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[5×1] In sub-parts (i) and (ii) choose the correct options and in sub-parts (iii) to (v), answer…
[5×1] In sub-parts (i) and (ii) choose the correct options and in sub-parts (iii) to (v), answer the questions as instructed.
(i)
The demand function of a monopolist is given by $x = 100 - 4p$. The quantity at which $\text{MR} = 0$ will be:
- (a)25
- (b)10
- (c)50
- (d)30
(ii)
If the lines of regression are parallel to coordinate axes, then the coefficient of correlation is:
- (a)1
- (b)0
- (c)$-1$
- (d)½
(iii)
Find the marginal cost function (MC), if the cost function is:
$C(x) = \frac{x^3}{3} + 5x^2 - 16x + 2$.
(iv)
If revenue function $R(x) = 3x^3 + 8x - 2$, find the average revenue function.
(v)
If $\sigma_x = 3$, $\sigma_y = 4$ and $b_{xy} = \frac{1}{3}$, then find the value of correlation coefficient ($r$).
Answer
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From ISC 2021 Specimen Mathematics Paper 1, question 19.