Samuel and Raj were playing a game with some narbles. In the first game, Samuel won \( \frac{4}{7} \) of \( \frac{1}{3} \) of his new total number of marbles to Raj. After the second game, Raj had 5 k marbles and Samuel had 4 k marbles. Nho had more marbles initially, and by how nuch? Find the difference in the number of narbles in terms of \( k \).

Convert the polar equation to rectangular form \[ r=5 \cot (\theta) \csc (\theta) \]

If the function \( f \) is a polynomial function of fourth degree and its domain is \( \mathbb{R} \), then the greatest number of the critical points of the function \( f(x) \) is (a) 1 (b) 2 (c) 3 (d) 4

\( 4 ; x ; y ;-11 \) are the first four terms of a quadratic number pattern. \( 2 p-4 ; p-3 ; \frac{p}{2}-1 \) are the first three first differences of the same quadratic number pattern. Calculate the values of \( p, x \) and \( y \).

All the following functions are increasing on their domain except the function \( f: f(x)= \)

1 Divide 150 in the ratio \( 2: 3 \). 2 Divide 72 in the ratio \( 2: 3: 4 \) 3 Divide 5 kg in the ratio \( 13: 7 \). 4 Divide 45 minutes in the ratio \( 2: 3 \). 5 Divide 1 hour in the ratio \( 1: 5 \).