JEE Advanced 2014 Paper 1 Offline

The reactivity of compound Z with different halogens under appropriate conditions is given belowThe observed pattern of electrophilic substitution can be explained by

Consider all possible isomeric ketones including stereoisomers of MW = 100. All these isomers are independently reacted with NaBH4 (Note : stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s...

The correct combination of names for isomeric alcohols with molecular formula C4H10O is/are

The total number(s) of stable conformers with non-zero dipole moment for the following compound is(are)

The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the peptide shown below is

Hydrogen bonding plays a central role in the following phenomena

A list of species having the formula XZ4 is given below.
XeF4, SF4 ,SiF4, \(BF_4^-\), \(BrF_4^-\), [Cu(NH3)4]2+, [FeCl4]2-, [CoCl4]2- and [PtCl4]2-
Defining shape on the basis of the location of X and Z atoms, the total number of species ha...

In the reaction shown below, the major product(s) formed is/are

The pair(s) of reagents that yield paramagnetic species is/are

Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi2S3 and SnS2 the total number of black coloured sulphides is

Upon heating with Cu2S, the reagent(s) that give copper metal is/are

In a galvanic cell, the salt bridge

An ideal gas in thermally insulated vessel at internal pressure = p1, volume = V1 and absolute temperature = T1 expands irreversibly against zero external pressure, as shown in the diagram.The final internal pressure, volume and absolute te...

The correct statement(s) for orthoboric acid is/are

For the reaction,\({I^ - } + ClO_3^ - + {H_2}S{O_4} \to C{l^ - } + HSO_4^ - + {I_2}\)the correct statement(s) in the balanced equation is/are

Consider the following list of reagents, acidified K2Cr2O7, alkaline KMnO4, CuSO4, H2O2, Cl2, O3, FeCl3, HNO3 and Na2S2O3. The total number of reagents that can oxidise aqueous iodide to iodine is

MX2 dissociates in M2+ and X- ions in an aqueous solution, with a degree of dissociation (\(\alpha\)) of 0.5. The
ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of
freezing point in...

If the value of Avogadro number is 6.023 \(\times\) 1023 mol-1 and the value of Boltzmann constant is 1.380 \(\times\) 10-23 J K-1, then the number of significant digits in the calculated value of the universal gas constant is

A compound H2X with molar weight of 80g is dissolved in a solvent having density of 0.4 gml–1 . Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is

In an atom, the total number of electrons having quantum numbers n = 4, |ml| = 1 and ms = –1/2 is

From a point \(P\left( {\lambda ,\lambda ,\lambda } \right),\) perpendicular \(PQ\) and \(PR\) are drawn respectively on the lines \(y=x, z=1\) and \(y=-x, z=-1.\) If \(P\) is such that \(\angle QPR\) is a right angle, then the possible val...

The slope of the tangent to the curve \({\left( {y - {x^5}} \right)^2} = x{\left( {1 + {x^2}} \right)^2}\) at the point \((1, 3)\) is

A circle S passes through the point (0, 1) and is orthogonal to the circles \({(x - 1)^2}\, + \,{y^2} = 16\,\,and\,\,{x^2}\, + \,{y^2} = 1\). Then

Let a \(\in\) R and f : R \(\to\) R be given by f(x) = x5 \(-\) 5x + a. Then,

The value of \(\int\limits_0^1 {4{x^3}\left\{ {{{{d^2}} \over {d{x^2}}}{{\left( {1 - {x^2}} \right)}^5}} \right\}dx}\) is

Let \(f:\left( {0,\infty } \right) \to R\) be given by \(f\left( x \right)\)= \(\int\limits_{{1 \over x}}^x {{{{e^{ - \left( {t + {1 \over t}} \right)}}} \over t}} dt\). Then

For every pair of continuous function f, g : [0, 1] \(\to\) R such that max {f(x) : x \(\in\) [0, 1]} = max {g(x) : x \(\in\) [0, 1]}. The correct statement(s) is (are)

Let \(f:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R\) be given by \(f(x) = {[\log (\sec x + \tan x)]^3}\). Then,

Let f : [0, 4\(\pi\)] \(\to\) [0, \(\pi\)] be defined by f(x) = cos\(-\)1 (cos x). The number of points x \(\in\) [0, 4\(\pi\)] satisfying the equation \(f(x) = {{10 - x} \over {10}}\) is

Let \(f:(a,b) \to [1,\infty )\) be a continuous function and g : R \(\to\) R be defined as $$g(x) = \left\{ {\matrix{
0 & , & {x < a} \cr
{\int_a^x {f(t)dt} } & , & {a \le x \le b} \cr
{\int_a^b {f(t)dt} } & , & {x > b} \cr

...

