Correct Answer: B. 1959

Correct Answer: C. metre

Explanation

Metre is the measurement and arrangement of regular number of stressed and unstressed syllabus within a line. It is determined by rhythm in a poem

Explanation

Position vector of A is (8i - 10j)

Position vector of B is (2i + 6j)

Position vector of C is (-10i + 4j).

Let position vector of N be (ai + bj).

ABCN is a parallelogram.

\(\therefore \overrightarrow{AB} = \overrightarrow{NC}\).

\(\begin{bmatrix} (2 - 8)i \\ (6 + 10)j \end{bmatrix} = \begin{bmatrix} (-10 - a)i \\ (4 - b)j \end{bmatrix}\)

Equating components,

\(2 - 8 = -10 - a \implies a = -4\)

\(6 + 10 = 4 - b \implies b = -12\)

The position vector of N is (-4i - 12j).

(b) \(\overrightarrow{AN} \cdot \overrightarrow{AB}\)

\(\overrightarrow{AN} = \bar{A} - \bar{N} \)

= \((8i - 10j) - (-4i - 12j)\)

= \(12i + 2j\)

\(\overrightarrow{AB} = \bar{A} - \bar{B}\)

= \((8i - 10j) - (2i + 6j)\)

= \(6i - 16j\)

\(\therefore \overrightarrow{AN} \cdot \overrightarrow{AB} = (12i + 2j) \cdot (6i - 16j)\)

= \(72 - 32 = 40\)

(c) Let \(\theta\) be the acute angle between \(\overrightarrow{AN}\) and \(\overrightarrow{AB}\).

\(\overrightarrow{AN} \cdot \overrightarrow{AB} = |AN||AB| \cos \theta\)

\(|AN| = |12i + 2j| = \sqrt{12^{2} + 2^{2}} = \sqrt{144 + 4} = \sqrt{148}\)

\(|AB| = |6i - 16j| = \sqrt{6^{2} + (-16)^{2}} = \sqrt{36 + 256} = \sqrt{292}\)

\(\therefore 40 = (\sqrt{148})(\sqrt{292}) \cos \theta\)

\(\cos \theta = \frac{40}{(\sqrt{148})(\sqrt{292})}\)

\(\cos \theta = \frac{40}{207.88} = 0.1924\)

\(\theta = \cos^{-1} (0.1924) = 78.907°\)

\(\approxeq 78.9°\)

Explanation

(a)

(b)

(ci) The number of candidates who scored marks between 24 and 58 = 146 - 14 = 132

(cii) if 12% of the candidates passed with distinction then 88% did not pass with distinction

⇒\(88% of 200 = \frac{88}{100}\times 200=176\)

From the cumulative frequency curve, 176 corresponds to 69 marks

∴ Thelowest mark for distinction = 69 marks

Correct Answer: C. 4m

Correct Answer: B. \(\frac{4}{7}\)

Explanation

\(P(X?Y)=\frac{5}{8}\)

\(P(X?Y)=P(X)\times P(Y)\)

Since X and Y are independent events, the probability of their union (X ? Y) can be calculated as:

\(P(X?Y)=P(X)+P(Y)-P(X?Y)\)

\(=\frac{5}{8}=\frac{1}{8}+P(Y)-\frac{1}{8}\times P(Y)\)

\(=\frac{5}{8}-\frac{1}{8}=P(Y)-\frac{1}{8}\times P(Y)\)

\(=\frac{1}{2}=P(Y)(1-\frac{1}{8})\)

\(=\frac{1}{2}=P(Y)(\frac{7}{8})\)

\(=P(Y)=\frac{1}{2}÷\frac{7}{8}\)

\(∴P(Y)=\frac{1}{2}x\frac{8}{7}=\frac{4}{7}\)

Correct Answer: C. theme

Correct Answer: C. 14

Correct Answer:

Explanation

There was a rich man who was always gorgeously dressed. He lived in a big and beautiful house. At his gate was a poor man named Lazarus who wore rags and had sores all over his body. He begged even to be fed with the crumbs that fell from the rich man's table, but he was daily ignored. The dogs came and licked his wounds. When both men died, Lazarus was carried to Abraham's bosom while the rich man was carried to Hades or hell where he was in great agony. He saw Abraham afar and Lazarus in his bosom. He cried, " Father Abraham, have mercy upon me and send Lazarus to dip the end of his finger in water and cool my tongue, for I am in anguish in this flame". Abraham replied: " Son, remember that you in your life time received your good things and Lazarus in like manner evil things, but now he is comforted here, and you are in anguish".

He was further told that there was a gulf between heaven and hell for either of them to cross over. The rich man requested Father Abraham to send Lazarus to his brothers on earth to tell them to be kind to the-poor. Abraham told him that his brothers had Moses and the prophets whom they should listen to. The rich man pressed further that if only someone from the dead would preach to them, they would listen. In his reply, Abraham said that if they could not listen to Moses and the Prophets, neither would they listen if someone should rise from the dead.

Lessons which can be learnt from the parable of the rich man and Lazarus are:

(i) The parable teaches concern for one another.

(ii) As the Jews rejected the teaching of Moses and the prophets, so also did they reject the son of God, Jesus who was sent to bring salvation to mankind.

(iii) If we misuse our opportunities on earth, it may be taken away from us when we get to heaven.

(iv) Over-indulgence of the physical appetite leaves no room for spiritual growth.

Correct Answer: A) give the Philistines into his hands

Explanation

The question is asking what Saul learnt from the spirit of Samuel about the LORD's plan. The options are A) give the Philistines into his hands, B) afflict him with sickness, C) bless Isaac's future wife, and D) pardon his iniquity. The correct option is A, which means that Saul learnt that the LORD would give the Philistines into his hands.

Saul was the first king of Israel and he sought guidance from Samuel, who was a prophet, on several occasions. In this scenario, Samuel had died and Saul was facing a battle against the Philistines. He was afraid and did not know what to do, so he sought out a medium to help him contact Samuel's spirit.

From the spirit of Samuel, Saul learnt that the LORD would give the Philistines into his hands. This was a message of encouragement and assurance that he would be victorious in battle. It also showed that the LORD was with him and supporting him in his mission as king of Israel.

It is important to note that seeking guidance from mediums or spirits is not a practice condoned in Christianity. The Bible strictly prohibits such practices, and believers are encouraged to seek guidance from God through prayer and reading the Bible.

In summary, Saul learnt from Samuel's spirit that the LORD would give the Philistines into his hands. This was a message of encouragement and assurance that the LORD was with him and supporting him in his mission as king of Israel.