If \( \alpha \) and \( \beta \) are the roots of the equation \( 3x^2 + bx - 2 = 0 \). Find the value of \( \frac{1}{\alpha} + \frac{1}{\beta} \)

If two graphs y = px2 + q and y = 2x2 − 1 intersect at x =2, find the value of p in terms of q

If U = {x : x is an integer and 1 ≤ x ≤ } E1 = {x: x is a multiple of 3} E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the p...

Given T = { even numbers from 1 to 12 } N = {common factors of 6, 8 and 12} Find T ∩ N

If \(y = x \sin x\), find \(\frac{dy}{dx}\) when \(x = \frac{\pi}{2}\)

Evaluate \( \sin 45^o + \sin 3^o \) in surd form.

What is the next number in the series 2, 1, \( \frac{1}{2} \), \( \frac{1}{4} \)...

If temperature t is directly proportional to heat h, and when t = 20oC, h = 50 J, find t when h = 60J

The curved surface area of a cylinder 5cm high is \(110\text{cm}^2\). Find the radius of its base \(\pi = \frac{22}{7}\)