JEE Advanced 2013 Paper 2 Offline

In the following reaction, the product/products formed is/are

The major product(s) of the following reaction is(are)

Match the chemical conversions in List I with the appropriate reagents in List II and select the correct answer using the code given below the lists :

After completion of the reactions (I and II), the organic compound(s) in the reaction mixtures is(are)

Compounds formed from P and Q are, respectively,

In the following reaction sequences V and W are, respectively,

The thermal dissociation equilibrium of CaCO3(s) is studied under different conditions
CaCO3(s) \(\leftrightharpoons\) CaO(s) + CO2(g). For this equilibrium, the correct statement(s) is (are)

In the nuclear transmutation
9Be4 + X \(\to\) 8Be4 + Y
(X, Y) is (are) :

An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List – I. The variation in
conductivity of these reactions in List – II. Match List – I with List – II and select the correct answer using
the code given below...

The standard reduction potential data at 25oC is given below:
Eo (Fe3+ , Fe2+) = +0.77V;
Eo (Fe2+ , Fe) = -0.44V;
Eo (Cu2+ , Cu) = +0.34V;
Eo (Cu+ , Cu) = +0.52V;
Eo [O2(g) + 4H+ + 4e- \(\to\) 2H2O] = +1.23V;
Eo [O2(g) + 2H2O + 4e- $$\...

The Ksp of Ag2CrO4 is 1.1 \(\times\) 10-12 at 298 K. The solubility (in mol/L) of Ag2CrO4 in a 0.1 M AgNO3 solution is

The carbon–based reduction method is NOT used for the extraction of

The correct statement(s) about O3 is(are)

P and Q, respectively, are the sodium salts of

R, S and T respectively, are

The unbalanced chemical reactions given in List I show missing reagent or condition (?) which are provided in List II. Match List I with List II and select the correct answer using the code given below the lists :

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The precipitate P contains

The coloured solution S contains

The succeeding operations that enable this transformation of states are

The pair of isochoric processes among the transformation of states is

Two lines \({L_1}:x = 5,{y \over {3 - \alpha }} = {z \over { - 2}}\) and \({L_2}:x = \alpha ,{y \over { - 1}} = {z \over {2 - \alpha }}\) are coplanar. Then \(\alpha\) can take value(s)

Consider the lines \({L_1}:{{x - 1} \over 2} = {y \over { - 1}} = {{z + 3} \over 1},{L_2} : {{x - 4} \over 1} = {{y + 3} \over 1} = {{z + 3} \over 2}\) and the planes \({P_1}:7x + y + 2z = 3,{P_2} = 3x + 5y - 6z = 4.\) Let \(ax+by+cz=d\) be...

The function \(f(x) = 2\left| x \right| + \left| {x + 2} \right| - \left| {\left| {x + 2} \right| - 2\left| x \right|} \right|\) has a local minimum or a local maximum at x =

Let \(f:\left[ {0,1} \right] \to R\) (the set of all real numbers) be a function. Suppose the function \(f\) is twice differentiable, \(f(0) = f(1)=0\) and satisfies $$f''\left( x \right) - 2f'\left( x \right) + f\left( x \right) \ge .{e^x}...

Let \(f:\left[ {0,1} \right] \to R\) (the set of all real numbers) be a function. Suppose the function \(f\) is twice differentiable, \(f(0) = f(1)=0\) and satisfies $$f''\left( x \right) - 2f'\left( x \right) + f\left( x \right) \ge .{e^x}...

Circle (s) touching x-axis at a distance 3 from the origin and having an intercept of length \(2\sqrt 7\) on y-axis is (are)

Let $\omega=\frac{\sqrt{3}+i}{2}$ and $P=\left\{\omega^n: n=1,2,3, \ldots\right\}$. Further
$\mathrm{H}_1=\left\{z \in \mathrm{C}: \operatorname{Re} z<\frac{1}{2}\right\}$ and
$\mathrm{H}_2=\left\{z \in \mathrm{C}: \operatorname{Re} z<\fr...

Let \(S = {S_1} \cap {S_2} \cap {S_3}\), where \({S_1} = \left\{ {z \in C:\left| z \right| < 4} \right\},{S_2} = \left\{ {z \in C:{\mathop{\rm Im}\nolimits} \left[ {{{z - 1 + \sqrt 3 i} \over {1 - \sqrt 3 i}}} \right] > 0} \right\}\) and $$...

Let \(S = {S_1} \cap {S_2} \cap {S_3}\), where \({S_1} = \left\{ {z \in C:\left| z \right| < 4} \right\},{S_2} = \left\{ {z \in C:{\mathop{\rm Im}\nolimits} \left[ {{{z - 1 + \sqrt 3 i} \over {1 - \sqrt 3 i}}} \right] > 0} \right\}\) and $$...

