Solve the equation z² =\(\overset { \_ }{ z } \) , where z = x + iy.

6

(a)

If ⁿC_r-1 = 36. ⁿC_r = 84 and ⁿC_r+1 = 126 then find ^rC₂

6

(a)

Find  \(\lim _{x \rightarrow 0} f(x) \text { and } \lim _{x \rightarrow 1} f(x), \text { where }\)
\(f(x)=\left\{\begin{array}{ll} 2 x+3, & x \leq 0 \\ 3(x+1), & x>0 \end{array}\right.\)

6

(a)

A box contains 200 bolts and 70 nuts. It is given that 60% bolts and 40% nuts are rusted.Two objects are selected at random from the box.Find the probability that either both are bolts or both are rusted.

6

(a)

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?

6

(a)