JEE Main 2016 (Offline)

The product of the reaction given below is :

\(2\)-chloro-\(2\)-methylpentane on reaction with sodium methoxide in methanol yields:

The absolute configuration of

is :

The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :

Thiol group is present in :

The species in which the $\mathrm{N}$ atom is in a state of $s p$ hybridization is :

The equilibrium constant at 298 K for a reaction A + B \(\leftrightharpoons\) C + D is 100. If the initial concentration of
all the four species were 1M each, then equilibrium concentration of D (in mol L–1) will be:

Decomposition of H2O2 follows a first order reaction. In fifty minutes the concentration of H2O2 decreases
from 0.5 to 0.125 M in one such decomposition. When the concentration of H2O2 reaches 0.05 M, the rate of formation of O2 will be :

Which of the following is an anionic detergent ?

In the Hofmann bromamide degradation reaction, the number of moles of NaOH and Br2 used per mole of
amine produced are:

Which one of the following complexes shows optical isomerism?
(en = ethylenediamine)

The pair having the same magnetic moment is :
[At. No.: Cr = 24, Mn = 25, Fe = 26, Co = 27]

The reaction of zinc with dilute and concentrated nitric acid, respectively, produces :

Which of the following compounds is metallic and ferromagnetic ?

Galvanization is applying a coating of :

The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found
to be 1000 ppb, 40 ppb, 100 ppm and 0.2 ppm, respectively. This water is unsuitable for drinking due to
high concentration of :

Two closed bulbs of equal volume \((V)\) containing an ideal gas initially at pressure \({p_i}\) and temperature \({T_1}\) are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the ...

The reaction of propene with HOCl (Cl2 + H2O) proceeds through the intermediate:

At 300 K and 1 atm, 15 mL of a gaseous hydrocarbon requires 375 mL air containing 20% O2 by volume
for complete combustion. After combustion the gases occupy 345 mL. Assuming that the water formed is
in liquid form and the volumes were meas...

Which one of the following statements about water is FALSE?

Which one of the following ores is best concentrated by froth floatation method?

The pair in which phosphorous atoms have a formal oxidation state of +3 is :

Which of the following statements about low density polythene is FALSE ?

Which of the following atoms has the highest first ionization energy?

The hottest region of Bunsen flame shown in the figure below is :

The main oxides formed on combustion of Li, Na and K in excess of air are, respectively :

18 g glucose (C6H12O6) is added to 178.2 g water. The vapor pressure of water (in torr) for this aqueous solution is :

A stream of electrons from a heated filament was passed between two charged plates kept at a potential
difference V esu. If e and m are charge and mass of an electron, respectively, then the value of h / \(\lambda\) (where
\(\lambda\) is ...

For a linear plot of log (x/m) versus log p in a Freundlich adsorption isotherm, which of the following
statements is correct ? (k and n are constants)

The heats of combustion of carbon and carbon monoxide are –393.5 and –283.5 kJ mol–1, respectively. The
heat of formation (in kJ) of carbon monoxide per mole is :

If the line, \({{x - 3} \over 2} = {{y + 2} \over { - 1}} = {{z + 4} \over 3}\,\) lies in the planes, \(lx+my-z=9,\) then \({l^2} + {m^2}\) is equal to :

The distance of the point \((1,-5,9)\) from the plane \(x-y+z=5\) measured along the line \(x=y=z\) is :

A wire of length \(2\) units is cut into two parts which are bent respectively to form a square of side \(=x\) units and a circle of radius \(=r\) units. If the sum of the areas of the square and the circle so formed is minimum, then:

Consider :
f \(\left( x \right) = {\tan ^{ - 1}}\left( {\sqrt {{{1 + \sin x} \over {1 - \sin x}}} } \right),x \in \left( {0,{\pi \over 2}} \right).\)
A normal to \(y =\) f\(\left( x \right)\) at \(x = {\pi \over 6}\) also passes through ...

The area (in sq. units) of the region \(\left\{ {\left( {x,y} \right):{y^2} \ge 2x\,\,\,and\,\,\,{x^2} + {y^2} \le 4x,x \ge 0,y \ge 0} \right\}\) is :

If the number of terms in the expansion of \({\left( {1 - {2 \over x} + {4 \over {{x^2}}}} \right)^n},\,x \ne 0,\) is 28, then the sum of the coefficients of all the terms in this expansion, is :

The centres of those circles which touch the circle, \({x^2} + {y^2} - 8x - 8y - 4 = 0\), externally and also touch the \(x\)-axis, lie on :

If one of the diameters of the circle, given by the equation, \({x^2} + {y^2} - 4x + 6y - 12 = 0,\) is a chord of a circle \(S\), whose centre is at \((-3, 2)\), then the radius of \(S\) is :

A value of \(\theta \,\) for which \({{2 + 3i\sin \theta \,} \over {1 - 2i\,\,\sin \,\theta \,}}\) is purely imaginary, is :

\(\mathop {\lim }\limits_{n \to \infty } {\left( {{{\left( {n + 1} \right)\left( {n + 2} \right)...3n} \over {{n^{2n}}}}} \right)^{{1 \over n}}}\) is equal to:

If a curve \(y=f(x)\) passes through the point \((1,-1)\) and satisfies the differential equation, \(y(1+xy) dx=x\) \(dy\), then \(f\left( { - {1 \over 2}} \right)\) is equal to :

If $f(x)+2 f\left(\frac{1}{x}\right)=3 x, x \neq 0$, and $\mathrm{S}=\{x \in \mathbf{R}: f(x)=f(-x)\}$; then $\mathrm{S}:$

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30o. After walking for 10 minutes from A in the same di...

The eccentricity of the hyperbola whose length of the latus rectum is equal to \(8\) and the length of its conjugate axis is equal to half of the distance between its foci, is :

The integral \(\int {{{2{x^{12}} + 5{x^9}} \over {{{\left( {{x^5} + {x^3} + 1} \right)}^3}}}} dx\) is equal to :

For \(x \in \,R,\,\,f\left( x \right) = \left| {\log 2 - \sin x} \right|\,\,\)
and \(\,\,g\left( x \right) = f\left( {f\left( x \right)} \right),\,\,\) then :

Let \(p = \mathop {\lim }\limits_{x \to {0^ + }} {\left( {1 + {{\tan }^2}\sqrt x } \right)^{{1 \over {2x}}}}\) then \(log\) \(p\) is equal to :

The Boolean expression
\(\left( {p \wedge \sim q} \right) \vee q \vee \left( { \sim p \wedge q} \right)\) is equivalent to :

If \(A = \left[ {\matrix{ {5a} & { - b} \cr 3 & 2 \cr } } \right]\) and \(A\) adj \(A=A\) \({A^T},\) then \(5a+b\) is equal to :

The system of linear equations
\(\matrix{ {x + \lambda y - z = 0} \cr {\lambda x - y - z = 0} \cr {x + y - \lambda z = 0} \cr }\)
has a non-trivial solution for :