IIT-JEE 2012 Paper 1 Offline

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

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

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

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

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

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

The substituents R1 and R2 for nine peptides are listed in the table given below. How many of these peptides are positively charged at pH = 7.0 ?


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The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons undergoes a nuclear reaction yielding element X as shown below. To which group, element X belongs in the periodic table?
\({}_{29}^{63}Cu\) + $${}_1...

An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its initial concentration are t1/8 and t1/10 respectively. What is the value of $$\left[ {{{{t_{1/8}}} \over {{t_{1/10}}}}} \ri...

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

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

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 der Waals constant a (atm L2 mol\(-\)2) is

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

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

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

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

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 (mL) of stock solution required to prepare a 200 mL solution of 0.4 M HCl is

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

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

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 reached by either of the two paths shown in the figure. Which of the following choice(s) is(are) correct? (Take $$\Delt...

The point \(P\) is the intersection of the straight line joining the points \(Q(2, 3, 5)\) and \(R(1, -1, 4)\) with the plane \(5x-4y-z=1.\) If \(S\) is the foot of the perpendicular drawn from the point \(T(2, 1, 4)\) to \(QR,\) then the l...

Let \(p(x)\) be a real polynomial of least degree which has a local maximum at \(x=1\) and a local minimum at \(x=3\). If \(p(1)=6\) and \(p(3)=2\), then \(p'(0)\) is

Let \(f:IR \to IR\) be defined as \(f\left( x \right) = \left| x \right| + \left| {{x^2} - 1} \right|.\) The total number of points at which \(f\) attains either a local maximum or a local minimum is

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

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20 to the circle \({x^2}\, + \,{y^2} = 9\) is

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 a cannot take the value

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

The ellipse \({E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1\) is inscribed in a rectangle \(R\) whose sides are parallel to the coordinate axes. Another ellipse \({E_2}\) passing through the point \((0, 4)\) circumscribes the rectangle $$...

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

Tangents are drawn to the hyperbola \({{{x^2}} \over 9} - {{{y^2}} \over 4} = 1,\) parallel to the straight line \(2x - y = 1,\) The points of contact of the tangents on the hyperbola are

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

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

Let \(f(x) = \left\{ {\matrix{ {{x^2}\left| {\cos {\pi \over x}} \right|,} & {x \ne 0} \cr {0,} & {x = 0} \cr } } \right.\)
x\(\in\)R, then f is

Let \(P = [{a_{ij}}]\) be a 3 \(\times\) 3 matrix and let \(Q = [{b_{ij}}]\), where \({b_{ij}} = {2^{i + j}}{a_{ij}}\) for \(1 \le i,j \le 3\). If the determinant of P is 2, then the determinant of the matrix Q is

Let \(S\) be the focus of the parabola \({y^2} = 8x\) and let \(PQ\) be the common chord of the circle \({x^2} + {y^2} - 2x - 4y = 0\) and the given parabola. The area of the triangle \(PQS\) is

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

A ship is fitted with three engines \({E_1},{E_2}\) and \({E_3}\). The engines function independently of each other with respective probabilities \({1 \over 2},{1 \over 4}\) and \({1 \over 4}\). For the ship to be operational at least two o...

The value of \(6 + {\log _{3/2}}\left( {{1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}...} } } } \right)\) is __________.

Let \(\theta ,\,\varphi \, \in \,\left[ {0,2\pi } \right]\) be such that
$$2\cos \theta \left( {1 - \sin \,\varphi } \right) = {\sin ^2}\theta \,\,\left( {\tan {\theta \over 2} + \cot {\theta \over 2}} \right)\cos \varphi - 1,\,\tan \le...

If \(\overrightarrow a ,\overrightarrow b\) and \(\overrightarrow c\) are unit vectors satisfying
$${\left| {\overrightarrow a - \overrightarrow b } \right|^2} + {\left| {\overrightarrow b - \overrightarrow c } \right|^2} + {\left| {\o...

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

A proton is fired from very far away towards a nucleus with charge Q = 120e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is ___...

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) having two turns is placed with its centre at z = \(\sqrt3\)R along the axis of the circular wire loop, as shown in the figu...

An infinitely long solid cylinder of radius R has a uniform volume charge density \(\rho\). It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at ...

A cubical region of side \(a\) has its center at the origin. It encloses three fixed point charges, \(-q\) at \(\left( {0, - a/4,0} \right), + 3q\) at \(\left( {0,0,0} \right)\) and \(-q\) at \(\left( {0, + a/4,0} \right).\) Choose the corr...

Consider a thin spherical shell of radius \(R\) with center at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field \(\left| {\overrightarrow E \left( r \right)} \right|\) and th...

Two large vertical and parallel metal plates having a separation of \(1\) \(cm\) are connected to a \(DC\) voltage source of potential difference \(X\). A proton is released at rest midway between the two plates. It is found to move at $${4...

A biconvex lens is formed with two planoconvex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both curved surface are of the same radius of curvature R = 14 cm. For this biconv...

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductively. The first and third plates are maintained at temperatures 2T and 3T, respec...

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 in a container. The ratio of the rms speeds $$\left( {{{{v_{rms}}\left( {helium} \right)} \over {{v_{rms}}\left( {\arg ...