Find the values of ^@p^@ and ^@q^@ for which the following pair of linear equations have an infinite number of solutions:@^6x + y = 3, (p + q)x + (p - q)y = (2p - 24)@^

A.

^@\begin{aligned}p = 21 \text{ and } & q = 16\end{aligned}^@

B.

^@\begin{aligned}p = 21 \text{ and } & q = 15\end{aligned}^@

C.

^@\begin{aligned}p = 26 \text{ and } & q = 15\end{aligned}^@

D.

^@\begin{aligned}p = 20 \text{ and } & q = 13\end{aligned}^@

Two poles of heights ^@ 20 \space metres^@ and ^@40 \space metres^@ stand vertically on a plane ground. If the distance between their feet is ^@21 \space metres^@, find the distance between their tops.

A chord of a circle of radius ^@ 28 \space cm ^@ subtends a right angle at the center. Find the area of the corresponding major segment.^@ \bigg[\pi = \dfrac { 22 } { 7 }\bigg] ^@

There is a cylindrical scale holder of height ^@ 12 \space cm^@ and diameter ^@ 14 \space cm^@. Now the scale holder is cut into two pieces such that the height of the new scale holder is reduced to ^@ \left(\dfrac{ 5 }{ 6 } \right)^{th} ^@ of the height. The diameter of the new scale holder remains the same. If the new scale holder is filled with water up to the brim, then find the amount of water held in liters. (Where ^@ \pi = 3.14 ^@)

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