List of top Questions asked in AIEEE- 2003

The displacement of a particle varies according to the relation $x = 4(cos\, pt + sin \,pt).$ the amplitude of the particle is

In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inner-orbit jumps of the electron for Bohr orbits in an atom of hydrogen ?

If $A = \begin{bmatrix}a&b\\ b&a\end{bmatrix}$ and $A^{2}\begin{bmatrix}\alpha&\beta \\ \beta&\alpha\end{bmatrix}$, then

During dehydration of alcohols to alkenes by heating with concentrated $H _{2} SO _{4}$ the initiation step is :

Which one of the following is an amphoteric oxide?

If $f (a + b - x) = f (x)$, then $\int\limits^{b}_{{a}}x\, f\, (x) \,dx$ is equal to

If $f(x) = \begin{cases} xe^{-\left(\frac{1}{\left|x\right|}+\frac{1}{x}\right)}, & \text{$x \ne0$} \\[2ex] 0, & \text{$x=0$} \end{cases}$ then $f (x)$ is

If $f (x) = x^n$, then the value of $f \left(1\right)-\frac{f '\left(1\right)}{1!}+\frac{f ''\left(1\right)}{2!}-\frac{f "'\left(1\right)}{3!}+\dots+\frac{\left(-1\right)^{n}f ^{n}\left(1\right)}{n!}$ is

The real number $x$ when added to its inverse gives the minimum value of the sum at $x$ equal to

The trigonometric equation $sin^{-1} x = 2\, sin^{-1}$ a, has a solution for

Let f (x) be a polynomial function of second degree. If $f (1) = f (- 1)$ and $a, b, c$ are in $A. P.,$ then $f' (a), f' (b)$ and $f' (c)$ are in

The sum of the series $\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{3\cdot4}-...... $ upto $8$ is equal to

If $\begin{vmatrix}a&a^{2}&1+a^{3}\\ b&b^{2}&1+b^{3}\\ c&c^{2}&1+c^{3}\end{vmatrix}=0 $ and vectors $(1, a, a^2) (1, b, b^2)$ and $(1, c, c^2)$ are non-coplanar, then the product abc equals

A tetrahedron has vertices at $ O (0, 0, 0), A(1, 2, 1) B(2, 1, 3 )$ and $C(-1, 1, 2)$. Then the angle between the faces OAB and ABC will be

If $z$ and $?$ are two non-zero complex numbers such that $|z?| = 1$, and Arg $(z)$ - Arg $\left(\omega\right)=\frac{\pi}{2},$ then $\bar{z}\omega$ is equal to

Ethyl isocyanide on hydrolysis in acidic medium generates

Several blocks of magnesium are fixed to the bottom of a ship to

When rain is accompanied by a thunderstorm, the collected rain water will have a pH value

Bottles containing $ {C6H5I}$ and $ {C6H5CH2I}$ lost their original labels. They were labelled A and B for testing. A and B were separately taken in test tubes and boiled with $ {NaOH }$ solution. The end solution in each tube was made acidic with dilute $ {HNO3}$ and then some $ {AgNO3}$ solution was added. Substance B gave a yellow precipitate. Which one of the following statements is true for this experiment ?

The atomic number of V, Cr, Mn and Fe are respectively 23, 24, 25 and 26.Which one of these may be expected to have the highest second ionisation enthalpy ?

According to the kinetic theory of gases, in an ideal gas, between two successive collisions, a gas molecule travels

For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liquid metal which does not solidify before glass. The metal used can be

A particle performing uniform circular motion has angular momentum $L$. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

A marble block of mass $2 \,kg$ lying on ice when given a velocity of $6\, m/s$ is stopped by friction in $10\, s$. then the coefficient of friction is

A horizontal force of $10\, N$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is