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]

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

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

View Question 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 (m

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

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

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

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

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

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

View Question 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

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

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

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

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

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

View Question 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

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

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

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

View Question ## 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

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

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

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

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

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

View Question 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} -

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

View Question 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

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

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

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

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

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

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

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

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

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

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

View Question 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

View Question ## Physics

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

View Question 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

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

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

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

View Question 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

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

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

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

View Question 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

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

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

View Question 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

View Question 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

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

View Question 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

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

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

View Question 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

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

View Question