List of top Questions asked in AIEEE- 2009

In a binomial distribution $B\left(n. p=\frac{1}{4}\right)$, if the probability of at least one success is greater than or equal to $\frac{9}{10}$, then n is greater than

If P and Q are the points of intersection of the circles $x^2 + y^2 + 3x + 7y + 2p - 5 = 0$ and $x^2 + y^2 + 2x + 2y - p^2 = 0$ , then there is a circle passing through $P, Q$ and $(1, 1)$ for

The projections of a vector on the three coordinate axis are $6, - 3, 2$ respectively. The direction cosines of the vector are

If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then

If $\vec{u}, \vec{v}, \vec{w}$ are non-coplanar vectors and $p, q$ are real numbers, then the equality $\left[3\vec{u}\, p\vec{v}\,p\vec{w}\right]-\left[p\vec{v}\,\vec{w}\,q\vec{u}\right]-\left[2\vec{w}\,q\vec{v}\,q\vec{u}\right]=0$ holds for

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is

Calculate the wavelength (in nanometer) associated with a proton moving at $1.0 \times 10^3ms^{-1}$ (Mass of proton $= 1.67 \times 10^{-27}\, kg$ and $h = 6.63 \times 10^{-34}\, Js$ ) :

A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of

A motor cycle starts from rest and accelerates along a straight path at $2\, m/s^2$. At the starting point of the motor cycle there is a stationary electric sire. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest? (speed of sound $= 330 \,ms^{-1}$).

A mixture of light, consisting of wavelength $590\, nm$ and an unknown wavelength, illuminates Young?s double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the $4^{th}$ bright fringe of the unknown light. From this data, the wavelength of the unknown light is

On the basis of the following thermochemical data $: \left(\Delta f G^{o}H^{+}_{\left(aq\right)}=0\right)$ $H_{2}O\left(\ell\right) \rightarrow H^{+}\left(aq\right)+OH^{-}\left(aq\right); \Delta H=57.32kj$ $H_{2}\left(g\right)+\frac{1}{2}O_{2}\left(g\right) \rightarrow H_{2}O\left(\ell\right); \Delta H=-286.20kj$ The value of enthalpy of formation of $OH^-$ ion at $25^o\,C$ is :

Copper crystallizes in fcc with a unit cell length of 361 pm. What is the radius of copper atom ?

Which of the following has an optical isomer ?

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is$CH_{3}OH\left(\ell\right)+\frac{3}{2}O_{2}\left(g\right) \rightarrow CO_{2}\left(g\right)+2H_{2}O\left(\ell\right)$ At $298K$ standard Gibb?s energies of formation for $CH_{3}OH\left(\ell\right), H_{2}O\left(\ell\right)$ and $CO_{2}\left(g\right)$ are $-166.2, -237.2$ and $-394.4\, kJ\, mol^{-1}$ respectively. If standard enthalpy of combustion of methanol is $-726kJ \,mol^{-1}$ , efficiency of the fuel cell will be

Given $: E^{o}_{Fe^{3+}/Fe}=-0.036V, E^{o}_{Fe^{2+}/Fe}=-0.439V$. The value of standard electrode potential for the change, $Fe^{3+}_{\left(aq\right)}+e^{-} \rightarrow Fe^{2+}\left(aq\right)$ will be :

In an atom, an electron is moving with a speed of $600\,m/s$ with an accuracy of $0.005\%.$ Certainity with which the position of the electron can be located is ($h = 6.6 ? 10^{-34} kg\, m^2\,s^{-1}$ , mass of electron, $e_m = 9.1?10^{- kg}$ )

A liquid was mixed with ethanol and a drop of concentrated $H_2SO_4$ was added. A compound with a fruity smell was formed. The liquid was :

The differential equation which represents the family of curves $y=c_1e^{c_2x}$, where $c_1$ and $c_2$ are arbitrary constants is

Due to the presence of the current $I_1$ at the origin

A particle has an initial velocity $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed after $10\, s$ is

A $p-n$ junction $(D)$ shown in the figure can act as a rectifier. An alternating current source $(V)$ is connected in the circuit.

The current $(I)$ in the resistor $(R)$ can be shown by

The logic circuit shown below has the input waveforms $A$ and $B$ as shown. Pick out the correct output waveform.

The transition from the state $n = 4$ to $n = 3$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

The magnitude of the magnetic field $(B)$ due to loop $ABCD$ at the origin $(O)$ is

Consider a rubber ball freely falling from a height $h\, =\, 4.9\, m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as function of time will be :