IIT-JEE 2008 Paper 2 Offline

Compound H is formed by the reaction of

The structure of compound I is :

The structures of compound J, K and L, respectively, are:

In the following reaction sequence, the correct structure of E, F and G are :

The correct stability order for the following species is :

Cellulose upon acetylation with excess acetic anhydride/H\(_2\)SO\(_4\) (catalytic) gives cellulose triacetate whose structure is :

Statement 1 : Aniline on reaction with NaNO\(_2\)/HCl at 0\(^\circ\)C followed by coupling with \(\beta\)-naphthol gives a dark blue coloured precipitate.
Statement 2 : The colour of the compound formed in the reaction of aniline with NaNO$...

Match the compounds in Column I with their characteristic test(s)/reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 matrix given in the ORS.

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Among the following, the coloured compound is :

Both [Ni(CO)\(_4\)] and [Ni(CN)\(_4\)]\(^{2-}\) are diamagnetic. They hybridisations of nickel in these complexes, respectively, are :

The IUPAC name of [Ni(NH\(_3\))\(_4\)] [NiCl\(_4\)] is :

Statement 1 : [Fe(H\(_2\)O)\(_5\)NO]SO\(_4\) is paramagnetic.
Statement 2 : The Fe in [Fe(H\(_2\)O)\(_5\)NO]SO\(_4\) has three unpaired electrons.

Statement 1 : The geometrical isomers of the complex [M(NH\(_3\))\(_4\)Cl\(_2\)] are optically inactive.
Statement 2 : Both geometrical isomers of the complex [M(NH\(_3\))\(_4\)Cl\(_2\)] possess axis of symmetry.

Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate 0.01 mol of H\(_2\) gas at the cathode is (1 Faraday = 96500 C mol\(^{-1}\)].

Solubility product constants (K\(_{sp}\)) of salts of types MX, MX\(_2\) and M\(_3\)X at temperature T are 4.0 \(\times\) 10\(^{-8}\), 3.2 \(\times\) 10\(^{-14}\) and 2.7 \(\times\) 10\(^{-15}\), respectively. Solubilities (mol dm\(^{-3}\))...

Match the conversions in Column I with the type(s) of reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 matrix given in the ORS.

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The number of atoms in this HCP unit cell is :

The volume of this HCP unit cell is :

The empty space in this HCP unit cell is :

Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 matrix given in the ORS.

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Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient condition is:

Statement 1 : There is a natural asymmetry between converting work to heat and converting heat to work.
Statement 2 : No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion int...

The distance of the point \((1, 1, 1)\) from the plane passing through the point \((-1, -2, -1)\) and whose normal is perpendicular to both the lines \({L_1}\) and \({L_2}\) is :

The area of the region between the curves \(y = \sqrt {{{1 + \sin x} \over {\cos x}}}\)
and \(y = \sqrt {{{1 - \sin x} \over {\cos x}}}\) bounded by the lines \(x=0\) and \(x = {\pi \over 4}\) is

Consider
\(\,{L_1}:\,\,2x\,\, + \,\,3y\, + \,p\,\, - \,\,3 = 0\)
\(\,{L_2}:\,\,2x\,\, + \,\,3y\, + \,p\,\, + \,\,3 = 0\)
where p is a real number, and \(\,C:\,{x^2}\, + \,{y^2}\, + \,6x\, - 10y\, + \,30 = 0\)
STATEMENT-1 : If line $...

A particle P stats from the point \({z_0}\) = 1 +2i, where \(i = \sqrt { - 1}\). It moves horizontally away from origin by 5 unit and then vertically away from origin by 3 units to reach a point \({z_1}\). From \({z_1}\) the particle moves...

Let \(g\left( x \right) = \int\limits_0^{{e^x}} {{{f'\left( t \right)} \over {1 + {t^2}}}} \,dt.\) Which of the following is true?

