List of top Questions asked in AIEEE- 2007

The reaction of toluene with $Cl_2$ in presence of $FeCl_3$ gives predominantly

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 ??10^{-2}\, cos\, \pi t$ metres. The time at which the maximum speed first occurs is

The compound formed as a result of oxidation of ethyl benzene by $KMnO_4$ is

The actinoids exhibits more number of oxidation states in general than the lanthanoids. This is because

Presence of a nitro group in a benzene ring

Photon of frequency $?$ has a momentum associated with it. If $c$ is the velocity of light, the momentum is

In the following sequence of reactions, $ {CH3CH2OH->[P+I_2]A->[Mg][ether]B->[HCHO]C->[H_2O]D}$ the compound $D$ is

In conversion of lime-stone to lime, $ {CaCO_3(s)->CaO(s) +CO2(g)}$ the vales of $?H^?? and $?S^?? are $+179.1\, kJ\, mol^{-1}$ and $160.2\, J/K$ respectively at $298\, K$ and $1 \,bar$. Assuming that $?H^?? do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is

If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

Identify the correct statement regarding a spontaneous process

For the given uniform square lamina $ABCD$, whose centre is $O$,

Equal masses of methane and oxygen are mixed in an empty container at $25^??$. The fraction of the total pressure exerted by oxygen is

Assuming that water vapour is an ideal gas, the internal energy $(?U)$ when 1 mol of water is vapourised at 1 bar pressure and $100^??$, (Given: Molar enthalpy of vapourization of water at 1 bar and $373 \,K = 41\, kJ \,mol^{-1}$ and $R = 8.3\, J \,mol^{-1}K^{-1}$) will be

A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB (= a)$ subtends an angle of $60^\circ$ at the foot of the tower, and the angle of elevation of the top of the tower from $A$ or $B$ is $30^??. The height of the tower is

A round uniform body of radius $R$, mass $M$ and moment of inertia $I$, rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration

The IUPAC name of

Consider a family of circles which are passing through the point (-1, 1) and are tangent to xaxis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

The set $S=\left\{1, 2, 3, \dots, 12\right\}$ is to be partitioned into three sets $A, B, C$ of equal size. Thus, $A\cup B\cup C=S, A\cap B = B\cap C = A \cap C=\phi.$ The number of ways to partition $S$ is

The largest interval lying in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ for which the function $f \left(x\right)=4^{-x^2}+cos^{-1}\left(\frac{x}{2}-1\right)+log\left(cos\,x\right)$ is defined, is

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

If $sin^{-1}\left(\frac{x}{5}\right)+cos\,ec^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2} $ then a value of $x$ is

In the binomial expansion of $(a - b)^n, n \geq 5,$ a the sum of $5^{th}$ and $6^{th}$ terms is zero, then $\frac{a}{b}$ equals

The sum of the series ${^{20}C_0} - {^{20}C_1} + {^{20}C_2} - {^{20}C_3} + ..... - .... + {^{20}C_{10}}$ is

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is

If one of the lines of $my^2 + (1 - m^2)xy - mx^2 = 0$ is a bisector of the angle between the lines $xy = 0$, then $m$ is