JEE Advanced 2015 Paper 2 Offline

The number of hydroxyl group(s) in Q is ___________.

Among the following the number of reactions that produces benzaldehyde is _________.

In the following reactions

Compound X is

In the following reactions

The major compound Y is

A closed vessel with rigid walls contains 1 mol of \({}_{92}^{238}U\) and 1 mol of air at 298 K. Considering complete decay of \({}_{92}^{238}U\) to \({}_{82}^{206}Pb\), the ratio of the final pressure to the initial pressure of the system ...

In dilute aqueous H2SO4, the complex diaquodioxalatoferrate(II) is oxidized by \(MnO_4^-\). For this reaction,
the ratio of the rate of change of [H+] to the rate of change of \([MnO_4^-]\) is

In the following reactions, the major product W is

In the complex acetylbromidodicarbonylbis(triethylphosphine) iron(II), the number of Fe-C bond(s) is ___________.

Among the complex ions, [Co(NH2-CH2-CH2-NH2)2Cl2]+, [CrCl2(C2O4)2]3\(-\), [Fe(H2O)4)OH)2]+, [Fe(NH3)2(CN)4]\(-\), [Co(NH2-CH2-CH2-NH2)2(NH3)Cl]2+ and [Co(NH3)4(H2O)Cl]2+, the number of complex ions that shows cis-trans isomerism is ________...

The pairs of ions where BOTH the ions are precipitated upon passing H2S gas in presence of dilute HCl, is(are)

The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of a weak acid HY (0.10 M). If \(\lambda _{{x^ - }}^0 \approx \lambda _{{y^ - }}^0\) the difference in their pKa v...

One mole of a monoatomic real gas satisfies the equation p(V \(-\) b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

In the following reactions, the product S is

The major product U in the following reactions is

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When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7o C was measured for the beaker and its contents (Expt. 1). Because the enthalpy of neutralizat...

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When 100 mL of 1.0 M KCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7o C was measured for the beaker and its contents (Expt. 1). Because the enthalpy of neutralizat...

Three moles of B2H6 are completely reacted with methanol. The number of moles of boron containing product formed is ____________.

The correct statements regarding (i) HClO, (ii) HClO2, (iii) HClO3 and (iv) HClO4 is (are)

Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain termination, respectively, are

When O2 is adsorbed on a metallic surface, electron transfer occurs from the metal to O2. The true statement(s) regarding this adsorption is(are)

Let \(f, g :\) \(\left[ { - 1,2} \right] \to R\) be continuous functions which are twice differentiable on the interval \((-1, 2)\). Let the values of f and g at the points \(-1, 0\) and \(2\) be as given in the following table:

.tg {bord...

Let \(F:R \to R\) be a thrice differentiable function. Suppose that
\(F\left( 1 \right) = 0,F\left( 3 \right) = - 4\) and \(F\left( x \right) < 0\) for all \(x \in \left( {{1 \over 2},3} \right).\) Let $$f\left( x \right) = xF\left( x \ri...

Let \(f:R \to R\) be a continuous odd function, which vanishes exactly at one point and \(f\left( 1 \right) = {1 \over {2.}}\) Suppose that \(F\left( x \right) = \int\limits_{ - 1}^x {f\left( t \right)dt}\) for all $$x \in \,\,\left[ { - 1...

For any integer k, let \({a_k} = \cos \left( {{{k\pi } \over 7}} \right) + i\,\,\sin \left( {{{k\pi } \over 7}} \right)\), where \(i = \sqrt { - 1} \,\). The value of the expression $${{\sum\limits_{k = 1}^{12} {\left| {{\alpha _{k + 1}} -...

Let \(f'\left( x \right) = {{192{x^3}} \over {2 + {{\sin }^4}\,\pi x}}\) for all \(x \in R\,\,\) with \(f\left( {{1 \over 2}} \right) = 0\).
If \(m \le \int\limits_{1/2}^1 {f\left( x \right)dx \le M,}\) then the possible values of \(m\) an...

If \(\alpha = \int\limits_0^1 {\left( {{e^{9x + 3{{\tan }^{ - 1}}x}}} \right)\left( {{{12 + 9{x^2}} \over {1 + {x^2}}}} \right)} dx\) where \({\tan ^{ - 1}}x\) takes only principal values, then the value of $$\left( {{{\log }_e}\left| {1 ...

The option(s) with the values of a and \(L\) that satisfy the following equation is (are)
$$${{\int\limits_0^{4\pi } {{e^t}\left( {{{\sin }^6}at + {{\cos }^4}at} \right)dt} } \over {\int\limits_0^\pi {{e^t}\left( {{{\sin }^6}at + {{\cos }...

Let \(f\left( x \right) = 7{\tan ^8}x + 7{\tan ^6}x - 3{\tan ^4}x - 3{\tan ^2}x\) for all \(x \in \left( { - {\pi \over 2},{\pi \over 2}} \right).\)
Then the correct expression(s) is (are)

Let \(F:R \to R\) be a thrice differentiable function. Suppose that
\(F\left( 1 \right) = 0,F\left( 3 \right) = - 4\) and \(F'\left( x \right) < 0\) for all \(x \in \left( {{1 \over 2},3} \right).\) Let $$f\left( x \right) = xF\left( x \r...

