IIT-JEE 2008 Paper 1 Offline

The structure of the product I is :

The structure of compounds J and K, respectively, are:

The structure of product L is :

Hyperconjugation involves overlapping of the following orbitals:

The correct statement(s) concerning the structures E, F and G is(are) :

Statement 1 : For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.
and
Statement 2 : At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

Under the same reaction conditions, initial concentration of 1.386 mol dm\(^{-3}\) of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio $$\left( {{{{k_1}} \over {{k_0}}}} ...

A gas described by van Der Waals equation

The major product of the following reaction is:

The correct statement(s) about the compound given below is(are):

Statement 1 : Bromobenzene upon reaction with Br\(_2\)/Fe gives 1, 4-dibromobenzene as the major product.
and
Statement 2: In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the ...

2.5 mL of \(\frac{2}{5}\)M weak monoacidic base (K\(_b\) = 1 \(\times\) 10\(^{-12}\) at 25\(^\circ\)C) is titrated with \(\frac{2}{15}\)M HCl in water at 25\(^\circ\)C. The concentration of H\(^+\) at equivalence point is (K\(_w\) = 1 $$\ti...

Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of:

A solution of colourless salt H on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after sometime. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt(s) H is(are):

Statement 1 : Pb\(^{4+}\) compounds are stronger oxidising agents than Sn\(^{4+}\) compounds.
and
Statement 2 : The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to 'inert pair ef...

Among the following, the correct statement is:

Among the following, the correct statement is :

White phosphorus on reaction with NaOH gives PH\(_3\) as one of the products. This is a:

Aqueous solutions of Na\(_2\)S\(_2\)O\(_3\) on reaction with Cl\(_2\) gives:

The freezing point of the solution M is :

The vapour pressure of the solution M is :

Water is added to the solution M such that the fraction of water in the solution becomes 0.9 mole. The boiling point of this solution is:

STATEMENT - 1 : The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards x-axis from the line of 45o slope as the atomic number is increased.
STATEMENT - 2 : Proton-proton electrostat...

Consider three planes
\(${P_1}:x - y + z = 1\)$
\(${P_2}:x + y - z = 1\)$
\(${P_3}:x - 3y + 3z = 2\)$
Let \({L_1},\) \({L_2},\) \({L_3}\) be the lines of intersection of the planes \({P_2}\) and \({P_3},\) \({P_3}\) and \({P_1},\) $${P...

The total number of local maxima and local minima of the function \(f(x) = \left\{ {\matrix{ {{{(2 + x)}^3},} & { - 3 < x \le - 1} \cr {{x^{2/3}},} & { - 1 < x < 2} \cr } } \right.\) is

The area of the region bounded by the curve \(y=f(x),\) the
\(x\)-axis, and the lines \(x=a\) and \(x=b\), where \(- \infty < a < b < - 2,\) is :

The equation of circle C is

Points E and F are given by

Equations of the sides QR, RP are

The number of elements in the set \(A \cap B \cap C\) is

Let z be any point in \(A \cap B \cap C\)
Then, \({\left| {z + 1 - i} \right|^2} + {\left| {z - 5 - i} \right|^2}\) lies between :

Let z be any point \(A \cap B \cap C\) and let w be any point satisfying \(\left| {w - 2 - i} \right| < 3\,\). Then, \(\left| z \right| - \left| w \right| + 3\) lies between :

\(\int\limits_{ - 1}^1 {g'\left( x \right)dx = }\)

If \(f\left( { - 10\sqrt 2 } \right) = 2\sqrt 2 ,\) then \(f''\left( { - 10\sqrt 2 } \right) =\)

Let \(f\) and \(g\) be real valued functions defined on interval \((-1, 1)\) such that \(g''(x)\) is continuous, \(g\left( 0 \right) \ne 0.\) \(g'\left( 0 \right) = 0\), \(g''\left( 0 \right) \ne 0\), and $$f\left( x \right) = g\left( x \ri...

Let \(P\left( {{x_1},{y_1}} \right)\) and \(Q\left( {{x_2},{y_2}} \right),{y_1} < 0,{y_2} < 0,\) be the end points of the latus rectum of the ellipse \({x^2} + 4{y^2} = 4.\) The equations of parabolas with latus rectum \(PQ\) are :

Consider the two curves \({C_1}:{y^2} = 4x,\,{C_2}:{x^2} + {y^2} - 6x + 1 = 0\). Then,

If \(0 < x < 1\), then
\(\sqrt {1 + {x^2}} {\left[ {{{\left\{ {x\cos \left( {{{\cot }^{ - 1}}x} \right) + \sin \left( {{{\cot }^{ - 1}}x} \right)} \right\}}^2} - 1} \right]^{1/2}} =\)

Let \(g(x) = {{{{(x - 1)}^n}} \over {\log {{\cos }^m}(x - 1)}};0 < x < 2,m\) and \(n\) are integers, \(m \ne 0,n > 0\), and let \(p\) be the left hand derivative of \(|x - 1|\) at \(x = 1\). If $$\mathop {\lim }\limits_{x \to {1^ + }} g(x) ...

Let \(f(x)\) be a non-constant twice differentiable function defined on \(\left( { - \infty ,\infty } \right)\)
such that \(f\left( x \right) = f\left( {1 - x} \right)\) and \(f'\left( {{1 \over 4}} \right) = 0.\) Then,

Consider the system of equations:
\(x-2y+3z=-1\)
\(-x+y-2z=k\)
\(x-3y+4z=1\)
Statement - 1 : The system of equations has no solution for \(k\ne3\).
and
Statement - 2 : The determinant $$\left| {\matrix{
1 & 3 & { - 1} \cr
{ - 1} & {...

Consider the system of equations \(ax+by=0; cx+dy=0,\)
where \(a,b,c,d\) \(\in \left\{ {0,1} \right\}\)
STATEMENT - 1 : The probability that the system of equations has a unique solution is \({3 \over 8}.\) and
STATEMENT - 2 : The proba...

Let \({S_n} = \sum\limits_{k = 1}^n {{n \over {{n^2} + kn + {k^2}}}}\) and \({T_n} = \sum\limits_{k = 0}^{n - 1} {{n \over {{n^2} + kn + {k^2}}}}\) for \(n\) \(=1, 2, 3, ............\) Then,

Let a and b be non-zero real numbers. Then, the equation \((a{x^2} + b{y^2} + c)({x^2} - 5xy + 6{y^2}) = 0\) represents :

A straight line through the vertex p of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then :

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors \(\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c\) such that $$\widehat a\,.\,\widehat b = \widehat b\,.\,\widehat c = \widehat c\,...

Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.

The quantum number n of the state finally populated in He\(^+\) ions is :

The wavelength of light emitted in the visible region by He\(^+\) ions after collisions with H atoms is

The ratio of the kinetic energy of the \(n=2\) electron for the H atom to that of He\(^+\) ion is