List of top Questions asked in AIEEE

: The variance of first $n$ even natural numbers is $\frac{n^{2}-1}{4}$ : The sum of first $n$ natural numbers is $\frac{n\left(n+1\right)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n\left(n+1\right)\left(2n+1\right)}{6}$

One ticket is selected at random from $50$ tickets numbered $00, 01, 02, ??, 49$. Then the probability that the sum of the digits on the selected ticket is $8$, given that the product of these digits is zero, equals

Let $A$ and $B$ denote the statements $A: cos\,\alpha + cos\,\beta + cos \,\gamma = 0$ $B: sin \alpha + sin\, \beta + sin\,\gamma = 0$ If $cos\left(\beta-\gamma\right)+cos\left(\gamma-\alpha\right)+cos\left(\alpha-\beta\right)=-\frac{3}{2}$, then

Knowing that the Chemistry of lanthanoids $(Ln)$ is dominated by its $+3$ oxidation state, which of the following statements in incorrect ?

Given $P(x) = x^4 + ax^3 + bx^2 + cx + d$ such that $x = 0$ is the only real root of $P'(x) = 0$ . If $P(-1) < P(1)$ , then in the interval $[-1, 1]$

Three distinct points $A, B$ and $C$ are given in the $2$ - dimensional coordinate plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $( - 1, 0)$ is equal to $\frac{1}{3}$. Then the circumcentre of the triangle $ABC$ is at the point

If $\left|Z-\frac{4}{z}\right|=2$, then the maximum value of $\left|Z\right|$ is equal to

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

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

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

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

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

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

Which of the following has an optical isomer ?

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 ?

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