Correct Answer: A. predestination

Correct Answer: D. i and iv

Explanation

Simplify \(^{n + 1}C_{4} - ^{n - 1}C_{4}\)

= \(\frac{(n + 1)!}{4! (n - 3)!} - \frac{(n - 1)!}{4! (n - 5)!}\)

= \(\frac{(n + 1)(n)(n - 1)(n - 2)(n - 3)!}{4! (n - 3)!} - \frac{(n - 1)(n - 2)(n - 3)(n - 4)(n - 5)!}{4! (n - 5)!}\)

= \(\frac{(n + 1)(n)(n - 1)(n - 2)}{4!} - \frac{(n - 1)(n - 2)(n - 3)(n - 4)}{4!}\)

= \(\frac{(n - 1)(n - 2) [n(n + 1) - (n - 3)(n - 4)]}{4!}\)

= \(\frac{(n - 1)(n - 2) [n^{2} + n - n^{2} + 7n - 12]}{24}\)

= \(\frac{(n - 1)(n - 2)[8n - 12]}{24}\)

= \(\frac{(n - 1)(n - 2)(2n - 3)}{6}\)

Correct Answer: C. Relief

Explanation

The poor in the poem do not have homes. They live "under bridges". But they come to terms with their situation with equanimity. They see themselves as significant and playing a particularly active and useful role in society.

By their situation, the poor rely on the rich for survival. But they work for their upkeep. They rise at daybreak and ply their trade and "beg for alms".

The curious thing about the occupation of the poor beggars is that it sustains the system. They are clear-eyed and fully aware that they form a "necessary part of your society". It is ironical, even paradoxical, that the rich should imagine that they are removed from the world of the poor.

As the persona puts it, the poor people are the "translators of your dreams". This refers to the rich of the society, who have everything while the poor have nothing. The poor say that they carry the burdens of the rich.

This is significant because it hits at the very root of offering alms. Anyone who gives alms wants to be blessed. In requesting and accepting alms, therefore, the poor are "angels" who "open gates of blessing" for the rich.

The link between poverty and wealth is put succinctly in the paradox of the couplet: "we are the lack that take your lack". The rich lack blessings as much as the poor lack wealth. When the wealthy give the poor a little of their possession, the acceptance of the offer of alms opens the gates of blessings for the givers. In this way, the fortunes of the poor and those of the wealthy are intertwined.

Correct Answer: C. birth and death rates

Correct Answer: C. 24.0N

Explanation

V.R = \(\frac{R}{r} = \frac{30}{6} = 5\)

\(\gamma = \frac{M.A}{V.R} \times \frac{100}{1} \)

M.A = \(\frac{100 \times 5}{100} = 5\)

Effort = \(\frac{L}{M.A} = \frac{120}{5}\)

= 24N

Correct Answer: A. elastic

Correct Answer: C. 5

Explanation

\((x * y) = \frac{x+y}{2}\)

\((3 * b) = \frac{3+b}{2}\)

\(x \circ y = \frac{x^{2}}{y}\)

\((\frac{3+b}{2}) \circ 48 = \frac{(\frac{3+b}{2})^{2}}{48} = \frac{1}{3}\)

\(\frac{(3+b)^{2}}{48 \times 4} = \frac{1}{3}\)

\((3 + b)^{2} = \frac{48 \times 4}{3} = 64\)

\(b^{2} + 6b + 9 = 64 \implies b^{2} + 6b + 9 - 64 = 0\)

\(b^{2} + 6b - 55 = 0 \implies b^{2} - 5b + 11b - 55 = 0\)

\(b(b - 5) + 11(b - 5) = 0 \implies (b - 5) = \text{0 or (} b + 11) = 0\)

Since b > 0, b - 5 = 0

b = 5.

Correct Answer: D. lords and serfs