Let \({E_1}\) and \({E_2}\) be two ellipses whose centres are at the origin. The major axes of \({E_1}\) and \({E_2}\) lie along the \(x\)-axis and the \(y\)-axis, respectively. Let \(S\) be the circle $${x^2} + {\left( {y - 1} \right)^2} ...

Consider the hyperbola \(H:{x^2} - {y^2} = 1\) and a circle \(S\) with center \(N\left( {{x_2},0} \right)\). Suppose that \(H\) and \(S\) touch each other at a point \(P\left( {{x_1},{y_1}} \right)\) with \({{x_1} > 1}\) and \({{y_1} > 0}\)...

If \(\alpha\) \(= 3{\sin ^{ - 1}}\left( {{6 \over {11}}} \right)\) and \(\beta = 3{\cos ^{ - 1}}\left( {{4 \over 9}} \right),\) where the inverse trigonimetric functions take only the principal values, then the correct options(s) is (are...

Let m and n be two positive integers greater than 1. If
\($\mathop {\lim }\limits_{\alpha \to 0} \left( {{{{e^{\cos \left( {{\alpha ^n}} \right)}} - e} \over {{\alpha ^m}}}} \right) = - \left( {{e \over 2}} \right)\)$
then the value of $$...

Suppose that the foci of the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 5} = 1\) are \(\left( {{f_1},0} \right)\) and \(\left( {{f_2},0} \right)\) where \({{f_1} > 0}\) and \({{f_2} < 0}\). Let \({P_1}\) and \({P_2}\) be two parabolas wit...

Let \({n_1}\) and \({n_2}\) be the number of red and black balls, respectively, in box \({\rm I}\). Let \({n_3}\) and \({n_4}\) be the number of red and black balls, respectively, in box \({\rm I}{\rm I}.\)
One of the two boxes, box $${\rm...

Let \({n_1}\) and \({n_2}\) be the number of red and black balls, respectively, in box \({\rm I}\). Let \({n_3}\) and \({n_4}\) be the number of red and black balls, respectively, in box \({\rm I}{\rm I}.\)
A ball is drawn at random from b...

Let \(S\) be the set of all non-zero real numbers \(\alpha\) such that the quadratic equation \(\alpha {x^2} - x + \alpha = 0\) has two distinct real roots \({x_1}\) and \({x_2}\) satisfying the inequality $$\left| {{x_1} - {x_2}} \right|...

Suppose that all the terms of an arithmetic progression (A.P) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130 and 140, then the co...

The coefficient of \({x^9}\) in the expansion of (1 + x) (1 + \({x^2)}\) (1 + \({x^3}\)) ....\((1 + {x^{100}})\) is

Suppose that \(\overrightarrow p ,\overrightarrow q\) and \(\overrightarrow r\) are three non-coplanar vectors in \({R^3}\). Let the components of a vector \(\overrightarrow s\) along \(\overrightarrow p ,\) \(\overrightarrow q\) and $$...

For a radioactive material, its activity A and rate of change of its activity R are defined as \(A = - {{dN} \over {dt}}\) and \(R = - {{dA} \over {dt}}\), where N(t) is the number of nuclei at time t. Two radioactive source P(mean life $...

A fission reaction is given by \(_{92}^{236}U \to _{54}^{140}Xe + _{38}^{94}Sr + x + y\), where x and y are two particles. Considering \(_{92}^{236}U\) to be at rest, the kinetic energies of the products are denoted by $${K_{Xe}},{K_{Sr}},{...

A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivities (\(\varepsilon\)1 = 2 and \(\varepsilon\)2 = 4) are introduced between the two...

In the following circuit, the current through the resistor R(=2\(\Omega\)) is I amperes. The value of I is :

An electron in an excited state of Li2+ ion has angular momentum \({{3h} \over {2\pi }}\). The de Broglie wavelength of the electron in this state is p\(\pi\)a0 (where a0 is the Bohr radius). The value of p is

In terms of potential difference V, electric current I, permittivity \({\varepsilon _0}\), permeability \({\mu _0}\) and speed of light c,
the dimensionally correct equation(s) is(are) :

Consider a uniform spherical charge distribution of radius \({R_1}\) centred at the origin \(O.\) In this distribution, a spherical cavity of radius \({R_2},\) centred at \(P\) with distance \(OP=a\) \(= {R_1} - {R_2}\) (see figure) is mad...

For two structures namely S1 with n1 = \({{\sqrt {45} } \over 4}\) and n2 = \({3 \over 2}\), and S2 with n1 = \({8 \over 5}\) and n2 = \({7 \over 5}\) and taking the refractive index of water to be \({4 \over 3}\) and that to air to be 1, t...

If two structures of same cross-sectional area, but different numeral apertures NA1 and NA2 (NA2 < NA1) are joined longitudinally, the numerical aperture of the combined structure is

A monochromatic beam of light is incident at 60\(^\circ\) on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle \(\theta\)(n) with the normal (see figure). For n = \(\sqrt 3\) the valu...