The largest value of the non-negative integer a for which \(\mathop {\lim }\limits_{x \to 1} {\left\{ {{{ - ax + \sin (x - 1) + a} \over {x + \sin (x - 1) - 1}}} \right\}^{{{1 - x} \over {1 - \sqrt x }}}} = {1 \over 4}\) is

Let f : R \(\to\) R and g : R \(\to\) R be respectively given by f(x) = | x | + 1 and g(x) = x2 + 1. Define h : R \(\to\) R by $$h(x) = \left\{ {\matrix{
{\max \{ f(x),g(x)\} ,} & {if\,x \le 0.} \cr
{\min \{ f(x),g(x)\} ,} & {if\,x ...

Let M be a 2 \(\times\) 2 symmetric matrix with integer entries. Then, M is invertible, if

Let M and N be two 3 \(\times\) 3 matrices such that MN = NM. Further, if M \(\ne\) N2 and M2 = N4, then

Let \({n \ge 2}\) be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue lin...

Let \({n_1}\, < {n_2}\, < \,{n_3}\, < \,{n_4}\, < {n_5}\) be positive integers such that \({n_1}\, + {n_2}\, + \,{n_3}\, + \,{n_4}\, + {n_5}\) = 20. Then the number of such destinct arrangements $$\,({n_1}\,,\,{n_2},\,\,{n_3},\,\,{n_4}\,,{n...

Let a, b, c be positive integers such that \({b \over a}\) is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of \({{{a^2} + a - 14} \over {a + 1}}\) is

For a point \(P\) in the plane, Let \({d_1}\left( P \right)\) and \({d_2}\left( P \right)\) be the distance of the point \(P\) from the lines \(x - y = 0\) and \(x + y = 0\) respectively. The area of the region \(R\) consisting of all point...

Let \(\overrightarrow x ,\overrightarrow y\) and \(\overrightarrow z\) be three vectors each of magnitude \(\sqrt 2\) and the angle between each pair of them is \({\pi \over 3}\). If \(\overrightarrow a\) is a non-zero vector perpendic...

Let \(\overrightarrow a \,\,,\,\,\overrightarrow b\) and \(\overrightarrow c\) be three non-coplanar unit vectors such that the angle between every pair of them is \({\pi \over 3}.\) If $$\overrightarrow a \times \overrightarrow b + \o...

At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I(t) = I0 cos (\(\omega\)t), with I0 = 1 A and \(\omega\) = 500 rad s-1 starts flowing in it with the initial direction shown...

A parallel plate capacitor has a dielectric slab of dielectric constant \(K\) between its plates that covers \(1/3\) of the area of its plates, as shown in the figure. The total capacitance of the capacitor is \(C\) while that of the portio...

Two ideal batteries of emf V1 and V2 and three resistances R1, R2 and R3 are connected as shown in the figure. The current in resistance R2 would be zero if

A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 \(\Omega\) resistance, it can be converted into a voltmeter of range 0-30V. If connected to a \({{2n} \over {249}}\Omega\) resistance, it becomes a...

Let \({E_1}\left( r \right),{E_2}\left( r \right)\) and \({E_3}\left( r \right)\) be the respective electric field at a distance \(r\) from a point charge \(Q,\) an infinitely long wire with constant linear charge density \(\lambda ,\) and ...

A transparent thin film of uniform thickness and refractive index n1 = 1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n2 = 1.5, as shown in the figure. Rays of light ...

A thermodynamic system is taken from an initial state i with internal energy Ui = 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and...

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle \(\theta\) with the horizontal floor. The coefficient of friction between the wall and the ladder is \(\mu\)1 and that between th...

Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X1 from one of the wires. When the wires carry current of magnitude I in the same di...

Airplanes A and B are flying with constant velocity in the same vertical plane at angles \(30^\circ\) and \(60^\circ\) with
respect to the horizontal respectively as shown in the figure. The speed of A is \(100\sqrt 3\) m/s. At time t = ...