List of top Questions asked in AIEEE- 2004

Among $ {Al_2O_3, SiO_2, P_2O_3}$ and $ {SO_2}$ the correct order of acidic strength is

Aluminium chloride exists as dimer,$ { Al_2Cl_6}$ in solid state as well as in solution of non-polar solvents such as benzene. When dissolved in water, it gives

The formation of the oxide ion $O^{2-}(g)$ requires first an exothermic and then an endothermic step as shown below $O\left(g\right) + e^{-}O^{-} \left(g\right)?H^{\circ} = -142kJmol^{-1}$ $O^{-} \left(g\right) + e^{-}O^{2-} \left(g\right)?H^{\circ} = 844kJmol^{-1}$

A wire fixed at the upper end stretches by length by applying a force $F$. The work done in stretching is

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is

A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

If $\displaystyle\lim_{x \to\infty} \left(1+ \frac{a}{x} + \frac{b}{x^{2}}\right)^{2x} = e^{2} $ , then the values of a and b, are

The range of the function $f\left(x\right) = ^{7-x}P_{x-3}$ is

The coefficient of the middle term in the binomial expansion in powers of x of $(1+ \alpha x)^4$ and of $ (1 - \alpha x)^6$ is the same if $\alpha$ equals

The coefficient of $x^n$ in expansion of $(1+ x)(1- x)^n$ is

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $60^{\circ}$ and when he retires $40$ meter away from the tree the angle of elevation becomes $30^{\circ}$. The breadth of the river is

Let $A=\begin{pmatrix} 1&-1 &1 \\[0.3em] 2 &1 &-3 \\[0.3em] 1 &1&1 \end{pmatrix}$ and $\,10\,B=\begin{pmatrix} 4&2 &2 \\[0.3em] -5 &0 & \alpha \\[0.3em] 1 &-2&3 \end{pmatrix} $. If B is the inverse of A , then $\alpha$ is

If $f: R \rightarrow S $ defined by $ f(x)=\sin x-\sqrt{3} \,\cos\,x+\,$ 1, is onto, function then S = ?

The graph of the function $y = f(x) $is symmetrical about the line $x = 2$, then

A machine gun fires a bullet of mass 40 g with a velocity 1200 $ms^{-1}$. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most ?

A light ray is incident perpendicular to one face of a $90^{\circ}$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $45^{\circ}$, we conclude that the refractive index $n$

A current $i$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

A coil having n turns and resistance $4R\, O$. This combination is moved in time t seconds from a magnetic field $W_1$ weber to $W_2$ weber. The induced current in the circuit is

If two soap bubbles of different radii are connected by a tube,

One mole of ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of diatomic gas $(\gamma = 7/5)$. What is $\gamma$ for the mixture? $\gamma$ Denotes the ratio of specific heat at constant pressure, to that at constant volume.

Two masses $m_1 = 5$ kg and $m_2 = 4.8$ kg tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift free to move? $(g = 9.8 m/s^2)$

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

Spherical balls of radius $'R'$ are falling in a viscous fluid of viscosity '$\eta$' with a velocity '$v$'. The retarding viscous force acting on the spherical ball is

A body of mass m, accelerates uniformly from rest to $v_1$ in time $t_1$. The instantaneous power delivered to the body as a function of time t is

Two long conductors, separated by a distance d carry current $I_1$ and $I_2$ in the same direction. They exert a force $F$ on each other. Now the current in one of them increased to two times and its direction reversed. The distance is also increased to $3d$. The new value of the force between them is