JEE Main 2004 Question Paper with Solutions

Let $\overrightarrow u ,\overrightarrow v ,\overrightarrow w$ be such that $\left| {\overrightarrow u } \right| = 1,\,\,\,\left| {\overrightarrow v } \right|2,\,\,\,\left| {\overrightarrow w } \right|3.$ If the projection ${\overrightarrow v }$ along ${\overrightarrow u }$ is equal to that of ${\overrightarrow w }$ along ${\overrightarrow u }$ and ${\overrightarrow v },$ ${\overrightarrow w }$ are perpendicular to each other then $\left| {\overrightarrow u - \overrightarrow v + \overrightarrow w } \right|$ equals :

Which of the following will have meso-isomer also?

The equilibrium constant for the reaction N 2 (g) + O 2 (g) ⇋ 2NO(g) at temperature T is 4 × 10 -4 . The value of K c for the reaction NO(g) ⇋ 1 2 N 2 (g) + 1 2 O 2 (g) at the same temperature is :

The conjugate base of H 2 PO 4 - is :

The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 kJ mol-1 respectively. The enthalpy of formation of carbon monoxide per mole is :

One mole of magnesium nitride on the reaction with an excess of water gives :

Let A ( 2 , − 3 ) and B ( − 2 , 1 ) be vertices of a triangle A B C . If the centroid of this triangle moves on the line 2 x + 3 y = 1 , then the locus of the vertex C is the line :

If one root of the equation ${x^2} + px + 12 = 0$ is 4, while the equation ${x^2} + px + q = 0$ has equal roots, then the value of $'q'$ is

Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$ . The relation $R$ is :

If $z = x - iy$ and ${z^{{1 \over 3}}} = p + iq$ , then ${{\left( {{x \over p} + {y \over q}} \right)} \over {\left( {{p^2} + {q^2}} \right)}}$ is equal to :

If $z = x - iy$ and ${z^{{1 \over 3}}} = p + iq$ , then ${{\left( {{x \over p} + {y \over q}} \right)} \over {\left( {{p^2} + {q^2}} \right)}}$ is equal to :

$\int {{{dx} \over {\cos x - \sin x}}}$ is equal to

If $\int {{{\sin x} \over {\sin \left( {x - \alpha } \right)}}dx = Ax + B\log \sin \left( {x - \alpha } \right), + C,}$ then value of $(A, B)$ is

The value of $\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx}$ is

A line with direction cosines proportional to $2,1,2$ meets each of the lines $x=y+a=z$ and $x+a=2y=2z$ . The co-ordinates of each of the points of intersection are given by :

The value of $\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx}$ is

Which one of the following ores is best concentrated by froth – floatation method?

The rate equation for the reaction 2A + B $\to$ C is found to be: rate k[A][B]. The correct statement in relation to this reaction is that the

Which one of the following aqueous solutions will exhibit highest boiling point?

Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?

Consider the following nuclear reactions 92 238 M → Y X N + 2 2 4 H e Y X N → B A L + 2 β + The number of neutrons in the element L is