IIT-JEE 2000
Paper was held on Tue, Apr 11, 2000 9:00 AM
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Chemistry

Calculate the energy required to excite one litre of hydrogen gas at 1 atm and 298 K to the first excited state of atomi
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Write down the M.O. electron distribution of O2. Specify its bond order and magnetic property.
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To 500 cm3 of water, 3.0 $$\times$$ 10-3 kg of acetic acid is added. If 23% of acetic acid is dissociated, what will be
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Copper sulphate solution (250 mL) was electrolysed using platinum anode and a copper cathode. A constant current of 2mA
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The following electrochemical cell has been set up. Pt(1) | Fe3+, Fe2+ (a = 1) | Ce4+, Ce3+ (a=1) | Pt(2) Eo (Fe3+, Fe2+
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A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in the presence of a catalyst at t
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Mathematics

In any triangle $$ABC,$$ prove that $$$\cot {A \over 2} + \cot {B \over 2} + \cot {C \over 2} = \cot {A \over 2}\cot {B
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If $$\alpha ,\,\beta $$ are the roots of $$a{x^2} + bx + c = 0$$, $$\,\left( {a \ne 0} \right)$$ and $$\alpha + \delta
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For any positive integer $$m$$, $$n$$ (with $$n \ge m$$), let $$\left( {\matrix{ n \cr m \cr } } \right) = {
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For every possitive integer $$n$$, prove that $$\sqrt {\left( {4n + 1} \right)} < \sqrt n + \sqrt {n + 1} < \s
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Let $$a,\,b,\,c$$ be possitive real numbers such that $${b^2} - 4ac > 0$$ and let $${\alpha _1} = c.$$ Prove by induc
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A coin probability $$p$$ of showing head when tossed. It is tossed $$n$$ times. Let $${p_n}$$ denote the probability tha
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The fourth power of the common difference of an arithmatic progression with integer entries is added to the product of a
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For points $$P\,\,\, = \left( {{x_1},\,{y_1}} \right)$$ and $$Q\,\,\, = \left( {{x_2},\,{y_2}} \right)$$ of the co-ordin
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Let $$ABC$$ and $$PQR$$ be any two triangles in the same plane. Assume that the prependiculars from the points $$A, B, C
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Let $$ABC$$ be an equilateral triangle inscribed in the circle $${x^2} + {y^2} = {a^2}$$. Suppose perpendiculars from $$
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Let $${C_1}$$ and $${C_2}$$ be respectively, the parabolas $${x^2} = y - 1$$ and $${y^2} = x - 1$$. Let $$P$$ be any poi
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If $${x^2} + {y^2} = 1$$ then
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Let $$ABC$$ be a triangle with incentre $$I$$ and inradius $$r$$. Let $$D,E,F$$ be the feet of the perpendiculars from $
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Suppose $$p\left( x \right) = {a_0} + {a_1}x + {a_2}{x^2} + .......... + {a_n}{x^n}.$$ If $$\left| {p\left( x \right)}
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For $$x>0,$$ let $$f\left( x \right) = \int\limits_e^x {{{\ln t} \over {1 + t}}dt.} $$ Find the function $$f\left( x
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A coin has probability $$p$$ of showing head when tossed. It is tossed $$n$$ times. Let $${p_n}$$ denote the probability
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Physics

A thin wire of length $L$ and uniform linear mass density $\rho$ is bent into a circular loop with centre at $O$ as show
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