AIEEE Solved Paper-2011 Total Questions - 90
question_answer1) A carnot engine operation between temperatrues \[{{T}_{1}}\] and \[{{T}_{2}}\] has efficiency \[\frac{1}{6}\]. When \[{{T}_{2}}\] is lowered by 62 K, its efficiency increases to\[\frac{1}{3}\]. Then \[{{T}_{1}}\] and \[{{T}_{2}}\] are respectively
AIEEE Solved Paper-2011
question_answer2) A pulley of radius 2 m is rotated about its axis by a force \[F=(20\,t-5{{t}^{2}})\] newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg \[{{m}^{2}}\], the number of rotations made by the pulley before its direction of motion if reversed is
AIEEE Solved Paper-2011
question_answer3) Three perfect gases at absolute temperatures \[{{T}_{1}},{{T}_{2}}\] and \[{{T}_{3}}\] are mixed. The masses of molecules are \[{{m}_{1}},{{m}_{2}}\] and \[{{m}_{3}}\] and the number of molecules are \[{{n}_{1}},{{n}_{2}}\] and \[{{n}_{3}}\] respectively. Assuming no loss of energy, the final temperature of the mixture is
AIEEE Solved Paper-2011
question_answer4) A boat is moving due east in a region where the earth's magnetic field is \[5.0\times {{10}^{-5}}N{{A}^{-1}}\] due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is \[1.50\,m{{s}^{-1}}\], the magnitude of the induced emf in the wire of aerial is
AIEEE Solved Paper-2011
question_answer5) A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect the angular speed of the disc
AIEEE Solved Paper-2011
question_answer6) Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance \[d(d<<l)\] apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance \[x\] between them
AIEEE Solved Paper-2011
question_answer7) 100 g of water is heated from \[{{30}^{o}}C\] to \[{{50}^{o}}C\]. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K)
AIEEE Solved Paper-2011
question_answer8) The half life of a radioactive substance is 20 minutes. The approximate time interval \[({{t}_{2}}-{{t}_{1}})\] between the time \[{{t}_{2}}\] when \[\frac{2}{3}\] of its has decayed and time \[{{t}_{1}}\] when \[\frac{1}{3}\] of its had decayed is
AIEEE Solved Paper-2011
question_answer10) The electrostatic potential inside a charged spherical ball is given by \[\phi =an{{r}^{2}}+b\] where r is the distance from the centre; a, b are constants. Then the charge density inside the ball is
AIEEE Solved Paper-2011
question_answer11) Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution \[=0.03\,\,N{{m}^{-1}}\])
AIEEE Solved Paper-2011
question_answer12) A resistor 'R' and \[2\mu F\] capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed. (\[{{\log }_{10}}2.5=0.4\])
AIEEE Solved Paper-2011
question_answer13) A current I flows in an infinitely long wire with corss section in the form of a semi-circular ring of raidus R. The magnitude of the magnetic induction along its axis is
AIEEE Solved Paper-2011
question_answer14) An object, moving with a speed of \[6.25\,m/s\], is decelerated at a rate given by \[\frac{dv}{dt}=-2.5\sqrt{v}\]where v is the instantaneous speed. The time taken by the object, to come to rest, would be
AIEEE Solved Paper-2011
question_answer15) Direction: The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the covex surface of a plane-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (coNvex) surface and the bottom (glass plate) surface of the film. Statement-1: When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of \[\pi \]. Statement-2: The centre of the interference pattern is dark.
AIEEE Solved Paper-2011
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is false
doneclear
C)
Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of Statement-1
doneclear
D)
Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
question_answer16) Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is
AIEEE Solved Paper-2011
question_answer17) This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals. Statement-2: The state of ionosphere varies from hour to hour, day to day and season to season.
AIEEE Solved Paper-2011
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is false
doneclear
C)
Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of Statement-1
doneclear
D)
Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
question_answer18) A fully charged capacitor C with initial charge \[{{q}_{0}}\] is connected to a coil of self inductance L at \[t=0\]. The time at which the energy is stored equally between the electric and the magnetic fields is
AIEEE Solved Paper-2011
question_answer19) This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: A metallic surface is irradiated by a monochromatic light of frequency \[v>{{v}_{0}}\] (the threshold frequency). The maximum kinetic energy and the stopping potential are \[{{K}_{\max }}\] and \[{{V}_{0}}\] respectively. If the frequency incident on the surface is doubled, both the\[{{K}_{\max }}\] and \[{{V}_{0}}\] are also doubled. Statement-2: The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.
