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A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

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Which one of the following molecules is expected to exhibit diamagnetic behaviour?

If $[a×bb×cc×a]=λ[abc]_{2}$, then l is equal to

The sum of coefficients of integral powers of x in the binomial expansion of $(1−2x )_{50}$ is:

Distance of the centre of mass of a solid uniform cone from its vertex is $Z_{0}$. If the radius of its base is R and its height is h then $Z_{0}$ is equal to :

The vapour pressure of acetone at $20_{∘}C$ is 185 torr. When 1.2 g of a non - volatile substance was dissolved in 100 g of acetone at $20_{∘}C$, its vapour pressure was 183 torr. The molar mass $(gmol_{−1})$ of the substance is :

Consider the following reaction: $xMnO_{4}+yC_{2}O_{4}+zH_{+}3/4 xMn_{2+}+2yCO_{2}+2z H_{2}O$ The values of x, y and z in the reaction are, respectively:

The order of stability of the following carbocations:

Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29 Å. The radius of sodium atom is approximately :