1. If \(\sum{f_ix_i} = 216\), \(\sum{f_i} = 16\), and the combined mean is \(13.5 + p\), then what is the value of \(p\)?

(a) 0 (b) 1 (c) 0.1 (d) 0.01

2. If \(x^2 - px + 12 = (x - 3)(x - a)\) is an identity, then the values of \(a\) and \(p\) respectively are?

(a) \(a = 4, p = 7\) (b) \(a = 7, p = 4\) (c) \(a = 4, p =-7\) (d) \(a =-4, p = 7\)

3. A conductor has three values: 4, 5, and 7, with their respective frequencies being (P-2), (P+1), and (P-1). If the weighted mean of the conductor is 5.4, determine the value of P.

(a) 4 (b) 1 (c) 2 (d) 3

4. If a planet's gravitational force on its satellite is directly proportional to the planet's mass (M) and inversely proportional to the square of their distance (D), and the square of the satellite's orbital period (T) is directly proportional to the cube of the distance and inversely proportional to the gravitational force, then for two sets of values \(m_1, d_1, t_1\) and \(m_2, d_2, t_2\) corresponding to M, D, and T respectively, prove that: \[ m_1 t_1^2 d_2^3 = m_2 t_2^2 d_1^3 \]