JEE Main 2002 Question Paper with Solutions

If the vectors $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ from the sides $B C, C A$ and $A B$ respectively of a triangle $A B C$ , then :

If $\left| {\overrightarrow a } \right| = 4,\left| {\overrightarrow b } \right| = 2$ and the angle between ${\overrightarrow a }$ and ${\overrightarrow b }$ is $\pi /6$ then ${\left( {\overrightarrow a \times \overrightarrow b } \right)^2}$ is equal to :

Number of atoms in 558.5 gram Fe (at. wt. of Fe = 55.85 g mol -1 ) is

1 M NaCL and 1 M HCL are present in an aqueous solution. The solution is

A metal M readily forms its sulphate MSO 4 , which is water-soluble. It forms its oxide MO which becomes inert on heating. It forms an insoluble hydroxide M(OH) 2 which is soluble in NaOH solution. The M is :

A heat engine absorbs heat Q 1 at temperature T 1 and heat Q 2 at temperature T 2 . Work done by the engine is J (Q 1 + Q 2 ). This data :

In a hydrogen atom, if energy of an electron in ground state is -13.6 eV, then that in the 2 nd excited state is

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are :

Locus of mid point of the portion between the axes of $x$ $cos$ $\alpha + y\,\sin \alpha = p$ where $p$ is constant is :

Locus of mid point of the portion between the axes of $x$ $cos$ $\alpha + y\,\sin \alpha = p$ where $p$ is constant is :

The maximum distance from origin of a point on the curve $x = a\sin t - b\sin \left( {{{at} \over b}} \right)$ $y = a\cos t - b\cos \left( {{{at} \over b}} \right),$ both $a,b > 0$ is

If f(x + y) = f(x).f(y) ∀ x, y and f(5) = 2, f'(0) = 3, then f'(5) is

The order and degree of the differential equation $\,{\left( {1 + 3{{dy} \over {dx}}} \right)^{2/3}} = 4{{{d^3}y} \over {d{x^3}}}$ are

If y = f ( x ) makes + v e intercept of 2 and 0 unit on x and y axes and encloses an area of 3 / 4 square unit with the axes then ∫ 0 2 x f ′ ( x ) d x is

$\mathop {\lim }\limits_{x \to \infty } {\left( {{{{x^2} + 5x + 3} \over {{x^2} + x + 2}}} \right)^x}$

Oxidation number of Cl in CaOCl 2 (bleaching powder) is :

The integrated rate equation is Rt = log C 0 - log C t . The straight line graph is obtained by plotting

The functional group, which is found in amino acid is

Units of rate constant of first and zero order reactions in terms of molarity M unit are respectively

Na and Mg crystallize in BCC and FCC type crystals respectively, then the number of atoms of Na and Mg present in the unit cell of their respective crystal is :