IIT-JEE 2009 Paper 1 Offline

The structure of the carbonyl compound P is

The structures of the products Q and R, respectively, are

The structure of the product S is

The correct acidity order of the following is

The IUPAC name of the following compound is

The correct statement(s) about the compound \(\mathrm{H_3C(HO)HC-CH=CH-CH(OH)CH_3~~(X)}\) is (are)

Match each of the diatomic molecules in Column I with its property/properties in Column II:

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-...

Match each of the compounds in Column I with its characteristic reaction(s) in Column II.

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-si...

The compound(s) that exhibit(s) geometrical isomerism is(are)

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is

The reaction of P\(_4\) with X leads selectively to P\(_4\)O\(_6\). The X is

Among cellulose, poly(vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of attraction is weakest is

The compound(s) formed upon combustion of sodium metal in excess air is (are)

The compound X is

The compound Y is

The compound Z is

The correct statement(s) regarding defects in solids is (are)

The Henry's law constant for the solubility of N\(_2\) gas in water at 298 K is 1.0 \(\times\) 10\(^5\) atm. The mole fraction of N\(_2\) in air is 0.8. The number of moles of N\(_2\) from air dissolved in 10 moles of water at 298 K and 5 a...

Given that the abundances of isotopes 54Fe, 56Fe and 57Fe are 5%, 90% and 5%, respectively, the atomic mass of Fe is :

Among the electrolytes Na\(_2\)SO\(_4\), CaCl\(_2\), Al\(_2\)(SO\(_4\))\(_3\) and NH\(_4\)Cl, the most effective coagulating agent for Sb\(_2\)S\(_3\) sol is

Let \(P(3,2,6)\) be a point in space and \(Q\) be a point on the line
\($\widehat r = \left( {\widehat i - \widehat j + 2\widehat k} \right) + \mu \left( { - 3\widehat i + \widehat j + 5\widehat k} \right)\)$
Then the value of \(\mu\) for...

Area of the region bounded by the curve \(y = {e^x}\) and lines \(x=0\) and \(y=e\) is

Let \(f\) be a non-negative function defined on the interval \([0,1]\).
If \(\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}dt} = \int\limits_0^x {f(t)dt,0 \le x \le 1} }\), and \(f(0) = 0\), then

Tangents drawn from the point P (1, 8) to the circle
\({x^2}\, + \,{y^2}\, - \,6x\, - 4y\, - 11 = 0\)
touch the circle at the points A and B. The equation of the cirumcircle of the triangle PAB is

Let \(z = x + iy\) be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation \(\overline z {z^3} + z{\overline z ^3} = 350\) is

Let \(z = \,\cos \,\theta \, + i\,\sin \,\theta\) . Then the value of \(\sum\limits_{m = 1}^{15} {{\mathop{\rm Im}\nolimits} } ({z^{2m - 1}})\,at\,\theta \, = {2^ \circ }\) is

Match the statements/expressions in Column I with the open intervals in Column II :

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14p...

In a triangle \(ABC\) with fixed base \(BC\), the vertex \(A\) moves such that
\($\cos \,B + \cos \,C = 4{\sin ^2}{A \over 2}.\)$
If \(a, b\) and \(c\) denote the lengths of the sides of the triangle opposite to the angles \(A, B\) and $$C...

The line passing through the extremity \(A\) of the major axis and extremity \(B\) of the minor axis of the ellipse \({x^2} + 9{y^2} = 9\) meets its auxiliary circle at the point \(M\). Then the area of the triangle with vertices at \(A\), ...

Match the conics in Column I with the statements/expressions in Column II :

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
ove...

Let \(L = \mathop {\lim }\limits_{x \to 0} {{a - \sqrt {{a^2} - {x^2}} - {{{x^2}} \over 4}} \over {{x^4}}},a > 0\). If L is finite, then

The number of matrices in A is

The number of matrices A in A for which the system of linear equations \(A\left[ {\matrix{ x \cr y \cr z \cr } } \right] = \left[ {\matrix{ 1 \cr 0 \cr 0 \cr } } \right]\) has a unique solution, is

The number of matrices A in A for which the system of linear equations \(A\left[ {\matrix{ x \cr y \cr z \cr } } \right] = \left[ {\matrix{ 1 \cr 0 \cr 0 \cr } } \right]\) is inconsistent, is

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

The probability that X = 3 equals

The probability that \(X\ge3\) equals :

The conditional probability that \(X\ge6\) given \(X>3\) equals :

If \({{{{\sin }^4}x} \over 2} + {{{{\cos }^4}x} \over 3} = {1 \over 5},\) then

If \(\overrightarrow a ,\overrightarrow b ,\overrightarrow c\) and \(\overrightarrow d\) are unit vectors such that \((\overrightarrow a \times \overrightarrow b )\,.\,(\overrightarrow c \times \overrightarrow d ) = 1\) and $$\overright...

The speed of the particle, that can take discrete values, is proportional to

In the core of nuclear fusion reactor, the gas becomes plasma because of

Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with kinetic energy 1.5 kT, when the separation between them is large enough to neglect Coulomb potential energy. Also neglec...

Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion?

For the circuit shown in the figure

The allowed energy for the particle for a particular value of \(n\) is proportional to

If the mass of the particle is \(m=1.0\times10^{-30}\) kg and \(a=6.6\) nm, the energy of the particle in its ground state is closest to

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $$I_1$...

A disk of radius \({a \over 4}\) having a uniformly distributed charge 6C is placed in the xy-plane with its centre at (\(-\)a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x ...

Three concentric metallic spherical shells of radii \(R,2R,3R\) are given charges \(Q_1,Q_2,Q_3\), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges giv...