IIT-JEE 2012 Paper 1 Offline

Paper was held on
Sat, Apr 7, 2012 9:00 PM

## Chemistry

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$$\alpha_0$$ is Bohr radius]

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In allene (C3H4), the type(s) of hybridisation of the carbon atoms is (are):

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Choose the correct reason for the stability of the Iyophobic colloidal particles

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29.2 % (w/w) HCl stock solution has density of 1.25 g mL -1 . The molecular weight of HCl is 36.5 g mol -1 .
The volume

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The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons undergoes a nuclear reaction

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An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its ini

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A compound MpXq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical fo

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The carboxyl functional group ($$-$$COOH) is present in

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As per IUPAC nomenclature, the name of the complex $$[Co{({H_2}O)_4}{(N{H_3})_2}]C{l_3}$$ is

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Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?

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For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. 1/V plot is shown below. The value of the van d

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The number of aldol reactions that occur in the given transformation are

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The colour of light absorbed by an aqueous solution of CuSO4 is

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The number of optically active products obtained from the complete ozonolysis of the given compound is ______.

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Which of the following hydrogen halides reacts with AgNO3(aq.) to give a precipitate that dissolves in Na2S2O3 (aq.) ?

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Identify the binary mixtures that can be separated into individual compounds, by differential extraction, as shown in th

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For an ideal gas, consider only P-V work in going from an initial state X to the final state Z. The final state Z can be

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Which of the following molecules, in pure form, is(are) unstable at room temperature?

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The substituents R1 and R2 for nine peptides are listed in the table given below. How many of these peptides are positiv

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When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is _

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## Mathematics

Let z be a complex number such that the imaginary part of z is non-zero and $$a\, = \,{z^2} + \,z\, + 1$$ is real. Then

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Let $$\theta ,\,\varphi \, \in \,\left[ {0,2\pi } \right]$$ be such that
$$2\cos \theta \left( {1 - \sin \,\varphi } \r

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The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person ge

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The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20

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The ellipse $${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ is inscribed in a rectangle $$R$$ whose sides are parall

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Tangents are drawn to the hyperbola $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1,$$ parallel to the straight line $$2x -

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Let $$S$$ be the focus of the parabola $${y^2} = 8x$$ and let $$PQ$$ be the common chord of the circle $${x^2} + {y^2} -

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Let $$f:IR \to IR$$ be defined as $$f\left( x \right) = \left| x \right| + \left| {{x^2} - 1} \right|.$$ The total numbe

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Let $$p(x)$$ be a real polynomial of least degree which has a local maximum at $$x=1$$ and a local minimum at $$x=3$$. I

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The integral $\int \frac{\sec ^2 x}{(\sec x+\tan x)^{9 / 2}} d x$ equals (for some arbitrary constant $$K$$)

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Let $$S$$ be the area of the region enclosed by $$y = {e^{ - {x^2}}}$$, $$y=0$$, $$x=0$$, and $$x=1$$; then

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If $$y(x)$$ satisfies the differential equation $$y' - y\,tan\,x = 2x\,secx$$ and $$y(0)=0,$$ then

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A ship is fitted with three engines $${E_1},{E_2}$$ and $${E_3}$$. The engines function independently of each other with

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The point $$P$$ is the intersection of the straight line joining the points $$Q(2, 3, 5)$$ and $$R(1, -1, 4)$$ with the

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If $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ are unit vectors satisfying
$${\left| {\overrig

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If $$\mathop {\lim }\limits_{x \to \infty } \left( {{{{x^2} + x + 1} \over {x + 1}} - ax - b} \right) = 4$$, then

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Let $$P = [{a_{ij}}]$$ be a 3 $$\times$$ 3 matrix and let $$Q = [{b_{ij}}]$$, where $${b_{ij}} = {2^{i + j}}{a_{ij}}$$ f

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Let $$f(x) = \left\{ {\matrix{
{{x^2}\left| {\cos {\pi \over x}} \right|,} & {x \ne 0} \cr
{0,} & {x = 0} \cr

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The function $$f:[0,3] \to [1,29]$$, defined by $$f(x) = 2{x^3} - 15{x^2} + 36x + 1$$, is

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The value of $$6 + {\log _{3/2}}\left( {{1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt

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## Physics

In the determination of Young's modulus $$\left( {Y = {{4MLg} \over {\pi l{d^2}}}} \right)$$
by using Searle's method, a

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A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K

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Two large vertical and parallel metal plates having a separation of $$1$$ $$cm$$ are connected to a $$DC$$ voltage sourc

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Consider a thin spherical shell of radius $$R$$ with center at the origin, carrying uniform positive surface charge dens

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A cubical region of side $$a$$ has its center at the origin. It encloses three fixed point charges, $$-q$$ at $$\left( {

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A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is underg

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A biconvex lens is formed with two planoconvex lenses as shown in the figure. Refractive index n of the first lens is 1.

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A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $$\omega$$, as shown i

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Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfa

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A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (se

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Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe width

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Consider the motion of a positive point charge in a region, there are simultaneous uniform electric and magnetic fields

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A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When t

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A small block of mass 0.1 kg lies on a fixed inclined plane PQ which makes an angle $$\theta$$ with the horizontal. A ho

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For the resistance network shown in the figure, choose the correct option(s).

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A circular wire loop of radius R is placed in the xy plane centred at the origin O. A square loop of side a(a << R

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An infinitely long solid cylinder of radius R has a uniform volume charge density $$\rho$$. It has a spherical cavity of

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A proton is fired from very far away towards a nucleus with charge Q = 120e, where e is the electronic charge. It makes

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A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as sh

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A cylinder cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and th

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