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

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The human axial skeleton is made up of 80 bones; This includes bones in your skull (cranial and facial bones), ears, neck, back (vertebrae, sacrum, and tailbone), and ribcage (sternum and ribs)

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\(\left| \begin{array}{cc} -x & 2 \\ 4x &1 \end{array} \right|\) = \(\left| \begin{array}{cc} 3 & 3x \\ 4 & -5 \end{array} \right|\), Means that the determinants of both Matrices are equal - x - 8x = -15 - 12x -9x = -15 - 12x 12x - 9x = - 15 3x = -15 x = \(\frac{-15}{3}\) = -5

Let \( A = \begin{pmatrix} 1 & -3 \\ 0 & 1 \end{pmatrix} \) (given as \( P^{-1} \)). Determinant of \( A \) = \( (1)(1) - (-3)(0) = 1 \). Inverse of \( A \) is \( \frac{1}{1} \begin{pmatrix} 1 & 3 \\ 0 & 1 \end{pmatrix} \), which is exactly \( P \).

POM is a diameter, so arc MP (lower semicircle via Q) = 180^\circ. ∠MNQ = 42^\circ is an inscribed angle subtending arc MQ. Therefore, arc MQ = 2 \times 42^\circ = 84^\circ Arc MQ + arc QP = lower semicircle: arc QP = 180^\circ − 84^\circ = 96^\circ - ∠QMP is an inscribed angle subtending arc QP. Therefore, ∠QMP = \(\frac{1}{2}\) \times 96^\circ = 48^\circ. (Alternatively: in right triangle PQM, ∠PQM = 90^\circ (angle in a semicircle), so the angles at M and P sum to 90^\circ; the arc method directly gives the result.)

The given line is 2y + 8x - 17 = 0. Rewrite in slope form: 2y = -8x + 17 y = -4x + \(\frac{17}{2}\) Slope = −4. The line through points \((-1, -p)\) and \((-2p, 2)\) must have the same slope (parallel lines). Slope = \(\frac{2 - (-p)}{-2p - (-1)} = \frac{2 + p}{1 - 2p}\) \(\frac{2 + p}{1 - 2p} = -4\) Cross-multiply: 2 + p = -4(1 - 2p) 2 + p = -4 + 8p 2 + 4 = 8p - p 6 = 7p p = \(\frac{6}{7}\)

To find the maximum of \(f(\theta) = \frac{4}{6 + 2\cos \theta}\) for \(\frac{\pi}{2} \leq \theta \leq 2\pi\), simplify to \(f(\theta) = \frac{2}{3 + \cos \theta}\). The maximum occurs when \(3 + \cos \theta\) is minimized. In the interval, \(\cos \theta\) ranges from \(-1\) to \(1\), with minimum \(-1\) at \(\theta = \pi\). Thus, minimum denominator is \(3 - 1 = 2\), so maximum \(f(\theta) = \frac{2}{2} = 1\).

(a) Cell is the basic and smallest unit of life. It is the functional unit of life, from which all living things are built. (b) Nucleus has a spherical body which is covered by a double membrane which contains hereditary materials, Chromosomes and genes often centrally located in the cell, embedded in cytoplasm. It contains nucleus and nucleoplasm. The nucleus controls the activities of the cell and initiates cell division. (ii) Mitochnodrion is oval/rod-shaped. It is bounded by a double membrane. The inner membrane is folded and the interior is filled with matrix. The matrix contains ribosomes. It acts as the site for tissue respiration. (ii) Animal-like features of Euglena are: (i) Presence of flagellum (for movement) (ii) Pellicle (covers the body) (iii) Contractile vacuole (for Osmoregulation) (iv) Eye spot (sensitive to light) (v) Presence of gullet. Gullet Plant-like features of Euglena are (i) Chloroplast (for photosynthesis or manufacture of own food) Eye spot (ii) Paramyium granules/pyrenoids (for storage of starch)