A binary operation * is defined by a* b =a^b, If  a * 2 =2 – a. Find the possible value of a

Find the inverse of P under the binary operation defined by $p*q=p+q-pq$where p and q are real numbers and zero is the identity

Evaluate $\tfrac{1}{2}-\tfrac{1}{4}+\tfrac{1}{8}-\tfrac{1}{16}+---$

The 3^rd term of an A.P is 4x – 2y and the 9^th is 10x – 8y. Find the common difference. 

Solve the inequality 2 –x > x²

The solution of the simultaneous inequality $2x-2\le y$ and $2y-x\le x$ represented by

A trader realizes 10 – x² naira profit from the sales of x bags of corns. How many bags will give him maximum profit.

If $\alpha \text{ and }\beta $are roots of the equation $3{{x}^{2}}+5x-2=0$. Find the value of $\tfrac{1}{\alpha }+\tfrac{1}{\beta }$.(A)  $-\tfrac{5}{2}$  (B)  $-\tfrac{3}{2}$  (C)  $\tfrac{1}{2}$  (D)$\tfrac{5}{2}$ 

if (x – 1), (x + 1) and (x – 2) are factors of the polynomial $a{{x}^{3}}+b{{x}^{2}}+cx-1$. Find a b c respectively 

In a youth club with 94 members, 60 like modern music and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?