There are five friends $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}$ and $\mathrm{T}. \mathrm{P}$ is younger to $\mathrm{Q}, \mathrm{T}$ is younger to $\mathrm{R}$ and $\mathrm{S}$ both, $\mathrm{P}$ is as old as $\mathrm{R}, \mathrm{P}$ is younger to as many as those who are younger to S. Who among the five friends is the eldest?

A, B, C, D, and E belong to five different cities, P, Q, R, S and T (not necessarily in that order). Each one of them comes from a different city. Further, it is given,

1. B and C do not belong to Q.

2. B and E do not belong to P and R.

3. A and C do not belong to R, S and T.

4. D and E do not belong to Q and T.

Which one of the following statements is not correct?

Each of the six different faces of a cube has been coated with a different colour, i.e., V, I, B, G, Y and O. Following information is given.

$1$. Colours Y, O and B are on the adjacent faces.

$2$. Colours I, G and Y are on the adjacent faces.

$3$. Colours B, G and Y are on the adjacent faces.

$4$. Colours O, V and B are on the adjacent faces.

Which is the colour of the face opposite to the face coloured with O?

Three persons A, B and C wore shirts of black, blue and orange colours (not necessarily in that order) and pants of green, yellow and orange colour (not necessarily in that order). No person wore a shirt and pant of the same colour. Further, it is given that

1. A did not wear shirt of black colour.

2. B did not wear shirt of blue colour.

3. C did not wear shirt of orange colour.

4. A did not wear pant of green colour.

5. B wore pant of orange colour.

What were the colours of the pant and shirt worn by C respectively?

In the figure shown below,

${\mathrm{S}}_1= \mathrm{a}+\mathrm{b}+\mathrm{c}, {\mathrm{S}}_2 = \mathrm{d}+\mathrm{e}+\mathrm{f}$

${\mathrm{S}}_3= \mathrm{g}+\mathrm{h}+\mathrm{i}, {\mathrm{S}}_4= \mathrm{a}+\mathrm{d}+\mathrm{g}$

${\mathrm{S}}_5= \mathrm{b}+\mathrm{e}+\mathrm{h}, {\mathrm{S}}_6 = \mathrm{c}+\mathrm{f}+\mathrm{i}$

$\mathrm{P} = \mathrm{a}\times \mathrm{e}\times \mathrm{i}$

If the numerical value of ${\mathrm{S}}_1, {\mathrm{S}}_2, {\mathrm{S}}_3, {\mathrm{S}}_4, {\mathrm{S}}_5, {\mathrm{S}}_6$  and $\mathrm{P}$ are known, what is the minimum number of values of the lowercase letters that must be given such that values of all the lowercase letters become known?

Seven players A, B, C, D, E, F, and G are to be seated such that,

1. B must always occupy the second position. 
2. F must always occupy the sixth position.
3. D and E must be seated adjacent to each other.

In how many different ways they can be seated?