JEE (Advanced) 2010 Paper-2
For the following questions answer them individually
One mole of an ideal gas is taken from a to b along two paths denoted bythe solid and the dashed lines as shownin the graph below. If the work done along the solid line path is $$W_s$$ and that along the dotted line path is $$W_d$$, then the integer closest to the ratio $$\frac{W_d}{W_s}$$ is
789
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123
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Two aliphatic aldehydes P and Q react in the presence of aqueous $$K_2CO_3$$ to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below:
The hydrogen-like species $$Li^{2+}$$ is in a spherically symmetric state $$S_1$$, with one radial node. Upon absorbing light the ion undergoes transition to a state $$S_2$$. The state $$S_2$$, has one radial node and its energy is equal to the groundstate energy of the hydrogen atom.
For the following questions answer them individually
Match the reactions in Column I with appropriate options in Column II.
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All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.
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For $$r = 0, 1, ...., 10$$, let $$A_r, B_r$$ and $$C_r$$ denote, respectively, the coefficient of $$x^r$$ in the expansions of $$(1 + x)^{10}, (1 + x)^{20}$$ and $$(1 + x)^{30}$$. Then
$$\sum_{r=1}^{10}A_r(B_{10}B_r = C_{10}A_r)$$ is equal to
