1. If the equation \(ax^2 - 5x + c = 0\) has both the sum and product of its roots equal to \(10\), then which of the following is correct?

2. If \( \cos\theta = p \) and \( \cot\theta = q \), then which of the following relationships is true?

(a) \(\cfrac{1}{p^2}+\cfrac{1}{q^2}=1\) (b) \(\cfrac{1}{p^2}-\cfrac{1}{q^2}=1\) (c) \(\cfrac{1}{p^2}-\cfrac{1}{q^2}=0\) (d) \(\cfrac{1}{q^2}+\cfrac{1}{p^2}=1\)

3. If \(x = r\cos\theta\cos\phi\), \(y = r\cos\theta\sin\phi\), and \(z = r\sin\theta\), then what is the value of \(x^2 + y^2 + z^2\)?

(a) \(r\) (b) \(1\) (c) \(r^2\) (d) \(-r^2\)

4. If \(a^2 b^2 + 1 = 2ab\), then which of the following is correct?

(a) \(a-b \propto b\) (b) \(a-b \propto a\) (c) \(a \propto b\) (d) \(a \propto \cfrac{1}{b}\)

5. If \(3x = 5\sin\theta\) and \(4y = 5\cos\theta\), then which of the following relations is correct?

(a) \(\cfrac{9x^2}{25}+\cfrac{16y^2}{25}=1\) (b) \(\cfrac{9x^2}{25}+\cfrac{16y^2}{25}=0\) (c) \(\cfrac{9x^2}{25}-\cfrac{16y^2}{25}=1\) (d) \(\cfrac{16x^2}{25}+\cfrac{9y^2}{25}=1\)