IIT-JEE 2012 Paper 2 Offline

The major product H of the given reaction sequence is
\(C{H_3} - C{H_2} - CO - C{H_3}\buildrel {\overline C N} \over \longrightarrow G\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{Heat}^{95\% \,{H_2}S{O_4}}} H\)

The compound that undergoes decarboxylation most readily under mild condition is

The compound I is

The compound K is

With reference to the scheme given, which of the given statement(s) about T, U, V and W is(are) correct?

Which of the given statement(s) about N, O, P and Q with respect to M is(are) correct?

The shape of XeO2F2 molecule is

\(NiC{l_2}{\{ P{({C_2}{H_5})_2}({C_6}{H_5})\} _2}\) exhibits temperature-dependent magnetic behaviour (paramagnetic/diamagnetic). The coordination geometries of Ni2+ in the paramagnetic and diamagnetic states are, respectively,

For the given aqueous reactions, which of the statement(s) is(are) true?

The electrochemical cell shown below is a concentration cell. M | M2+ (saturated solution of a sparingly soluble salt, MX2) || M2+ (0.001 mol dm–3) | M The emf of the cell depends on the difference in concentrations of M2+ ions at the two e...

The electrochemical cell shown below is a concentration cell. M | M2+ (saturated solution of a sparingly soluble salt, MX2) || M2+ (0.001 mol dm–3) | M The emf of the cell depends on the difference in concentrations of M2+ ions at the two e...

In the cyanide extraction process of silver from argentite ore, the oxidising and reducing agents used are

The reaction of white phosphorous with aqueous NaOH gives phosphine along with another phosphorus containing compound. The reaction type; the oxidation states of phosphorus in phosphine and the other product are, respectively,

Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is

25 mL of household bleach solution was mixed with 30 mL of 0.50 M KI and 10 mL of 4 N acetic acid. In the titration of the liberated iodine, 48 mL of 0.25 N Na2S2O3 was used to reach the end point. The molarity of the household bleach solut...

With respect to graphite and diamond, which of the statement(s) given below is(are) correct?

For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in 100 g of water. the elevation in boiling point at 1 atm pressure is 2oC. Assuming concentration of solute is much lower than the concentration of solvent, th...

The given graphs/data I, II, III and IV represent general trends observed for different physisorption and chemisorption processes under mild conditions of temperature and pressure. Which of the following choice(s) about I, II, III and IV is...

Using the data provided, calculate the multiple bond energy (kJ mol\(-\)1) of a C=C bond in C2H2. That energy is (take the bond energy of C-H bond as 350 kJ mol\(-\)1).
$$\matrix{
\hfill {2C(s) + {H_2}(g) \to {C_2}{H_2}} & \hfill {\Delta...

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is(are) correct?

The equation of a plane passing through the line of intersection of the planes \(x+2y+3z=2\) and \(x-y+z=3\) and at a distance \({2 \over {\sqrt 3 }}\) from the point \((3, 1, -1)\) is

If the straight lines \(\,{{x - 1} \over 2} = {{y + 1} \over k} = {z \over 2}\) and \({{x + 1} \over 5} = {{y + 1} \over 2} = {z \over k}\) are coplanar, then the plane (s) containing these two lines is (are)

Let \(f\left( x \right) = {\left( {1 - x} \right)^2}\,\,{\sin ^2}\,\,x + {x^2}\) for all \(x \in IR\) and let
\(g\left( x \right) = \int\limits_1^x {\left( {{{2\left( {t - 1} \right)} \over {t + 1}} - In\,t} \right)f\left( t \right)dt}\) ...

If \(f\left( x \right) = \int_0^x {{e^{{t^2}}}} \left( {t - 2} \right)\left( {t - 3} \right)dt\) for all \(x \in \left( {0,\infty } \right),\) then

Let \(f\left( x \right) = {\left( {1 - x} \right)^2}\,\,{\sin ^2}\,\,x + {x^2}\) for all \(x \in IR\) and let
\(g\left( x \right) = \int\limits_1^x {\left( {{{2\left( {t - 1} \right)} \over {t + 1}} - In\,t} \right)f\left( t \right)dt}\) ...

A tangent PT is drawn to the circle \({x^2}\, + {y^2} = 4\) at the point P \(\left( {\sqrt 3 ,1} \right)\). A straight line L, perpendicular to PT is a tangent to the circle \({(x - 3)^2}\) + \({y^2}\) = 1.
A possible equation of L is

A tangent PT is drawn to the circle \({x^2}\, + {y^2} = 4\) at the point P \(\left( {\sqrt 3 ,1} \right)\). A straight line L, perpendicular to PT is a tangent to the circle \({(x - 3)^2}\) + \({y^2}\) = 1
A common tangent of the two circl...

