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This is a standard trigonometric derivative Therefore, \(\frac{d}{dx}\)(2 sec x) = 2 sec x tan x.

The given central angle of \(120^\circ\) corresponds to the minor arc The central angle corresponding to the major arc is therefore \(360^\circ - 120^\circ = 240^\circ.\) The length of an arc of a circle of radius \(r\) that subtends an angle \(\theta\) (in degrees) at the centre is given by \(\frac{\theta}{360^\circ} \times 2\pi r.\) Substitute \(r = 14\) cm and \(\theta = 240^\circ\): \(\frac{240}{360} \times 2\pi \times 14 = \frac{2}{3} \times 28\pi = \frac{56\pi}{3}\ \text{cm}.\) = 58.67 cm

The interquartile range (IQR) is given by: IQR = Q\(_3\) − Q\(_1\)

Total number of pears = 100 Number of unripe pears = 20 Number of ripe pears = 100 - 20 = 80. Probability that a randomly picked pear is ripe \(P(\text{ripe}) = \frac{\text{Number of ripe pears}}{\text{Total number of pears}} = \frac{80}{100} = \frac{4}{5}\) = 0.8

\(\frac{1}{2} + \frac{1}{3} \times \frac{3}{4}\) Using BODMAS \(\frac{1}{2} + \frac{1}{3} \times \frac{3}{4}\) = \(\frac{1}{2} + \frac{1}{4}\) = \(\frac{2 + 1}{4}\) = \(\frac{3}{4}\)

If Log\(_k243\) = 5 Convert to index form. k\(^5\) = 243 k\(^5\) = 3\(^5\) Since the powers on both sides are equal, equate the bases. k = 3

0.000371 has three significant figures (3, 7, and 1). To write it with two significant figures, retain the first two digits and examine the following digit: First two significant digits: 3 and 7 Next digit: 1 (which is less than 5), so no rounding up occurs. Therefore: 0.000371 \(\approx\) 0.00037.

P varies directly as N and inversely as M P = \(\frac{\text{k N}}{\text{M}}\) 9 = \(\frac{ 8k}{12}\) 8k = 12 x 9 K = \(\frac{108}{8}\) = 13.5 P = \(\frac{13.5 N}{\text{M}}\) Find N, when M = 17, P = 27 27 = \(\frac{13.5 N}{17}\) 13.5 N = 27 x 17 = 459 N = \(\frac{459}{13.5\) = 34.

\(\begin{pmatrix} 2 & 0 & 1 \\ 3 & 2 & 4 \\ 1 & 4 & 1 \end{pmatrix}\) = 2\(\begin{pmatrix} 2& 4 \\ 4 & 1 \end{pmatrix}\) - 0\(\begin{pmatrix} 3 & 4 \\ 1 & 1 \end{pmatrix}\) + 1\(\begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix}\) = 2(2 - 16) - 0 + 1(12 - 2) = 2(-14) + 1(10) = - 28 + 10 = - 18.

The parts labelled I, II and III are: I: Collenchyma – Located in the hypodermis (just below the epidermis), providing flexible mechanical support to the young stem. II: Parenchyma – Comprises the main bulk of the cortex, consisting of thin-walled cells responsible for food storage and metabolic functions. III: Sclerenchyma – Forms the protective pericycle caps (bundle caps) over the vascular bundles, providing rigid mechanical strength. Option C is the correct answer

Rod-shaped bacteria are called bacilli (singular: bacillus). They have an elongated, cylindrical, or rod-like form.

Chromosomes are the structures inside the cell nucleus that package and organize long strands of DNA. Ribosomes are the site where RNA builds proteins, not where DNA is stored, blood contains cells (like white blood cells), but DNA is specifically housed within the nucleus of those cells rather than the blood fluid itself while the enzymes are proteins that speed up chemical reactions, not the storage units for genetic information

A photometer is a scientific instrument specifically designed to measure the intensity of light or the strength of electromagnetic radiation. It is widely used in photography, astronomy, and agriculture to track lighting conditions.

The evolutionary theory associated with natural selection is the theory of evolution by natural selection, first proposed by Charles Darwin.

Vitamin K aids in blood clotting in humans. A deficiency of vitamin K is rare in healthy adults, but it can lead to a longer clotting time, easy bruising, or dangerous bleeding.