JEE Advanced 2014 Paper 2 Offline

For the identification of \(\beta\)-naphthol using dye test, it is necessary to use

The acidic hydrolysis of ether (X) shown below is fastest when

The major product in the following reaction is

Different possible thermal decomposition pathways for peroxyesters are shown below. Match each pathway from List I with an appropriate structure from List II and select the correct answer using the code given below the lists.

Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure.

The correct order of their boiling point is

Match the orbital overlap figures shown in List I with the description given in List II and select the correct answer using the code given below the lists.

Assuming 2s – 2p mixing is NOT operative, the paramagnetic species among the following is

The value of d in cm (shown in the figure), as estimated from Graham's law, is

The experimental value of d is found to be smaller than the estimate obtained using Graham's law. This is due to

For the elementary reaction M \(\to\) N, the rate of disappearance of M increases by a factor of 8 upon
doubling the concentration of M. The order of the reaction with respect to M is

Match the four starting materials (P, Q, R, S) given in List I with the corresponding reaction schemes (I, II, III, IV) provided in List II and select the correct answer using the code given below the lists.

Match each coordination compound in List I with an appropriate pair of characteristics from List II and select the correct answer using the code given below the lists.
{en = H2NCH2CH2NH2; atomic numbers : Ti = 22, Cr = 24; Co = 27; Pt = 78}...

The product X is

The correct statement with respect to product Y is

Hydrogen peroxide in its reaction with KIO4 and NH2OH respectively, is acting as a

The product formed in the reaction of SOCl2 with white phosphorus is

Under ambient conditions, the total number of gases released as products in the final step of the reaction scheme shown below is

M1, Q and R, respectively, are

Reagent S is

For the process
H2O(l) \(\to\) H2O(g)
at T = 100oC and 1 atmosphere pressure, the correct choice is

Let \({z_k}\) = \(\cos \left( {{{2k\pi } \over {10}}} \right) + i\,\,\sin \left( {{{2k\pi } \over {10}}} \right);\,k = 1,2....,9\)
List-I
P. For each \({z_k}\) = there exits as \({z_j}\) such that \({z_k}\).\({z_j}\) = 1
Q. T...

Given that for each \(a \in \left( {0,1} \right),\,\,\,\mathop {\lim }\limits_{h \to {0^ + }} \,\int\limits_h^{1 - h} {{t^{ - a}}{{\left( {1 - t} \right)}^{a - 1}}dt}\) exists. Let this limit be \(g(a).\) In addition, it is given that the ...

Given that for each \(a \in \left( {0,1} \right),\,\,\,\mathop {\lim }\limits_{h \to {0^ + }} \,\int\limits_h^{1 - h} {{t^{ - a}}{{\left( {1 - t} \right)}^{a - 1}}dt}\) exists. Let this limit be \(g(a).\) In addition, it is given that the ...

List - \(I\)
P.\(\,\,\,\,\) The number of polynomials \(f(x)\) with non-negative integer coefficients of degree \(\le 2\), satisfying \(f(0)=0\) and \(\int_0^1 {f\left( x \right)dx = 1,}\) is
Q.\(\,\,\,\,\) The number of points in the in...

The following integral \(\int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\left( {2\cos ec\,\,x} \right)}^{17}}dx}\) is equal to

The function \(y=f(x)\) is the solution of the differential equation
\({{dy} \over {dx}} + {{xy} \over {{x^2} - 1}} = {{{x^4} + 2x} \over {\sqrt {1 - {x^2}} }}\,\) in \((-1,1)\) satisfying \(f(0)=0\). Then $$\int\limits_{ - {{\sqrt 3 } \ove...

Let \(f:\left[ {0,2} \right] \to R\) be a function which is continuous on \(\left[ {0,2} \right]\) and is differentiable on \((0,2)\) with \(f(0)=1\). Let
\(F\left( x \right) = \int\limits_0^{{x^2}} {f\left( {\sqrt t } \right)dt}\) for $...