Let a solution \(y=y(x)\) of the differential equation,
\(x\sqrt {{x^2} - 1} \,\,dy - y\sqrt {{y^2} - 1} \,dx = 0\) satify \(y\left( 2 \right) = {2 \over {\sqrt 3 }}.\)
STATEMENT-1 : $$y\left( x \right) = \sec \left( {{{\sec }^{ - 1}}x - ...

Let \(g(x) = \log f(x)\), where \(f(x)\) is a twice differentiable positive function on (0, \(\infty\)) such that \(f(x + 1) = xf(x)\). Then for N = 1, 2, 3, ..., \(g''\left( {N + {1 \over 2}} \right) - g''\left( {{1 \over 2}} \right) =\)

Which of the following is true?

Consider a branch of the hyperbola
\(${x^2} - 2{y^2} - 2\sqrt 2 x - 4\sqrt 2 y - 6 = 0\)$
with vertex at the point \(A\). Let \(B\) be one of the end points of its latus rectum. If \(C\) is the focus of the hyperbola nearest to the point ...

Let \(I = \int {{{{e^x}} \over {{e^{4x}} + {e^{2x}} + 1}}dx,\,\,J = \int {{{{e^{ - x}}} \over {{e^{ - 4x}} + {e^{ - 2x}} + 1}}dx.} }\) Then
for an arbitrary constant \(C\), the value of \(J -I\) equals :

Let the function \(g:\left( { - \infty ,\infty } \right) \to \left( { - {\pi \over 2},{\pi \over 2}} \right)\) be given by
\(g\left( u \right) = 2{\tan ^{ - 1}}\left( {{e^u}} \right) - {\pi \over 2}.\) Then, \(g\) is

Which of the following is true?

Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

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An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is :

Let \(a,\,b,c\), \(p,q\) be real numbers. Suppose \(\alpha ,\,\beta\) are the roots of the equation \({x^2} + 2px + q = 0\) and \(\alpha ,{1 \over \beta }\) are the roots of the equation \(a{x^2} + 2bx + c = 0,\) where $${\beta ^2} \in \le...

Suppose four distinct positive numbers \({a_1},\,{a_{2\,}},\,{a_3},\,{a_4}\,\) are in G.P. Let \({b_1} = {a_1},{b_2} = {b_1} + {a_2},\,{b_3} = {b_2} + {a_{3\,\,}}\,\,\,and\,\,\,{b_4} = {b_3} + {a_4}\).
STATEMENT-1: The numbers $${b_1},\,...

Consider three points \(P = ( - \sin (\beta - \alpha ), - cos\beta ),Q = (cos(\beta - \alpha ),\sin \beta )\) and \(R = (\cos (\beta - \alpha + \theta ),\sin (\beta - \theta ))\) where \(0 < \alpha ,\beta ,\theta < {\pi \over 4}\). T...

Consider the lines given by:
\({L_1}:x + 3y - 5 = 0\)
\({L_2}:3x - ky - 1 = 0\)
\({L_3}:5x + 2y - 12 = 0\)
Match the Statement/Expressions in Column I with the Statements/Expressions in Column II.

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Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

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Let two non-collinear unit vectors \(\widehat a\) and \(\widehat b\) form an acute angle. A point \(P\) moves so that at any time \(t\) the position vector \(\overrightarrow {OP}\) (where \(O\) is the origin) is given by $$\widehat a\cos t...

The unit vector perpendicular to both \({L_1}\) and \({L_2}\) is :

The shortest distance between \({L_1}\) and \({L_2}\) is :

A radioactive sample S1 having activity of 5 \(\mu\)Ci has twice the number of nuclei as another sample S2 which has an activity of 10 \(\mu\)Ci. The half lives of S1 and S2 can be :

Consider a system of three charges \({q \over 3},{q \over 3}\) and \(- {{2q} \over 3}\) placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60\(^\circ\)

A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is \(\frac{d}{3}\) initially. Suppose the liquid level decreases at a constant speed V, the tim...

STATEMENT 1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and
STATEMENT 2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given ...

The electric field at r = R is :

For a = 0, the value of d (maximum value of \(\rho\) as shown in the figure) is