The value of the integral \(\int\limits_{ - \pi /2}^{\pi /2} {\left( {{x^2} + 1n{{\pi + x} \over {\pi - x}}} \right)\cos xdx}\) is

Let \(f:( - 1,1) \to R\) be such that \(f(\cos 4\theta ) = {2 \over {2 - {{\sec }^2}\theta }}\) for \(\theta \in \left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 4},{\pi \over 2}} \right)\). Then the value(s) of $$f\left( {{1 \o...

For every integer n, let an and bn be real numbers. Let function f : R \(\to\) R be given by
$$f(x) = \left\{ {\matrix{
{{a_n} + \sin \pi x,} & {for\,x \in [2n,2n + 1]} \cr
{{b_n} + \cos \pi x,} & {for\,x \in (2n - 1,2n)} \cr

} ...

If P is a 3 \(\times\) 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 \(\times\) 3 identity matrix, then there exists a column matrix $$X = \left[ {\matrix{
x \cr
y \cr
z \cr

} } \right] \ne \...

If the ad joint of a 3 \(\times\) 3 matrix P is \(\left[ {\matrix{ 1 & 4 & 4 \cr 2 & 1 & 7 \cr 1 & 1 & 3 \cr } } \right]\), then the possible value(s) of the determinant of P is(are)

Let \({{a_n}}\) denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let \({{b_n}}\) = the number of such n-digit integers ending with digit 1 and \({{c_n}}\) =t...

Let \({{a_n}}\) denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let \({{b_n}}\) = the number of such n-digit integers ending with digit 1 and \({{c_n}}\) =t...

Let \(X\) and \(Y\) be two events such that \(P\left( {X|Y} \right) = {1 \over 2},\) \(P\left( {Y|X} \right) = {1 \over 3}\) and \(P\left( {X \cap Y} \right) = {1 \over 6}.\) Which of the following is (are) correct ?

Four fair dice \({D_1,}\) \({D_2,}\) \({D_3}\) and \({D_4}\) ; each having six faces numbered \(1, 2, 3, 4, 5\) and \(6\) are rolled simultaneously. The probability that \({D_4}\) shows a number appearing on one of \({D_1},\) \({D_2}\) and ...

Let \(PQR\) be a triangle of area \(\Delta\) with \(a=2\), \(b = {7 \over 2}\) and \(c = {5 \over 2}\); where \(a, b,\) and \(c\) are the lengths of the sides of the triangle opposite to the angles at \(P.Q\) and \(R\) respectively. Then $...

Let \(\alpha\)(a) and \(\beta\)(a) be the roots of the equation \((\root 3 \of {1 + a} - 1){x^2} + (\sqrt {1 + a} - 1)x + (\root 6 \of {1 + a} - 1) = 0\) where \(a > - 1\). Then \(\mathop {\lim }\limits_{a \to {0^ + }} \alpha (a)\) and ...

Let \({a_1},{a_2},{a_3},.....\) be in harmonic progression with \({a_1} = 5\) and \({a_{20}} = 25.\) The least positive integer \(n\) for which \({a_n} < 0\) is

If \(\overrightarrow a\) and \(\overrightarrow b\) are vectors such that \(\left| {\overrightarrow a + \overrightarrow b } \right| = \sqrt {29}\) and $$\,\overrightarrow a \times \left( {2\widehat i + 3\widehat j + 4\widehat k} \right...

In the given circuit, the AC source has \(\omega\) = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

What is the maximum energy of the anti-neutrino?

If the anti-neutrino had a mass of 3 eV/c2 (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron?

In the given circuit, a charge of \(+80\) \(\mu C\) is given to the upper plate of the \(4\) \(\mu F\) capacitor. Then in the steady state, the charge on the upper plate of the \(3\) \(\mu F\) capacitor is

A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it, the correct statement(s) is(are)

Six point charges are kept at the vertices of a regular hexagon of side \(L\) and center \(O,\) as shown in the figure. Given that \(K = {1 \over {4\pi {\varepsilon _0}}}{q \over {{L^2}}},\) which of the following statement(s) is (are) corr...

For light incident from air on a meta-material, the appropriate ray diagram is

Choose the correct statement.

Two spherical planets P and Q have the same uniform density r, masses MP and MQ and surface
areas A and 4A respectively. A spherical planet R also has uniform density r and its mass is (MP
+ MQ). The escape velocities from the planets P, Q ...

Two moles of ideal helium gas are in a rubber balloon at 30oC. The balloon is fully expandable
and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35oC. The amount of heat...