The common tangents to the circle \({x^2} + {y^2} = 2\) and the parabola \({y^2} = 8x\) touch the circle at the points \(P, Q\) and the parabola at the points \(R\), \(S\). Then the area of the quadrilateral \(PQRS\) is

Let f1 : R \(\to\) R, f2 : [0, \(\infty\)) \(\to\) R, f3 : R \(\to\) R, and f4 : R \(\to\) [0, \(\infty\)) be defined by
$${f_1}\left( x \right) = \left\{ {\matrix{
{\left| x \right|} & {if\,x < 0,} \cr
{{e^x}} & {if\,x \g...

Match List \(I\) with List \(II\) and select the correct answer using the code given below the lists:
\(\,\,\,\,\) \(\,\,\,\,\) \(\,\,\,\,\) List-\(I\)
(P.)\(\,\,\,\,\) Let $$y\left( x \right) = \cos \left( {3{{\cos }^{ - 1}}x} \right),x \i...

Coefficient of \({x^{11}}\) in the expansion of \({\left( {1 + {x^2}} \right)^4}{\left( {1 + {x^3}} \right)^7}{\left( {1 + {x^4}} \right)^{12}}\) is

Let \(a, r, s, t\) be nonzero real numbers. Let \(P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)\) and \(S\,\,\left( {a{s^2},2as} \right)\) be distinct points on the parabola \({y^2} = 4ax\). Suppose that $$PQ...

Let \(a, r, s, t\) be nonzero real numbers. Let \(P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)\) and \(S\,\,\left( {a{s^2},2as} \right)\) be distinct points on the parabola \({y^2} = 4ax\). Suppose that $$PQ...

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1...

Box \(1\) contains three cards bearing numbers \(1,2,3;\) box \(2\) contains five cards bearing numbers \(1,2,3,4,5;\) and box \(3\) contains seven cards bearing numbers \(1,2,3,4,5,6,7.\) A card is drawn from each of the boxes. Let $${x_i}...

Box \(1\) contains three cards bearing numbers \(1,2,3;\) box \(2\) contains five cards bearing numbers \(1,2,3,4,5;\) and box \(3\) contains seven cards bearing numbers \(1,2,3,4,5,6,7.\) A card is drawn from each of the boxes. Let $${x_i}...

Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

In a triangle the sum of two sides is \(x\) and the product of the same sides is \(y\). If \({x^2} - {c^2} = y\), where \(c\) is the third side of the triangle, then the ratio of the in radius to the circum-radius of the triangle is

The quadratic equation \(p(x)\) \(= 0\) with real coefficients has purely imaginary roots. Then the equation \(p(p(x))=0\) has

For \(x \in \left( {0,\pi } \right),\) the equation \(\sin x + 2\sin 2x - \sin 3x = 3\) has

If \(\lambda\)Cu is the wavelength of K\(\alpha\) X-ray line of copper (atomic number 29) and \(\lambda\)Mo is the wavelength of the K\(\alpha\) X-ray line of molybdenum (atomic number 42), then the ratio \(\lambda\)Cu/\(\lambda\)Mo is clos...

During an experiment with a metre bridge, the galvanometer shall a null point when the jockey is pressed at 40.0 cm using a standard resistance of 90\(\Omega\), as shown in the figure. The least count of the scale used in the meter bridge i...

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u1 and u2, respectively. If the ratio u1 : u2 = 2 : 1 and hc = 1240 eV n...

Four charges Q1, Q2, Q3 and Q4 of same magnitude are fixed along the x axis at x = \(-\)2a, \(-\)a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charg...

Charges \(Q,\) \(2Q\) and \(4Q\) are uniformly distributed in three dielectric solid spheres \(1,2\) and \(3\) of radii \(R/2,R\) and \(2R\) respectively, as shown in figure. If magnitude of the electric fields at point \(P\) at a distance ...

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the below figure. It is found that the light emerging from the block to...

Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select...

A planet of radius R = \({1 \over {10}} \times\) (radius of Earth) has the same mass density as Earth. Scientists dig a well of
depth \({R \over 5}\)
on it and lower a wire of the same length and of linear mass density 10-3 kg m-1 into it....

Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be

Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be