JEE Main 2003 Question Paper with Solutions

Consider points $A, B, C$ and $D$ with position vectors $7\widehat i - 4\widehat j + 7\widehat k,\widehat i - 6\widehat j + 10\widehat k, - \widehat i - 3\widehat j + 4\widehat k$ and $5\widehat i - \widehat j + 5\widehat k$ respectively. Then $ABCD$ is a :

In an irreversible process taking place at constant T and P and in which only pressure-volume work is being done, the change in Gibbs free energy (dG) and change in entropy (dS), satisfy the criteria :

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

The pair of species having identical shapes for molecules of both species is

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

Which one of the following is an amphoteric oxide?

If ${\left( {{{1 + i} \over {1 - i}}} \right)^x} = 1$ then :

If the equation of the locus of a point equidistant from the point $\left( {{a_{1,}}{b_1}} \right)$ and $\left( {{a_{2,}}{b_2}} \right)$ is $\left( {{a_1} - {a_2}} \right)x + \left( {{b_1} - {b_2}} \right)y + c = 0$ , then the value of $'c'$ is :

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set :

If in a Δ A B C a cos 2 ( C 2 ) + c cos 2 ( A 2 ) = 3 b 2 , then the sides a , b and c :

The value of ' $a$ ' for which one root of the quadratic equation $ ( a 2 − 5 a + 3 ) x 2 + ( 3 a − 1 ) x + 2 = 0 $ is twice as large as the other is

The value of $\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {{{\sec }^2}tdt} } \over xsinx}$ is

If the function $f\left( x \right) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1,$ where $a>0,$ attains its maximum and minimum at $p$ and $q$ respectively such that ${p^2} = q$ , then $a$ equals

The number of d-electrons retained in Fe 2+ (At no of Fe = 26) ion is :

How many unit cells are present in a cubeshaped ideal crystal of NaCl of mass 1.00 g? [Atomic masses: Na = 23, Cl = 35.5]

The reaction of chloroform with alcoholic K O H and p-toluidine forms

Which one of the following characteristics is not correct for physical adsorption?

The reason for double helical structure of $DNA$ is operation of