List of top Questions asked in AIEEE- 2006

If the terminal speed of a sphere of gold (density $= 19.5 kg/m^3$) is $0.2\, m/s$ in a viscous liquid (density $= 1.5\, kg/m^3$), find the terminal speed of a sphere of silver (density $= 10.5\, kg/m^3$) of the same size in the same liquid.

If the expansion in powers of $x$ of the function $\frac{1}{\left(1-ax\right)\left(1-bx\right)}$ is $a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+ ..... ,$ then $a_n$ is :

HBr reacts with $CH_2=CH??CH_3$ under anhydrous conditions at room temperature to give :

Consider a two particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance $d$, by what distance should the second particle be moved, so as to keep the centre of mass at the same position ?

Total volume of atoms present in a face-centred cubic unit cell of a metal is (r is atomic radius):

According to Bohr?? theory, the angular momentum of an electron in 5th orbit is :

According to Bohr?? theory, the angular momentum of an electron in 5th orbit is :

$\int\limits^{-\pi/2}_{{-3\pi/2}}$$\left[\left(x+\pi\right)^{3}+cos^{2} \left(x+3\pi\right)\right]dx$ is equal to :

Suppose a population $A$ has 100 observations $101, 102,..., 200 $ and another population $B$ has $ 100$ observations $151, 152, ..., 250.$ If $V_A$ and $V_B$ represent the variances of the two population respectively, then $\frac{V_{A}}{V_{B}}$ is :

All the values of m for which both roots of the equation $x^{2}-2mx+m^{2}-1=0$ are greater than -2but less than 4 lie in the interval :

The value of $\displaystyle \sum_{k=1}^{10}$$\left(sin\, \frac{2k\pi}{11}+i\,cos\, \frac{2k\pi}{11}\right)$ is :

The value of the integral $I=\int\limits^{6}_{{3}}$$\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}}dx$ is :

any three vectors such that $\vec{a}\cdot\vec{b} \ne 0, \vec{b}\cdot\vec{c} \ne 0,$ then $\vec{a}$ and $\vec{c}$ are :

If $A$ and fl are square matrices of size $n \times n$ such that $A^{2}-B^{2}=\left(A-B\right)\left(A+B\right)$, then which of the following will be always true ?

If x is real, the maximum value of $\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}$ is

$A B C$ is a triangle, right angled at $A .$ The resultant of the forces acting along $\overline{A B}, \overline{B C}$ with magnitudes $\frac{1}{A B}$ and $\frac{1}{A C}$ respectively is the force along $\overline{A D},$ where $D$ is the foot of the perpendicular from $A$ onto $B C$. The magnitude of the resultant is

The term anomers of glucose refers to :

Which of the following molecules/ions does not contain unpaired electrons ?

Phenyl magnesium bromide reacts with methanol to give :

The IUPAC name for the complex $[Co(NO_2)(NH_3)_5]Cl_2$ is:

Total volume of atoms present in a face-centred cubic unit cell of a metal is (r is atomic radius):

The energy spectrum of $\beta$-particles [number N(E) as a function of $\beta$-energy E] emitted from a radioactive source is :

In a common-base mode of a transistor, the collector current is 5.488 mA for an emitter current of 5.60 mA. The value of the base current amplification factor ($\beta$) will be :

In a series resonant $LCR$ circuit, the voltage across $R$ is $100$ volts and $R = 1\,\Omega$ with $C = 2\mu F$. The resonant frequency $\omega$ is $200$ rad/s. At resonance the voltage across $L$ is :

A long solenoid has $200$ turns per cm and carries a current $i$. The magnetic field at its centre is $6.28 \times 10^{-2}$ weber/$m^2$. Another long solenoid has 100 turns per cm and it carries a current $i/3$. The value of the magnetic field at its centre is: