JEE Advanced 2015 Paper 1 Offline

The number of resonance structure for N is _________.

The major product of the following reaction is

The total number of stereoisomers that can exist for M is ___________.

The structure of D-(+)-glucose is

The structure of L-(\(-\))-glucose is

Among the triatomic molecules/ions, BeCl2, \(N_3^-\), N2O, \(NO_2^+\), O3, SCl2, \(ICl_2^-\), \(I_3^-\) and XeF2, the total number of linear molecule(s)/ion(s) where the hybridization of the central atom does not have contribution from the ...

The % yield of ammonia as a function of time in the reaction
N2(g) + 3H2(g) \(\rightleftharpoons\) 2NH3(g), \(\Delta\)H < 0 at (P, T1) is given below:

If this reactions is conducted at (P, T2), with T2 > T1, the % yield of ammonia as a fun...

The major product of the reaction is

For the octahedral complexes of Fe3+ in SCN\(-\) (thiocyana-to-S) and in CN\(-\) ligand environments, the difference between the spin-only magnetic moments in Bohr magnetons (when approximated to the nearest integer) is __________.
[Atomic ...

The correct statements about Cr2+ and Mn3+ is(are) (Atomic numbers of Cr = 24 and Mn = 25)

All the energy released from the reaction \(X \to Y, \Delta _tG^o\) = -193 kJ mol-1 is used for oxidizing M+ as M+ \(\to\) M3+ + 2e-, Eo = -0.25 V
Under standard conditions, the number of moles of M+ oxidized when one mole of X is convert...

Compound(s) that on hydrogenation produce(s) optically inactive compound(s) is(are)

In the following reaction, the major product is

Match the anionic species given in Column-I that are present in the ore(s) given in Column-II


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Copper is purified by electrolytic refining of blister copper. The correct statement(s) about this process
is(are)

The number of lone pairs of electrons in N2O3 is ___________.

Fe3+ is reduced to Fe2+ by using

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are

If the freezing point of a 0.01 molal aqueous solution of a cobalt (III) chloride-ammonia complex(which
behaves as a strong electrolyte) is – 0.0558oC, the number of chloride(s) in the coordination sphere of the
complex is [Kf of water = 1....

Not considering the electronic spin, the degeneracy of the second excited state( n = 3) of H atom is 9, while
the degeneracy of the second excited state of H– is ___________.

Match the thermodynamics processes given under column I with expression given under column II
Column I
(A) Freezing water at 273 K and 1 atm
(B) Expansion of 1 mol of an ideal gas into a vacuum under isolated conditions.
(C) Mixing of equal...

In \({R^3},\) consider the planes \(\,{P_1}:y = 0\) and \({P_2}:x + z = 1.\) Let \({P_3}\) be the plane, different from \({P_1}\) and \({P_2}\), which passes through the intersection of \({P_1}\) and \({P_2}.\) If the distance of the point ...

In \({R^3},\) let \(L\) be a straight lines passing through the origin. Suppose that all the points on \(L\) are at a constant distance from the two planes \({P_1}:x + 2y - z + 1 = 0\) and \({P_2}:2x - y + z - 1 = 0.\) Let \(M\) be the loc...

A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of \(V\) \(m{m^3}\), has a \(2\) mm thick solid wall and is open at the top. The bottom of the container is a soli...

Let \(F\left( x \right) = \int\limits_x^{{x^2} + {\pi \over 6}} {2{{\cos }^2}t\left( {dt} \right)}\) for all \(x \in R\) and \(f:\left[ {0,{1 \over 2}} \right] \to \left[ {0,\infty } \right]\) be a continuous function. For $$a \in \left[ ...

Let \(f:R \to R\) be a function defined by \(f\left( x \right) = \left\{ {\matrix{ {\left[ x \right],} & {x \le 2} \cr {0,} & {x > 2} \cr } } \right.\) where \(\left[ x \right]\) is the greatest integer less than or equal to $$...

Let \(y(x)\) be a solution of the differential equation \(\left( {1 + {e^x}} \right)y' + y{e^x} = 1.\)
If \(y(0)=2\), then which of the following statement is (are) true?

Consider the family of all circles whose centres lie on the straight line \(y=x,\) If this family of circle is represented by the differential equation \(Py'' + Qy' + 1 = 0,\) where \(P, Q\) are functions of \(x,y\) and \(y'\) $$\left( {her...

