IIT-JEE 2011 Paper 1 Offline

The structure of compound P is

The structure of the compound Q is

Among the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any) is(are)

Among the following compounds, the most acidic is

A decapeptide (mol. wt. 796) on complete hydrolysis gives glycine (mol. wt. 75), alanine and phenylalanine. Glycine contributes 47.0% to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is ...

Bombardment of aluminium by \(\alpha\)-particle leads to its artificial disintegration in two ways : (i) and (ii) as shown. Products X, Y and Z, respectively, are

The major product of the following reaction is

Geometrical shapes of the complexes formed by the reaction of Ni2+ with Cl-, CN- and H2O respectively are

AgNO3(aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance (\(\Lambda\)) versus the volume of AgNO3 is

To an evacuated vessel with movable piston under external pressure of 1 atm, 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm, at 0oC) are introduced. Considering the ideal gas behaviour, the total volume (in litre...

According to kinetic theory of gases

The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholic KOH is _______.

Extraction of metal from the ore cassiterite involves

Extra very pure N2 can be obtained by heating

The difference in the oxidation numbers of the two types of sulphur atoms in Na2S4O6 is

Reaction of Br2 with Na2CO3 in aqueous solution gives sodium bromide and sodium bromate with evolution of CO2 gas. The number of sodium bromide molecules involved in the balanced chemical equation is ________.

The metal rod M is

The compound N is

The final solution contains :

Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of the solution is

The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum number, ms = − 1/2 , is

The work function
( φ )
of some metals is listed below. The number of metals which will show
photoelectric effect when light of 300 nm wavelength falls on the metal is


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The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)

Let the straight line \(x=b\) divide the area enclosed by
\(y = {\left( {1 - x} \right)^2},y = 0,\) and \(x=0\) into two parts \({R_1}\left( {0 \le x \le b} \right)\) and
\({R_2}\left( {b \le x \le 1} \right)\) such that $${R_1} - {R_2} =...

If z is any complex number satisfying \(\,\left| {z - 3 - 2i} \right| \le 2\), then the minimum value of \(\left| {2z - 6 + 5i} \right|\) is

The value of \(\,\int\limits_{\sqrt {\ell n2} }^{\sqrt {\ell n3} } {{{x\sin {x^2}} \over {\sin {x^2} + \sin \left( {\ell n6 - {x^2}} \right)}}\,dx}\) is

Let \(f:[1,\infty ) \to [2,\infty )\) be a differentiable function such that \(f(1) = 2\). If \(6\int\limits_1^x {f(t)dt = 3xf(x) - {x^3} - 5}\) for all \(x \ge 1\), then the value of f(2) is ___________.

Let \(f\left( \theta \right) = \sin \left( {{{\tan }^{ - 1}}\left( {{{\sin \theta } \over {\sqrt {\cos 2\theta } }}} \right)} \right),\) where \(- {\pi \over 4} < \theta < {\pi \over 4}.\)
Then the value of $${d \over {d\left( {\tan \...

Let the eccentricity of the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\) be reciprocal to that of the ellipse \({x^2} + 4{y^2} = 4\). If the hyperbola passes through a focus of the ellipse, then

Let f : R \(\to\) R be a function such that \(f(x + y) = f(x) + f(y),\,\forall x,y \in R\). If f(x) is differentiable at x = 0, then

Let M and N be two 3 \(\times\) 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2(MTN)\(-\)1(MN\(-\)1)T is equal to

If the point P(a, b, c), with reference to (E), lies on the plane 2x + y + z = 1, then the value of 7a + b + c is

Let \(\omega\) be a solution of \({x^3} - 1 = 0\) with \({\mathop{\rm Im}\nolimits} (\omega ) > 0\). If a = 2 with b and c satisfying (E), then the value of \({3 \over {{\omega ^a}}} + {1 \over {{\omega ^b}}} + {3 \over {{\omega ^c}}}\) is ...

Let b = 6, with a and c satisfying (E). If \(\alpha\) and \(\beta\) are the roots of the quadratic equation ax2 + bx + c = 0, then \(\sum\limits_{n = 0}^\infty {{{\left( {{1 \over \alpha } + {1 \over \beta }} \right)}^n}}\) is

Consider the parabola \({y^2} = 8x\). Let \({\Delta _1}\) be the area of the triangle formed by the end points of its latus rectum and the point \(P\left( {{1 \over 2},2} \right)\) on the parabola and \({\Delta _2}\) be the area of the tria...

The probability of the drawn ball from \({U_2}\) being white is

Given that the drawn ball from \({U_2}\) is white, the probability that head appeared on the coin is

Let \(\alpha\) and \(\beta\) be the roots of \({x^2} - 6x - 2 = 0,\) with \(\alpha > \beta .\) If \({a_n} = {\alpha ^n} - {\beta ^n}\) for \(\,n \ge 1\) then the value of \({{{a_{10}} - 2{a_8}} \over {2{a_9}}}\) is

Let \(\left( {{x_0},{y_0}} \right)\) be the solution of the following equations
\(\matrix{ {{{\left( {2x} \right)}^{\ell n2}}\, = {{\left( {3y} \right)}^{\ell n3}}} \cr {{3^{\ell nx}}\, = {2^{\ell ny}}} \cr }\)
Then \({x_0}\)...

The minimum value of the sum of real numbers \({a^{ - 5}},\,{a^{ - 4}},\,3{a^{ - 3}},\,1,\,{a^8}\) and \({a^{10}}\) where \(a > 0\) is

Let \({{a_1}}\), \({{a_2}}\), \({{a_3}}\)........ \({{a_{100}}}\) be an arithmetic progression with \({{a_1}}\) = 3 and \({S_p} = \sum\limits_{i = 1}^p {{a_i},1 \le } \,p\, \le 100\). For any integer n with \(1\,\, \le \,n\, \le 20\), let m...

A straight line \(L\) through the point \((3, -2)\) is inclined at an angle \({60^ \circ }\) to the line \(\sqrt {3x} + y = 1.\) If \(L\) also intersects the x-axis, then the equation of \(L\) is

Let \(P = \{ \theta :\sin \theta - \cos \theta = \sqrt 2 \cos \theta \}\) and \(Q = \{ \theta :\sin \theta + \cos \theta = \sqrt 2 \sin \theta \}\) be two sets. Then

The positive integer value of \(n\, > \,3\) satisfying the equation \({1 \over {\sin \left( {{\pi \over n}} \right)}} = {1 \over {\sin \left( {{{2\pi } \over n}} \right)}} + {1 \over {\sin \left( {{{3\pi } \over n}} \right)}}\) is

The vector (s) which is/are coplanar with vectors \({\widehat i + \widehat j + 2\widehat k}\) and \({\widehat i + 2\widehat j + \widehat k,}\) and perpendicular to the vector \({\widehat i + \widehat j + \widehat k}\) is/are

Let \(\overrightarrow a = \widehat i + \widehat j + \widehat k,\,\overrightarrow b = \widehat i - \widehat j + \widehat k\) and \(\overrightarrow c = \widehat i - \widehat j - \widehat k\) be three vectors. A vector $$\overrightarrow v ...

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 \(\mathop A\limits^o\). The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

A \(2\) \(\mu F\) capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch \(S\) is turned to position \(2\) is

A meter bridge is set up as shown, to determine an unknown resistance X using a standard 10 \(\Omega\) resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm, respectively, for t...

The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10\(-\)25 kg. The mass (in mg) of the radioactive sample is _________.