If f(x) = \(\begin{cases} 1+x,-1 \leq x<0 \\ x^{2}-1, \quad 0\end{cases}\)
Then, find f(3), f(-2), f(0), \(f(\frac { 1 }{ 2 } )\), f(2-h) and f(-1+h), where h > 0 is very small.

6

(a)

Find the domain of the function \(f(x)=\frac { { x }^{ 2 }+2x+1 }{ { x }^{ 2 }-8x+12 } \)

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)

If 4digit numbers greater than 5000 are randomly formed the digits 0,1,3,5 and 7.What is the probability of forming a number divisible by 5 when the repetition of digits are not allowed?

6

(a)