AIEEE Solved Paper-2011
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is false
doneclear
C)
Statement-1 is true, Statement-2 is true and Statement-2 is a correct explanation for Statement-1
doneclear
D)
Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
question_answer20) Water is flowing continuously from a tap having an internal diameter \[8\times {{10}^{-3}}m\]. The water velocity as it leaves the tap is \[0.4\,m{{s}^{-1}}\]. The diameter of the water stream at a distance \[2\times {{10}^{-1}}m\] below the tap is close to
AIEEE Solved Paper-2011
question_answer21) A mass M, attached to a horizontal spring, executes S.H.M. with amplitude \[{{A}_{1}}\]. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude \[{{A}_{2}}\]. The ratio of\[\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right)\]is
AIEEE Solved Paper-2011
question_answer22) Two particles are executing simple harmonic motion of the same amplitude A and frequency \[\omega \] along the x-axis. Their mean position is separated by distance \[{{X}_{0}}({{X}_{0}}>A)\]. If the maximum separation between them is \[({{X}_{0}}+A)\], the phase difference between their motion is
AIEEE Solved Paper-2011
question_answer24) A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is
AIEEE Solved Paper-2011
question_answer25) A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats\[\gamma \]. It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
AIEEE Solved Paper-2011
question_answer26) A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading: 0 mm Circular scale reading: 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is
AIEEE Solved Paper-2011
question_answer27) A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is
AIEEE Solved Paper-2011
question_answer28) The transverse displacement \[y(x,t)\] of a wave on a string is given by \[y(x,t)={{e}^{-\left( a{{x}^{2}}+b{{t}^{2}}+2\sqrt{ab}xt \right)}}\] This represents a
AIEEE Solved Paper-2011
A)
Standing wave of frequency \[\frac{1}{\sqrt{b}}\]
doneclear
B)
Wave moving in \[+x\] direction with speed \[\sqrt{\frac{a}{b}}\]
doneclear
C)
Wave moving in \[-x\] direction with speed \[\sqrt{\frac{b}{a}}\]
question_answer29) A car is fitted with a convex side-view mirror of focal length 20 cm. A second car \[2.5\] m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is
AIEEE Solved Paper-2011
question_answer30) Let the \[x-z\] plane be the boundary between two transparent media. Medium 1 in \[z\ge 0\] has a refractive index of 2 and medium 2 with \[z>0\] has a refractive index of 3. A ray of light in medium 1 given by the vector \[\vec{A}=6\sqrt{3}\hat{i}+8\sqrt{3}\hat{j}-10\hat{k}\] is incident on the plane of separation. The angle of refraction in medium 2 is
AIEEE Solved Paper-2011
question_answer32) In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is
AIEEE Solved Paper-2011
question_answer35) The rate of a chemical reaction doubles for every \[{{10}^{o}}C\] rise of temperature. If the temperature is raised by \[{{50}^{o}}C\], the rate of the reaction increases by about
AIEEE Solved Paper-2011
question_answer37) The hybridisation of orbitals of N atom in \[N{{O}_{3}}^{-},N{{O}_{2}}^{+}\] and \[N{{H}_{4}}^{+}\] are respectively
AIEEE Solved Paper-2011
question_answer38) Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at \[-{{6}^{o}}C\] will be: (\[{{K}_{f}}\] for water \[=1.86\] K \[kgmo{{l}^{-1}}\] and molar mass of ethylene glycol \[=62kgmo{{l}^{-1}}\])
AIEEE Solved Paper-2011
question_answer41) Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of :
AIEEE Solved Paper-2011
question_answer42) The degree of dissociation \[(\alpha )\] of a weak electrolyte, \[{{A}_{x}}{{B}_{y}}\] is related to van't Hoff factor (i) by the expression:
AIEEE Solved Paper-2011
question_answer43) A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :
AIEEE Solved Paper-2011
question_answer45) The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of \[10\,d{{m}^{3}}\] at \[{{27}^{o}}C\] is to a volume of \[100\,d{{m}^{3}}\]
AIEEE Solved Paper-2011
question_answer47) Trichloroacetaldehyde was subject to Cannizzaro's reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is :
AIEEE Solved Paper-2011
question_answer49) Phenol is heated with a solution of mixture of KBr and \[KBr{{O}_{3}}\]. The major product obtained in the above reaction is:
AIEEE Solved Paper-2011
question_answer54) A vessel at 1000 K contains \[C{{O}_{2}}\] with a pressure of \[0.5\] atm. Some of the \[C{{O}_{2}}\] is converted into CO on the addition of graphite. If the total pressure at equilibrium is \[0.8\] atm, the value of K is.
AIEEE Solved Paper-2011
question_answer56) Which one of the following orders presents the correct sequence of the increasing basic nature of the given oxides?
AIEEE Solved Paper-2011
question_answer57) A 5.2 molal aqueous solution of methyl alcohol, \[C{{H}_{3}}OH\] is supplied. What is the mole fraction of methyl alcohol in the solution?
AIEEE Solved Paper-2011
question_answer61) Consider 5 independent Bernoulli?s trials each with probability of success \[\rho \]. If the probability of at least one failure is greater than or equal to \[\frac{31}{32}\], then \[\rho \] lies in the interval.