Let \(f(x) = \sin \left( {{\pi \over 6}\sin \left( {{\pi \over 2}\sin x} \right)} \right)\) for all \(x \in R\) and g(x) = \({{\pi \over 2}\sin x}\) for all x\(\in\)R. Let \((f \circ g)(x)\) denote f(g(x)) and \((g \circ f)(x)\) denote g...

Let \(g:R \to R\) be a differentiable function with \(g(0) = 0\), \(g'(0) = 0\) and \(g'(1) \ne 0\). Let
\(f(x) = \left\{ {\matrix{ {{x \over {|x|}}g(x),} & {x \ne 0} \cr {0,} & {x = 0} \cr } } \right.\)
and \(h(x) = {e^{|x|}}\)...

Let X and Y be two arbitrary, 3 \(\times\) 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 \(\times\) 3, non-zero, symmetric matrix. Then which of the following matrices is(are) skew symmetric?

Which of the following values of \(\alpha\) satisfy the equation
$$\left| {\matrix{
{{{(1 - \alpha )}^2}} & {{{(1 + 2\alpha )}^2}} & {{{(1 + 3\alpha )}^2}} \cr
{{{(2 + \alpha )}^2}} & {{{(2 + 2\alpha )}^2}} & {{{(2 + 3\alpha )}^2}} ...

If the normals of the parabola \({y^2} = 4x\) drawn at the end points of its latus rectum are tangents to the circle \({\left( {x - 3} \right)^2} + {\left( {y + 2} \right)^2} = {r^2}\), then the value of \({r^2}\) is

Let \(P\) and \(Q\) be distinct points on the parabola \({y^2} = 2x\) such that a circle with \(PQ\) as diameter passes through the vertex \(O\) of the parabola. If \(P\) lies in the first quadrant and the area of the triangle $$\Delta OPQ$...

Let the curve \(C\) be the mirror image of the parabola \({y^2} = 4x\) with respect to the line \(x+y+4=0\). If \(A\) and \(B\) are the points of intersection of \(C\) with the line \(y=-5\), then the distance between \(A\) and \(B\) is

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that ...

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least \(0.96,\) is

Match the following :

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The number of distinct solutions of the equation
\({5 \over 4}{\cos ^2}\,2x + {\cos ^4}\,x + {\sin ^4}\,x + {\cos ^6}\,x + {\sin ^6}\,x\, = \,2\) in the interval \(\left[ {0,\,2\pi } \right]\) is

Let \(\Delta PQR\) be a triangle. Let \(\vec a = \overrightarrow {QR} ,\vec b = \overrightarrow {RP}\) and \(\overrightarrow c = \overrightarrow {PQ} .\) If $$\left| {\overrightarrow a } \right| = 12,\,\,\left| {\overrightarrow b } \right...

Match the following :




Column I

Column II







(A)

In $ \mathbb{R}^2 $, if the magnitude of the projection vector of the vector

$ \alpha \hat{i} + \beta \hat{j} $ on

$ \sqrt{3}\hat{i} + \h...

Match the nuclear processes given in Column I with the
appropriate option(s) in Column II:

Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n is (hc = 1242 eV nm)

A nuclear power plant supplying electrical power to a village uses a radioactive material of half life T years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is 12.5 % of the electri...

In an aluminium (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure. The electrical resistivities of Al and Fe are 2.7 \(\times\) 10\(-\)8\(\Omega\) m and 1.0 \(\times\) 10\(-\)7 $...

For photo-electric effect with incident photon wavelength \(\lambda\), the stopping potential is V0. Identify the correct variation(s) of V0 with \(\lambda\) and \({1 \over \lambda }\).

An infinitely long uniform line charge distribution of charge per unit length \(\lambda\) lies parallel to the y-axis in the y-z plane at \(z = {{\sqrt 3 } \over 2}\)a (see figure). If the magnitude of the flux of the electric field through...

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density \(\lambda\) are kept parallel to each other. In their resulting electric field, point charges \(q\) and $$-q$...

Two identical glass rods S1 and S2 (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligne...

Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index = 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirr...

A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches
its maximum height, its acceleration due to the planet’s gravity is \({\left( {{1 \over 4}} \right)^{th}}\) of its value at the sur...