Explanation

No. of red = 10, No of green = 8

Total = 18

P(RG) = P(R) x P(G)

= \(\frac{10}{18} \times \frac{8}{17} = \frac{40}{152}\)

P(GR) = P(G) x P(R)

= \(\frac{8}{18} \times \frac{10}{17} = \frac{40}{153}\)

P(one red and one green)

= \(\frac{40}{153} + \frac{40}{153} = \frac{80}{153}\)

(b) P = 20% = \(\frac{20}{100}\) = 0.2

q = 1 - P = 1 - 0.2 = 0.8

n = 12

P(2 \(\leq x \leq 5\)) = P(5) - P(2)

= \(^{12}C_5(0.5)^5 (0.8)^7 - ^{12}C_2(0.2)^2(0.8)^{10}\)

= 792 x (0.2)\(^5\) (0.8)\(^7\) - 65(0.2)\(^2\)(0.8)\(^10\)

= 0.04892 - 0.2791

= 0.2302

Correct Answer: B. My daddy’s clock is not quartz.

Correct Answer: D. has the mandate of the people to rule

Explanation

Legitimacy of government is the popular acceptance of a government, political regime, or system of governance.

Correct Answer: A. clearing

Explanation

(a) The apparent cubic expansivity of a liquid is defined as the apparent increase in volume per unit volume per unit rise in temperature.

(b)(i)

Procedure: Density bottle dried and weighed, M,, fill bottle with liquid, replace the stopper and wipe the bottle dry. Weigh bottle and content M\(_2\), suspend the bottle with content in a water bath. Record the initial temperature of the water in the bath T\(_1\). Then heat water gradually up to boiling point. Notice that some liquid is expelled through the orifice of the stopper and the water in the bath is allowed to continue boiling until no more liquid is expelled through the orifice of the stopper.Record the final temperature T\(_2\) of the water bath. Remove the bottle from the bath, allow it to cool, wipe, dry it and reweigh M\(_3\).

Calculation: Mass of the liquid expelled from the bottle = (M\(_2\) - M\(_3\)) Mass of the liquid left in the bottle = (M\(_3\) - M\(_1\) Temperature change, (T\(_2\) - T\(_1\)) Apparent cubic expansivity

\(\alpha\) a = \(\frac{\text{Mass of the liquid expelled}}{\text{ Mass of remaining liquid \times change in temperature}}\)

\(\alpha\) a = \(\frac{M_2 - M_3}{(M_3 - M_1) - (T_2 - T_1)}\)

(ii) Precautions;

(1) Avoid parallax in reading thermometer

(2) Bottle should not be submerged

(c) Apparent cubic expansivity

\(\alpha\) a = \(\frac{M_2 - M_3}{(M_3 - M_1) - (T_2 - T_1)} = \frac{44.25 - 42.02}{42.02 \times 50}\)

\(\alpha\) a = 1.06 x 10\(^{-3} k^{-1}\)

But real cubic expansivity = \(\alpha\) a =+ \(\alpha\) g

Where \(\alpha\) g is the cubic expansivity of the containing vessel i.e. glass

\(\alpha\) a = 1.09 x 10\(^3 K^{-1}\)

Correct Answer: A. crop rotation

Correct Answer: B. legitimacy

Explanation

Authority is having the legitimate right to hold power (police and military commanders have the authority to command others, professors have the authority to teach, certified mechanics have the authority to repair cars.

Correct Answer: A. 20 and 80

Explanation

Marriage is an important theme in the play. All the major characters are deeply concerned with the issue of marriage and at one time or the other express strong views on this issue. It serves as a force which motivates most of the important actions in the play. Further, it forms the subject of many arguments and very lively, if not heated, debates.

The issue of marriage is brought into every conversation, however trivial it may be. Right at the start of the play Algernon broaches the subject in a conversation with his butler, Lane. He asks the question: "why is it that at a bachelor's establishment the servants invariably drink the champagne?" Lane's response hits straight home at the point: "I attribute it to the superior quality of the wine... I have often observed that in married households the champagne is rarely of a first-rate brand." They then launch into a short conversation on the nature of marriage in which Lane remarks that he does not find the subject of marriage an interesting topic for discussion. This leads to Algernon's comments, when Lane insists that "Lane's views on marriage seem somewhat lax".

The conversation between the friends, Jack and Algernon, inevitably touches on the issues of marriage. Jack's sincere belief in the romanticism of marriage is countered by Algernon's cynical views. While Jack expresses the wish to always enjoy the company of his wife when he does marry, Algernon insists that the married man should always create an alter ego which will give him an opportunity to run away from his wife from time to time. Algernon's views, of course, change when he falls in love with Cecily.

The question of marriage occupies the top spot in Lady Bracknell's list of priorities. Her perspective on marriage is expressed solely from a materialistic viewpoint. Her "list of eligible young men" does not, therefore, include Jack who wants to marry her niece, Gwendolyn.

Lady Bracknell puts status first: "a man should always have an occupation of some kind". Her "list of eligible young men" is based on social status and wealth. Therefore, Jack with his "nondescript origin" having been found abandoned in a handbag at Victoria Station will never make her list.

Lady Bracknell' s interview of Jack accentuates the ludicrousness of her criteria for eligibility. For her, "a man who desires to get married should know either everything or nothing. To Jack's response that he knows nothing she says: "I am pleased to hear it". Wilde is certainly poking fun at Victorian ideals of marriage here. The important issues, such as a person's character takes the back seat: "I am not in favour of long engagements. They give people the opportunity of finding out each other's character before marriage, which I think is not good thing" (Lady Bracknell). As it turns out, Jack is actually Lady Bracknell's nephew - and Algernon's brother! This accentuates the foolishness of prohibiting marriage on the grounds that the proposed suitor's background is undistinguished. After all, she admits herself that when she married Lord Bracknell she had no fortune of her own but that she "never dreamed for one moment of allowing that to stand in my way".

Correct Answer: D) It lowers the blood pressure

Explanation

The question is asking which of the options is not true about the sympathetic nervous system. The sympathetic nervous system is part of the autonomic nervous system that helps the body respond to stress or danger by stimulating various organs and tissues. Option A states that the sympathetic nervous system stimulates many parts of the body in times of danger, and this is true. In response to danger or stress, the sympathetic nervous system activates the fight-or-flight response, which increases heart rate, dilates pupils, and increases blood flow to muscles. Option B says that the sympathetic nervous system stimulates the heartbeat, and this is also true. The sympathetic nervous system stimulates the heart to beat faster and stronger during times of stress. Option C states that the sympathetic nervous system functions like the adrenal glands. This option is not entirely clear, but it is true that the adrenal glands release hormones in response to sympathetic nerve stimulation. Option D, which is the correct answer, states that the sympathetic nervous system lowers the blood pressure. This is not true. The sympathetic nervous system actually increases blood pressure by constricting blood vessels and increasing heart rate. In summary, the sympathetic nervous system is responsible for the body's response to stress or danger and stimulates various organs and tissues. It increases heart rate, dilates pupils, and increases blood flow to muscles. It does not lower blood pressure, but rather increases it by constricting blood vessels and increasing heart rate.