AIEEE Solved Paper-2011
question_answer64) Let R be the set of real numbers. Statement-1: \[A=\{(x,y)\in R\times R:y-x\] is an integer} is an equivalence relation on R. Statement-2: \[B=\{(x,y)\in R\times R:x=\alpha y\] for some rational number ?} is an equivalence relation on R.
AIEEE Solved Paper-2011
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
doneclear
C)
Statement-1 is true, Statement-2 is true Statement-2 is not a correct explanation for Statement-1
question_answer65) Let \[\alpha ,\beta \] be real and z be a complex number. If \[{{z}^{2}}+\alpha z+\beta =0\] has two distinct roots on the line Re \[z=1\], then it is necessary that.
AIEEE Solved Paper-2011
question_answer67) The number of values of k for which the linear equations \[4x+ky+2z=0\] \[kx+4y+z=0\] \[\left. 2x+2y+z=0 \right|\] possess a non-zero solution is.
AIEEE Solved Paper-2011
question_answer68) Statement-1: The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line : \[\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\]. Statement-2: The line: \[\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\] bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).
AIEEE Solved Paper-2011
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
doneclear
C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
question_answer69) Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement ?Suman is brilliant and dishonest if and only if Suman is rich? can be expressed as.
AIEEE Solved Paper-2011
question_answer70) The lines \[{{L}_{1}}:y-x=0\] and \[{{L}_{2}}:2x+y=0\] intersect the line \[{{L}_{3}}:y+2=0\] at P and Q respectively. The bisector of the acute angle between \[{{L}_{1}}\] and \[{{L}_{2}}\] intersects \[{{L}_{3}}\] at R. Statements 1 : The ratio PR : RQ equals \[2\sqrt{2}:\sqrt{5}\]. Statement 2 : In any traingle, bisector of an angle divides the triangle into two similar triangles.
AIEEE Solved Paper-2011
A)
Statement-1 is true, Statement-2 is false
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1
doneclear
C)
Statement-1 is true, Statement-2 is true; Statement-2 is the not the correct explanation of Statement-1
question_answer71) A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after.
AIEEE Solved Paper-2011
question_answer72) Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity \[(-3,1)\]\[\sqrt{\frac{2}{5}}\] is.
AIEEE Solved Paper-2011
question_answer75) If the angle between the line \[x=\frac{y-1}{2}=\frac{z-3}{\lambda }\]and the plane \[x+2y+3z=4\] is \[{{\cos }^{-1}}\left( \sqrt{\frac{5}{14}} \right)\], then \[\lambda \] equals.
AIEEE Solved Paper-2011
question_answer78) If the mean deviation about the median of the numbers \[a,2a,\,........\,,50a\] is 50, then \[\left| a \right|\] equals.
AIEEE Solved Paper-2011
question_answer79) If \[\vec{a}=\frac{1}{\sqrt{10}}(3\hat{i}+\hat{k})\] and \[b=\frac{1}{7}(2\hat{i}+3\hat{j}-6\hat{k})\], then the value of \[(2\vec{a}-\vec{b}.[(\vec{a}\times \vec{b})\times (\vec{a}+2\vec{b})]\]is.
AIEEE Solved Paper-2011
question_answer80) The values of p and q for which the function
\[f(x)=\left\{ \begin{align}
& \frac{\sin (p+1)x+sinx}{x},\,\,\,\,\,\,x
& q,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\
& \frac{\sqrt{x+{{x}^{2}}}-\sqrt{x}}{{{x}^{3/2}}},\,\,\,\,\,\,\,x>0 \\
\end{align} \right.\]
is continuous for all \[x\] in R, are.
AIEEE Solved Paper-2011
question_answer82) Let I be the purchase value of an equipment and \[V(t)\] be the value after it has been used for t years. The value \[V(t)\] depreciates at a rate given by differential equation \[\frac{dV(t)}{dt}=-k(T-t)\], where \[k>0\] is a constant and T is the total life in years of the equipment. Then the scrap value \[V(T)\] of the equipment is.
AIEEE Solved Paper-2011
question_answer83) If C and D are two events such that \[C\subset D\] and \[P(D)\ne 0\], then the correct statement among the following is.
AIEEE Solved Paper-2011
question_answer84) Let A and B be two symmetric matrices of order 3. Statement-1: A(BA) and (AB)A are symmetric matrices. Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.
AIEEE Solved Paper-2011
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
doneclear
C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
question_answer86) Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is \[^{9}{{C}_{3}}\]. Statement-2: The number of ways of choosing any 3 places from 9 different places is \[^{9}{{C}_{3}}\].
AIEEE Solved Paper-2011
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1
doneclear
C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
question_answer90) The vectors \[\vec{a}\] and \[\vec{b}\] are not perpendicular and \[\vec{c}\] and \[\vec{d}\] are two vectors satisfying \[\vec{b}\times \vec{c}=\vec{b}\times \vec{d}\]and \[\vec{a}.\,\vec{d}=0\]. Then the vector \[\vec{d}\] is equal to
AIEEE Solved Paper-2011