Match List \(I\) with List \(II\) and select the correct answer using the code given below the lists:
List \(I\)
\(P.\)\(\,\,\,\,\,\) $${\left( {{1 \over {{y^2}}}{{\left( {{{\cos \left( {{{\tan }^{ - 1}}y} \right) + y\sin \left( {{{\tan }...

\(a \in R\) (the set of all real numbers), a \(\ne\) \(-\)1, \(\mathop {\lim }\limits_{n \to \infty } {{({1^a} + {2^a} + ... + {n^a})} \over {{{(n + 1)}^{a - 1}}[(na + 1) + (na + 2) + ... + (na + n)]}} = {1 \over {60}}\), Then a = ?

Let \(\omega\) be a complex cube root of unity with \(\omega\) \(\ne\) 1 and P = [pij] be a n \(\times\) n matrix with pij = \(\omega\)i + j. Then P2 \(\ne\) 0, when n = ?

Let \(PQ\) be a focal chord of the parabola \({y^2} = 4ax\). The tangents to the parabola at \(P\) and \(Q\) meet at a point lying on the line \(y=2x+a\), \(a>0\).
Length of chord \(PQ\) is

A line \(L:y=mx+3\) meets \(y\)-axis at R\((0, 3)\) and the arc of the parabola \({y^2} = 16x,\) \(0 \le y \le 6\) at the point \(F\left( {{x_0},{y_0}} \right)\). The tangent to the parabola at \(F\left( {{x_0},{y_0}} \right)\) intersects t...

Let \(PQ\) be a focal chord of the parabola \({y^2} = 4ax\). The tangents to the parabola at \(P\) and \(Q\) meet at a point lying on the line \(y=2x+a\), \(a>0\).
If chord \(PQ\) subtends an angle \(\theta\) at the vertex of $${y^2} = 4a...

A box \({B_1}\) contains \(1\) white ball, \(3\) red balls and \(2\) black balls. Another box \({B_2}\) contains \(2\) white balls, \(3\) red balls and \(4\) black balls. A third box \({B_3}\) contains \(3\) white balls, \(4\) red balls and...

A box \({B_1}\) contains \(1\) white ball, \(3\) red balls and \(2\) black balls. Another box \({B_2}\) contains \(2\) white balls, \(3\) red balls and \(4\) black balls. A third box \({B_3}\) contains \(3\) white balls, \(4\) red balls and...

In a triangle \(PQR\), \(P\) is the largest angle and \(\cos P = {1 \over 3}\). Further the incircle of the triangle touches the sides \(PQ\), \(QR\) and \(RP\) at \(N,L\) and \(M\) respectively, such that the lengths of \(PN, QL\) and $$RM...

If \({3^x}\, = \,{4^{x - 1}},\) then \(x\, =\)

match List \(I\) with List \(II\) and select the correct answer using the code given below the lists:
\(\,\,\,\,\) \(\,\,\,\,\) \(\,\,\,\,\) List \(I\)
(P.)\(\,\,\,\,\) Volume of parallelopiped determined by vectors $$\overrightarrow a ,\...

In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 10. If the power of the consumers has to be supplied at 200 V, the ratio of the num...

The radius of the orbit of an electron in a hydrogen-like atom is 4.5a0, where a0 is the Bohr radius. Its orbital angular momentum is \({{3h} \over {2\pi }}\). It is given that h is Planck constant and R is Rydberg constant. The possible wa...

The correct statement is

The kinetic energy (in keV) of the alpha particle, when the nucleus \(_{84}^{210}Po\) at rest undergoes alpha decay, is

Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists :

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If the direct transmission method with a cable of resistance 0.4 \(\Omega\) km\(-\)1 is used, the power dissipation (in %) during transmission is

Using the expression \(2d\sin \theta = \lambda\), one calculates the values of d by measuring the corresponding angles \(\theta\) in
the range 0 to 90o. The wavelength \(\lambda\) is exactly known and the error in \(\theta\) is constan...

Two non-conducting spheres of radii \({R_1}\) and \({R_2}\) and carrying uniform volume charge densities \(+ \rho\) and \(- \rho ,\) respectively, are placed such that they partially overlap, as shown in the figure. At all points in the ...

A right-angled prism of refractive index \(\mu\)1 is placed in a rectangular block of refractive index \(\mu\)2, which is surrounded by a medium of refractive index \(\mu\)3, as shown in the figure. A ray of light e enters the rectangular b...

Two bodies, each of mass M, are kept fixed with a separation \(2L\). A particle of mass m is projected from
the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The
correct statement(s)...