IIT-JEE 2009 Paper 2 Offline

Match each of the compounds given in Column I with the reaction(s), that they can undergo, given in Column II.

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Aria...

In the following carbocation, H/CH\(_3\) that is most likely to migrate to the positively charged carbon is :

The correct stability order of the following resonance structures is

The total number of cyclic structural as well as stereoisomers possible for a compound with the molecular formula C\(_5\)H\(_{10}\) is ____________.

The correct statement(s) about the following sugar X and Y is(are)

For a first-order reaction A \(\to\) P, the temperature (T) dependent rate constant (k) was found to follow the equation \(\log k = - (2000){1 \over T} + 6.0\). The pre-exponential factor A and activation energy \(E_a\), respectively, are

The total number of \(\alpha\) and \(\beta\) particles emitted in the nuclear reaction \(_{92}^{238}U \to _{82}^{214}Pb\) is _________.

The spin only magnetic moment value (in Bohr magneton units) of Cr(CO)\(_6\) is

The number of water molecule(s) directly bonded to the centre in CuSO\(_4\) . 5H\(_2\)O is __________.

The oxidation number of Mn in the product of alkaline oxidative fusion of MnO\(_2\) is ___________.

For the reduction of NO\(_3^ -\) ion in an aqueous solution, E\(^0\) is + 0.96 V. Values of E\(^0\) for some metal ions are given below:
$$\matrix{
{{V^{2 + }}(aq.) + 2{e^ - } \to V} & {{E^0} = - 1.19\,V} \cr
{F{e^{3 + }}(aq.) + 3...

At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is ___________.

The dissociation constant of a substituted benzoic acid at 25\(^\circ\)C is 1.0 \(\times\) 10\(^{-4}\). The pH of a 0.01 M solution of its sodium salt is __________.

In the reaction
\(\mathrm{2X+B_2H_6\to[BH_2(X)_2]^+[BH_4]^-}\)
the amine(s) X is(are) :

The nitrogen oxide(s) that contain(s) N-N bond(s) is(are)

Match each of the reactions given in Column I with the corresponding product(s) given in Column II:

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-ser...

The coordination number of Al in the crystalline state of AlCl\(_3\) is ___________.

Among the following, the state function(s) is(are)

In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was burnt in excess oxygen at 298.0 K. The temperature of the calorimeter was found to increase from 298.0 K to 298.45 K due to the combustion process. Given that the...

A line with positive direction cosines passes through the point P(2, \(-\)1, 2) and makes equal angles with the coordinate axes. The line meets the plane \(2x + y + z = 9\) at point Q. The length of the line segment PQ equals

Let \(p(x)\) be a polynomial of degree \(4\) having extremum at
\(x = 1,2\) and \(\mathop {\lim }\limits_{x \to 0} \left( {1 + {{p\left( x \right)} \over {{x^2}}}} \right) = 2\).
Then the value of \(p (2)\) is

For the function
\($f\left( x \right) = x\cos \,{1 \over x},x \ge 1,\)$

The maximum value of the function \(f(x) = 2{x^3} - 15{x^2} + 36x - 48\) on the set \(A = \{ x|{x^2} + 20 \le 9x|\}\) is __________.

The centres of two circles \({C_1}\) and \({C_2}\) each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segement joining the centres of \({C_1}\) and \({C_2}\) and C a circle touching circles ...

If \({I_n} = \int\limits_{ - \pi }^\pi {{{\sin nx} \over {(1 + {\pi ^x})\sin x}}dx,n = 0,1,2,}\) .... then

Let \(f:R \to R\) be a continuous function which satisfies \(f(x) = \int\limits_0^x {f(t)dt}\). Then, the value of \(f(\ln 5)\) is ____________.

Match the statements/expressions in Column I with the values given in Column II:

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
...

The normal at a point \(P\) on the ellipse \({x^2} + 4{y^2} = 16\) meets the \(x\)- axis \(Q\). If \(M\) is the mid point of the line segment \(PQ\), then the locus of \(M\) intersects the latus rectums of the given ellipse at the points

An ellipse intersects the hyperbola \(2{x^2} - 2{y^2} = 1\) orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes then

If the function \(f(x) = {x^3} + {e^{x/2}}\) and \(g(x) = {f^{ - 1}}(x)\), then the value of \(g'(1)\) is _________.

The locus of the orthocentre of the triangle formed by the lines \((1 + p)x - py + p(1 + p) = 0,\)
\((1 + q)x - qy + q(1 + q) = 0\)
and \(y = 0\), where \(p \ne q\), is :

The tangent \(PT\) and the normal \(PN\) to the parabola \({y^2} = 4ax\) at a point \(P\) on it meet its axis at points \(T\) and \(N\), respectively. The locus of the centroid of the triangle \(PTN\) is a parabola whose

Let \(\left( {x,\,y,\,z} \right)\) be points with integer coordinates satisfying the system of homogeneous equation:
\($\matrix{ {3x - y - z = 0} \cr { - 3x + z = 0} \cr { - 3x + 2y + z = 0} \cr }\)$
Then the number of su...

Let ABC and ABC' be two non-congruent triangles with sides AB = 4, AC = AC' = 2\(\sqrt2\) and angle B = 30\(^\circ\). The absolute value of the difference between the areas of these triangles is ___________.

The smallest value of \(k\), for which both the roots of the equation
\(${x^2} - 8kx + 16\left( {{k^2} - k + 1} \right) = 0\)$
are real, distinct and have values at least 4, is

If the sum of first \(n\) terms of an A.P. is \(c{n^2}\), then the sum of squares of these \(n\) terms is

Match the statements/expressions in Column I with the values given in Column II:

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
...

For \(0 < \theta < {\pi \over 2},\) the solution (s) of
\($\sum\limits_{m = 1}^6 {\cos ec\,\left( {\theta + {{\left( {m - 1} \right)\pi } \over 4}} \right)\,\cos ec\,\left( {\theta + {{m\pi } \over 4}} \right) = 4\sqrt 2 }\)$ is (are)...

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions \(\phi_p=2.0~\mathrm{eV}\), \(\phi_q=2.5~\mathrm{eV}\) and \(\phi_r=3.0~\mathrm{eV}\), respecticely. A light beam containing ...

Two metallic rings A and B, identical in shape and size but having different resistivities \(\rho_A\) and \(\rho_B\), are kept on top of two identical solenoids as shown in the figure below. When current I is switched on in both the solenoi...

A solid sphere of radius R has a charge Q distributed in its volume with a charge density \(\rho = K{r^a}\), where K and a are constants and r is the distance from its centre. If the electric field at \(r = R/2\) is 1/8 times than at $$r =...

The figure shows the PV plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semicircle and CDA is half of an ellipse. Then,

Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II:

.tg {border-collapse:collapse...

A metal rod AB of length 10x has its one end A in ice at 0\(^\circ\)C and the other end B in water at 100\(^\circ\)C. If a point P on the rod is maintained at 400\(^\circ\)C, then it is found that equal amounts of water and ice evaporate an...

A piece of wire is bent in the shape of a parabola y = kx2 (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is no...

A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is \(k\left( {{{{\mu _0}I} \over {48\pi x}}} \right)\), f...

Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m\(^2\). The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Fin...

A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. ...

A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure below, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then,

The mass M shown in the figure below oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is