List of top Questions asked in AIEEE- 2011

A wooden cube (density of wood $'d'$) of side $'\ell'$ floats in a liquid of density $'\rho'$ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period $'T'$. Then, $'T'$ is equal to :
Identify the compound that exhibits tautomerism.
There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points. then :
For each natural number $n, (n + 1)^7 - n^7 -1$ is divisible by 7. For each natural number $n, n^7 - n$ is divisible by 7.
The correct order of acid strength of the following compounds: 
(A) Phenol\(\quad\) 
(B) p-Cresol \(\quad\)
(C) m-Nitrophenol \(\quad\)
(D) p-Nitrophenol is :
The change in the optical rotation of freshly prepared solution of glucose is known as
The frequency of light emitted for the transition n = 4 to n = 2 of $He^+$ isequalto the transition in H atom corresponding to which of the following?
Two positive charges of magnitude $'q'$ are placed at the ends of a side (side 1) of a square of side $'2a'$. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge $Q$ moves from the middle of side $1$ to the centre of square, its kinetic energy at the centre of square is :
The specific heat capacity of a metal at low temperature (T) is given as : $C_{p} \left(kjK^{-1} kg^{-1}\right) = 32 \left(\frac{T}{400}\right)^{3}$ A 100 gram vessel of this metal is to be cooled from $20^{\circ}K$ to $4^{\circ}K$ by a special refrigerator operating at room temperature $\left(27^{\circ}C\right)$. The amount of work required to cool the vessel is :
An aluminium sphere of 20 cm diameter is heated from 0$^{\circ}$C to 100$^{\circ}$C. Its volume changes by (given that coefficient of linear expansion for aluminium $\alpha_{AI} = 23 ? 10^{-6}/^{\circ}C)$
A thin circular disk of radius $R$ is uniformly charged with density $\sigma$ > 0 per unit area. The disk rotates about its axis with a uniform angular speed $\omega$. The magnetic moment of the disk is :
If a spring of stiffness $'k'$ is cut into two parts $'A'$ and $'B'$ of length $\ell_A : \ell_B = 2 : 3$, then the stiffness of spring $'A'$ is given by :
The non aromatic compound among the following is :
A reactant (A) forms two products : $ {A ->[k_1] B,} $ Activation Energy $Ea_1$ $ {A ->[k_2] C,}$ Activation Energy $Ea_2$ If $Ea_2 = 2 Ea_1$, then $k_1$ and $k_2$ are related as :
Sachin and Rahul attempted to solve a quadratic equaiton. Sachin made a mistake in writing down the constant term and ended up in roots (4, 3). Rahul made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of equation are :
A 5% solution of cane sugar (molar mass 342) is isotonic with 1% of a solution of an unknown solute. The molar mass of unknown solute in g/mol is:
The molality of a urea solution in which 0.0100 g of urea, $[(NH_2)_2CO]$ is added to 0.3000 $dm^3$ of water at STP is:
The number of values of k for which the linear equations $4x + ky + 2z = 0$ , $kx + 4y + z = 0$ and $2x + 2y + z = 0$ possess a non-zero solution is
An acid HA ionises as $HA {\rightleftharpoons} H^{+} + A^{-}$ The pH of 1.0 M solution is 5. Its dissociation constant would be:
A vessel at 1000 K contains $CO_2$ with a pressure of 0.5 atm. Some of the $CO_2$ is converted into CO on the addition of graphite. It the total pressure at equilibrium is 0.8 atm, the value of K is
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
A particle of mass $m$ is projected with a velocity $\upsilon$ making an angle of 30$^{\circ}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is :
Identify the incorrect statement from the following:
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 $0.4 ms ^{-1}$. The diameter of the water stream at a distance $2 \times 10^{-1} m$ below the tap is close to
The reduction potential of hydrogen half-cell will be negative if :