IIT-JEE 2011 Paper 2 Offline

Match the reactions in Column I with appropriate types of steps/reactive intermediate involved in these reactions as given in Column II :




















Column I



Column II









(A)



(P)

N...

The total number of contributing structure showing hyper-conjugation (involving C-H bonds) for the following carbocation is _________.

The following carbohydrate is

The equilibrium
\(2C{u^+} \to Cu^\circ + C{u^{2+}}\)
In aqueous medium at 25\(^\circ\)C shifts towards the left in the presence of

For the first order reaction
2N2O5 (g) \(\to\) 4NO2 (g) + O2 (g)

Amongst the compounds given, the one that would from a brilliant coloured dye on treatment with NaNO2 in dil. HCl followed by addition to an alkaline solution of \(\beta\)-naphthlol is

Among the following complexes (K-P),
K3[Fe(CN)6] (K), [Co(NH3)6]Cl3 (L), Na3[Co(oxalate)3] (M), [Ni(H2O)3]Cl2 (N), K2[Pt(CN)4] (O) and [Zn(H2O)6(NO3)2] (P)
The diamagnetic complexes are

Consider the following cell reaction:
2Fe(s) + O2(g) + 4H+(aq) \(\to\) 2Fe2+ (aq) + 2H2O (l); Eo = 1.67 V
At [Fe2+] = 10-3 M, P(O2) = 0.1 atm and pH = 3, the cell potential at 25oC is

The major product of the following reaction is

The maximum number of isomers (including stereoisomers) that are possible on mono-chlorination of the following compound, is ____________.

In 1 L saturated solution of AgCl [Ksp(AgCl) = 1.6 \(\times\) 10-10], 0.1 mol of CuCl [Ksp(CuCl) = 1.0 \(\times\) 10-6] is added. The resultant concentration of Ag+ in the solution is 1.6 \(\times\) 10-x. The value of "x" is

Oxidation states of the metal in the minerals haematite and magnetite, respectively are

Among the following, the number of compounds that can react with PCl5 to given POCl3 is _____________.
O2, CO2, SO2, H2O, H2SO4, P4O10

The correct functional group X and the reagent/reaction condition Y in the following scheme are

Reduction of the metal centre in aqueous permanganate ion involves

Passing H2S gas into a mixture of Mn2+, Ni2+, Cu2+ and Hg2+ ions in an acidified aqueous solution precipitates

The number of hexagonal faces that are present in a truncated octahedron is ____________.

The freezing point (in oC) of a solution containing 0.1 g of K3[Fe(CN)6] (Mol. wt. 329) in 100 g of water (Kf = 1.86 K kg mol-1) is

The volume (in mL) of 0.1 M AgNO3 required for complete precipitation of chloride ions present in 30 mL of 0.01 M solution of \([Cr{({H_2}O)_5}Cl]C{l_2}\), as silver chloride is close to ____________.

Match the transformations in column I with appropriate options in column II
Column I
(A) CO2(s) \(\to\) CO2(g)
(B) CaCO3(s) \(\to\) CaO(s) + CO2(g)
(C) 2H \(\to\) H2(g)
(D) P(white, solid) \(\to\) P(red, solid)
Column II
(p) phase transitio...

Let f \(:\)\(\left[ { - 1,2} \right] \to \left[ {0,\infty } \right]\) be a continuous function such that
\(f\left( x \right) = f\left( {1 - x} \right)\) for all \(x \in \left[ { - 1,2} \right]\)
Let $${R_1} = \int\limits_{ - 1}^2 {xf\left(...

The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point.

The straight line 2x - 3y = 1 divides the circular region \({x^2}\, + \,{y^2}\, \le \,6\) into two parts.
If $$S = \left\{ {\left( {2,\,{3 \over 4}} \right),\,\left( {{5 \over 2},\,{3 \over 4}} \right),\,\left( {{1 \over 4} - \,{1 \over 4}...

Let \(\omega = {e^{{{i\pi } \over 3}}}\), and a, b, c, x, y, z be non-zero complex numbers such that
\(a + b + c = x\)
\(a + b\omega + c{\omega ^2} = y\)
\(a + b{\omega ^2} + c\omega = z\)
Then the value of $${{{{\left| x \righ...

Let \(y'\left( x \right) + y\left( x \right)g'\left( x \right) = g\left( x \right),g'\left( x \right),y\left( 0 \right) = 0,x \in R,\) where \(f'(x)\) denotes \({{df\left( x \right)} \over {dx}}\) and \(g(x)\) is a given non-constant differ...

