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o (angle in the same segment of a circle are equal) But o (angle in a semicircle) also o (angles in a triangle = 180o) o + 90o = 190o o = 180o PSQ = 180o - 128o PSQ = 52o

RTS = RQT (angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment) But R = Q + T = 180 RQT = 180o - (50 + 60) = 180o - 110o = 70o Since RQT = RTS = 70o

A\(\bigtriangleup\) = \(\sqrt{S(S - a) (S - b)(S - c)}\) (Hero's Formula) S = \(\frac{a + b + c}{2}\) = \(\frac{5 + 6 + 7}{2}\) \(\frac{18}{2} = 9\) A\(\bigtriangleup\) = \(\sqrt{9 \times 4 \times 3 \times 2}\) \(\sqrt{216} = 6 \sqrt{6}cm^3\) A\(\bigtriangleup\) = \(\frac{1}{2} \times 6 \times h\) 6\(\sqrt{6} = \frac{1}{2} \times 7 \times h\) h = \(\frac{12}{7} \sqrt{6}\)cm

\(\frac{x}{r}\) = \(\frac{x + h}{2r}\) 2 x r = r (x + h) Total height of cone = x + h but x = h total height = 2h

Gradient of line = \(\frac{\text{Change in y}}{\text{Change in x}} = \frac{y_2 - y_1}{x_2 - x_1}\) y2 = 0, y1 = 4 x2 = 3 and x1 = 0 \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{3 - 0} = \frac{-4}{3}\) Equation of straight line = y = mx + c where m = gradient and c = y intercept = 4 y = \(\frac{-4x}{3}\) + 4, multiple through by 3 3y = - 4x + 12

Percentage of students who obtained C4 = \(\frac{43.2}{360}\) x 100% = = \(\frac{4320}{360}\) = 12%

No expanded working has been attached for this question yet. The verified answer is Option D.

No expanded working has been attached for this question yet. The verified answer is Option A.

The sentence introduces Mr. Pam and specifies that he is a tailor. It implies he is not the only tailor but one among others who may also be tailors. The sentence is neutral and does not suggest exclusivity either to his name or profession.

The word “shall” expresses obligation or requirement, especially in formal or legal English. When we rewrite sentences expressing obligation using expressions like: It is obligatory that… It is essential that… It is necessary that… We use the subjunctive form of the verb.

A. amorous: This term refers to feelings of love or affection, which is not the opposite of "humorous." It's unrelated to the context of cartoons. B. grievous: This term means causing great pain or sorrow, and it is not the opposite of "humorous." It represents a serious and somber tone. C. hilarious: This term is similar in meaning to "humorous." It does not convey an opposite meaning; rather, it reinforces the idea of something being funny. D. grave: This term is the most appropriate opposite in meaning to "humorous." "Grave" refers to something serious, solemn, or dignified, contrasting with the light and amusing nature of "humorous." So, the correct answer is D. grave, as it provides the opposite meaning to "humorous" in the context of cartoons.

invaluable means extremely useful; indispensable. (something is said to be invaluable mostly when a price cant be put on it. ) example "an invaluable source of information". the opposite of invaluable is worthless. which means having no real value or use.

The word "obfuscating" means to make something unclear, confusing or difficult to understand by giving too much irrelevant or complex information. In the sentence, it means the lecture was making the issue more confusing rather than clearer.

The underlined word “exacerbating” means making something worse or more severe, especially something unpleasant like pain, a situation, or a problem. The opposite is alleviating, which means reducing or lessening pain or hardship.

No expanded working has been attached for this question yet. The verified answer is Option C.