# Tutor profile: Vishal S.

## Questions

### Subject: Number Theory

Find the smallest number which when divided by 5 or 11 leaves a remainder of 4 and is greater than the remainder.

Lets consider set of such numbers are of the form: K[ LCM(5,11)] + 4 Where K is a whole number. We can only get the smallest number of the above given form by putting the value of K=1 1[ LCM(5,11)] + 4 55 + 4 = 59

### Subject: Chemistry

In periodic table, explain why the elements of the first transition series possess many properties different from those of heavier transition elements.

The heavier transition elements belong to fourth (4d), fifth (5d) and sixth (6d) transition series. Their properties are expected to be different from the elements belonging to the first (3d) series due to the following reasons : (i) Atomic radii of heavier transition elements (4d and 5d series) are larger than those of the corresponding elements of the first transition series though those of 4d and 5d series are very close to each other. (ii) Ionization enthalpies of 5d series are higher than the corresponding elements of 3d and 4d series. (iii) Enthalpies of atomisation of 4d and 5d series are higher than the corresponding elements of the first series, (IV) Melting and boiling points of heavier transition elements are greater than those of the first transition series due to stronger intermetallic bonding.

### Subject: Physics

Suppose an uncharged capacitor is connected to a battery. Explain why half the energy supplied by the battery is lost as heat while charging the capacitor.

Suppose the capacitance of the capacitor is C and the emf of the battery is V. The charge given to the capacitor is Q=CV. The work done by the battery is: W=QV The battery supplies this energy. The energy stored in the capacitor is U=1/2(C$$V^{2}$$) The remaining energy QV - 1/2(QV) = 1/2(QV) Thus, half the energy supplied by the battery is lost as heat.

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