Let f(x) = x2 and g(x) = sin x for all x \(\in\) R. Then the set of all x satisfying \((f \circ g \circ g \circ f)(x) = (g \circ g \circ f)(x)\), where \((f \circ g)(x) = f(g(x))\), is

Let \(f:(0,1) \to R\) be defined by \(f(x) = {{b - x} \over {1 - bx}}\), where b is a constant such that \(0 < b < 1\). Then

Match the statements given in Column I with the intervals/union of intervals given in Column II :

Let \(P(6, 3)\) be a point on the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\). If the normal at the point \(P\) intersects the \(x\)-axis at \((9, 0)\), then the eccentricity of the hyperbola is

If \(\mathop {\lim }\limits_{x \to 0} {[1 + x\ln (1 + {b^2})]^{1/x}} = 2b{\sin ^2}\theta\), \(b > 0\) and \(\theta \in ( - \pi ,\pi ]\), then the value of \(\theta\) is

If \(f(x) = \left\{ {\matrix{ { - x - {\pi \over 2},} & {x \le - {\pi \over 2}} \cr { - \cos x} & { - {\pi \over 2} < x \le 0} \cr {x - 1} & {0 < x \le 1} \cr {\ln x} & {x > 1} \cr } } \right.\), then

Let \(\omega\) \(\ne\) 1 be a cube root of unity and S be the set of all non-singular matrices of the form \(\left[ {\matrix{ 1 & a & b \cr \omega & 1 & c \cr {{\omega ^2}} & \omega & 1 \cr } } \right]\), where each of a,...

Let M be a 3 \(\times\) 3 matrix satisfying \(M\left[ {\matrix{ 0 \cr 1 \cr 0 \cr } } \right] = \left[ {\matrix{ { - 1} \cr 2 \cr 3 \cr } } \right]\), $$M\left[ {\matrix{
1 \cr
{ - 1} \cr
0 \c...

Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by

Let \((x, y)\) be any point on the parabola \({y^2} = 4x\). Let \(P\) be the point that divides the line segment from \((0, 0)\) to \((x, y)\) in the ratio \(1 : 3\). Then the locus of \(P\) is

Let \(E\) and \(F\) be two independent events. The probability that exactly one of them occurs is \(\,{{11} \over {25}}\) and the probability of none of them occurring is \(\,{{2} \over {25}}\). If \(P(T)\) denotes the probability of occurr...

The number of distinct real roots of \({x^4} - 4{x^3} + 12{x^2} + x - 1 = 0\)

A value of \(b\) for which the equations
\($\matrix{ {{x^2} + bx - 1 = 0} \cr {{x^2} + x + b = 0} \cr }\)$
have one root in common is

Let \(\overrightarrow a = - \widehat i - \widehat k,\overrightarrow b = - \widehat i + \widehat j\) and \(\overrightarrow c = \widehat i + 2\widehat j + 3\widehat k\) be three given vectors. If \(\overrightarrow r\) is a vector such t...

Match the statements given in Column -\(I\) with the values given in Column-\(II.\)
\(\,\,\,\,\) \(\,\,\,\,\) \(\,\,\,\,\) Column-\(I\)
(A) \(\,\,\,\,\)If $$\overrightarrow a = \widehat j + \sqrt 3 \widehat k,\overrightarrow b = - \wideh...

A series RC-current is connected to AC voltage source. Consider two cases : (A) When C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capa...

A series RC combination is connected to an AC voltage of angular frequency \(\omega\) = 500 rad/s. If the impedance of the RC circuit is R\(\sqrt{1.25}\), the time constant (in millisecond) of the circuit is __________.

Two batteries of different emfs and different internal resistance are connected as shown. The voltage across AB in volts is __________.

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquire...

Which of the following statement(s) is/are correct?

Which of the field patterns given below is valid for electric field as well as for magnetic field ?

Water (with refractive index = 4/3) in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature R = 6 cm as shown. Consider oil to act a thin lens. An object S is placed 24 cm above wate...

A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is
ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its
ejection, the ki...

One mole of a monatomic gas is taken through a cycle ABCDA as shown in the PV diagram. Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I.











Column I

...

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet
of mass 0.01 kg, traveling with a velocity V m/s in a horizontal
direction, hits the center of the ball. After the collision, the ball and
bullet travel independently. T...