JEE Main 2008 Question Paper with Solutions

The non-zero vectors are a → , b → and c → are related by a → = 8 b → and c → = − 7 b → . Then the angle between a → and c → is :

The bond dissociation energy of B - F in BF 3 is 646 kJ mol -1 whereas that of C - F in CF 4 is 515 kj mol -1 . The correct reason for higher B - F bond dissociation energy as compared to that of C - F is

The absolute configuration of

The treatment of C H 3 M g X with C H 3 C ≡ C − H produces

In context with the industrial preparation of hydrogen from water gas (CO + H 2 ), which of the following is the correct statement?

For the following three reactions a, b and c, equilibrium constants are given: a. CO (g) + H 2 O (g) $\leftrightharpoons$ CO 2 (g) + H 2 (g) ; K 1 b. CH 4 (g) + H 2 O (g) $\leftrightharpoons$ CO(g) + 3H 2 (g) ; K 2 c. CH 4 (g) + 2H 2 O (g) $\leftrightharpoons$ CO 2 (g) + 4H 2 (g) ; K 3

The conjugate of a complex number is ${1 \over {i - 1}}$ then that complex number is :

In a shop there are five types of ice-cream available. A child buys six ice-cream. Statement - 1: The number of different ways the child can buy the six ice-cream is 10 C 5 . Statement - 2: The number of different ways the child can buy the six ice-cream is equal to the number of different ways of arranging 6 A and 4 B's in a row.

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at :

Let R be the real line. Consider the following subsets of the plane $R \times R$ : $S = \left\{ {(x,y):y = x + 1\,\,and\,\,0 < x < 2} \right\}$ $T = \left\{ {(x,y): x - y\,\,\,is\,\,an\,\,{\mathop{\rm int}} eger\,} \right\}$ , Which one of the following is true ?

A focus of an ellipse is at the origin. The directrix is the line $x=4$ and the eccentricity is ${{1 \over 2}}$ . Then the length of the semi-major axis is :

The value of $cot\left( {\cos e{c^{ - 1}}{5 \over 3} + {{\tan }^{ - 1}}{2 \over 3}} \right)$ is :

Let $a, b, c$ be any real numbers. Suppose that there are real numbers $x, y, z$ not all zero such that $x=cy+bz,$ $y=az+cx,$ and $z=bx+ay.$ Then ${a^2} + {b^2} + {c^2} + 2abc$ is equal to :

The value of $\sqrt 2 \int {{{\sin xdx} \over {\sin \left( {x - {\pi \over 4}} \right)}}}$ is

$AB$ is a vertical pole with $B$ at the ground level and $A$ at the top. $A$ man finds that the angle of elevation of the point $A$ from a certain point $C$ on the ground is ${60^ \circ }$ . He moves away from the pole along the line $BC$ to a point $D$ such that $CD=7$ m. From $D$ the angle of elevation of the point $A$ is ${45^ \circ }$ . Then the height of the pole is :

The area of the plane region bounded by the curves $x + 2{y^2} = 0$ and $\,x + 3{y^2} = 1$ is equal to :

Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being :

The coordination number and the oxidation state of the element ‘E’ in the complex [E(en) 2 (C 2 O 4 )]NO 2 (where (en) is ethylene diamine) are, respectively,

For a reaction ${1 \over 2}A \to 2B$ rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the expression

In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $\Delta _o$ be the highest?

The organic chloro compound, which shows complete stereochemical inversion during a S N 2 reaction, is