Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x)

A binary operation * is defined on the set of real numbers R, by p*q = p + q - \(\frac{pq}{2}\), where p, q \(\in\) R. Find the: (a) inverse of -1 under * gi...

Marks 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 80 - 89 90 - 99 Frequency 2 2 2 8 13 11 12 10 4 The table shows the distribution of marks score...

If \(\frac{3x^2 + 3x - 2}{(x - 1)(x + 1)}\) = P + \(\frac{Q}{x - 1} + \frac{R}{x - 1}\) Find the value of Q and R

Given that w = 8i + 3j, x = 6i - 5j, y = 2i + 3j and |z| = 41. find z in the direction of w + x - 2y.

(a) A bag contains 10 red and 8 green identical balls. Two balls are drawn at random from the bag, one after the other, without replacement. Find the probabi...

(a) Two functions p and q are defined on the set of real numbers, R, by p : y \(\to\) 2y +3 and q : y -> y - 2. Find QOP (b) How many four digits odd numbers...

Forces F\(_1\)(10N, 090°) and F\(_2\)(20N, 210\(^o\)) and (4N,330°) act on a particle, Find, correct to one decimal place, the magnitude of the resultant force.

Evaluate; \(\int^3_1(3x - 2)^5 dx\)