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(a) Solving the eqns of the two lines simultaneously: x + 2y = 7 - - -- - - - - - -(i) x - y = 4 - - - - - - - - - - - -(ii) subtract eqn (ii) from (i) x - x + 2y - (- y) = 7 - 4 3y = 3 y = 1 put y = 1 into eqn (ii) x - 1 = 4 x = 4 + 1 = 5 The point of intersection of lines is (5, 1) ⇒ If the line passes through Origin (0, 0) and (5, 1) Using: \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}\) \(\frac{1 - 0}{5 - 0} = \frac{y - 0}{x - 0}\) \(\frac{1}{5} = \frac{\text{y}}{\text{x}}\) Therefore, the equation of the line = x - 5y = 0 (b) Given that the ratio of the interior angle to the exterior angle of a regular polygon = 4: 1 Thus, I = 4E But, the sum of the interior angles and the exterior angles of a regular polygon = 180 i.e. I + E = 180 4E + E = 180 5E = 180 E = \(\frac{180}{5}\) = 36º Since, I = 4E = 4 x 36 = 144º (ii) value of the exterior angle = 36º (i) Number of sides of the polygon = \(\frac{360}{\text{n}}\) = E, n = \(\frac{360}{36}\) = 10 (since E = 36º) (iii) Sum of the interior angles of the polygon. = (n - 2)180 = (10 - 2)180 = 8 x 180 = 1,440.

(i) 2 x T\(\widehat{S}\)Q = P\(\widehat{O}\)Q (2 times angle at circumference = angle at centre of circle) T\(\widehat{S}\)Q = \(\frac{P\widehat{O}Q}{2}\) = \(\frac{56}{28}\) = 28º T\(\widehat{Q}\)P = T\(\widehat{S}\)Q (angles in alternate segment} (ii) S\(\widehat{T}\)O + T\(\widehat{S}\)Q + S\(\widehat{V}\)P = 180º (sum of angles in a \(\triangle\)) S\(\widehat{T}\)O + 28º + 109º = 180º S\(\widehat{T}\)O = 180º - 28º - 109º = 43º Now, O\(\widehat{T}\)Q = O\(\widehat{Q}\)T (base angles of an isosceles triangle) O\(\widehat{T}\)Q + O\(\widehat{Q}\)T + P\(\widehat{O}\)Q = 180º 2(O\(\widehat{T}\)Q) = 180 - 56 = 124º O\(\widehat{T}\)Q = \(\frac{124}{2}\) = 62º Q\(\widehat{T}\)S = S\(\widehat{T}\)O + O\(\widehat{T}\)Q = 42 + 62 = 105º (b) \(\frac{2n^2 - 3n - 2 }{2n^2 + 3n + 1} \times \frac{n^2 - 1}{n^2 - 4}\) = \(\frac{(2n + 1)(n - 2)}{(2n + 1)(n + 1)} \times \frac{(n + 1)(n - 1)}{(n + 2)(n - 2)}\) After canceling common factors = \(\frac{n - 1}{n + 2}\)

(a) \(\frac{B\widehat{T}Q}{2}\) = B\(\widehat{T}\)C = C\(\widehat{T}\)Q (\(\overline{TC}\) bisects \(\angle\)BTQ) B\(\widehat{T}\)Q = B\(\widehat{A}\)T = 44º(angles in alternate segments) B\(\widehat{T}\)C = \(\frac{∠BTQ}{2}\) = \(\frac{44}{2}\) = 22º A\(\widehat{B}\)T = P\(\widehat{T}\)A = 60º (angles in alternate segments) Now, A\(\widehat{C}\)T + B\(\widehat{T}\)C = A\(\widehat{B}\)T (sum of opp. interior angles is equal to the exterior angle of a triangle) A\(\widehat{C}\)T + 22º = 60º A\(\widehat{C}\)T = 60 - 22 = 38º (b) (i) Given: Circumference of base, 2\(\pi\)r = 11 -- - - - - - - - - - -(i) Also, height, h = 6r + 3 - - - - - - - - - -(ii) From, eqn (i), 2\(\pi\)r = 11, r = \(\frac{11}{2\pi}\) = 1.75 m (ii) From equation (ii); height, h = 6r + 3 = 6(1.75) + 3 = 13.5 m (iii) Volume of cylinder, V = \(\pi r^2\)h = \(\frac{22}{7} \times 1.75^2\) x 13.5 = 130 m\(^3\)

Inbreeding is the mating of organisms that are more closely related than would normally occur in nature. This can include mating between siblings, parents and children, or first cousins. Studies have confirmed an increase in several genetic disorders due to inbreeding such as blindness, hearing loss, neonatal diabetes, limb malformations, disorders of sex development, schizophrenia and several others. In adults, inbreeding can lead to deafness, visual impairment, and mental deficiency.

The diagram is that of the virus. Viruses are obligate parasites, meaning they can't produce their own energy or proteins. They enter the host cell and use the cell's machinery to make their own nucleic acids and proteins. Viruses also use the host cell's lipids and sugar chains to create their membranes and glycoproteins. This parasitic replication can severely damage the host cell, which can lead to disease or cell death. They usually enter your body through your mucous membranes. These include your eyes, nose, mouth, penis, vagina and anus. Viruses are a unique type of organism that are not plants, animals, or bacteria. They are often classified in their own kingdom. However, for the sake of the question, since most of their attributes and metabolic activities are more of the bacteria, we'll go with option A - Monera

Specimen L - Thoracic vertebra Specimen M - Humerus bone Specimen P - Femur bone Specimen Q - Lumbar Vertebra (a) Region of the human body where each of specimens L and Q are located. L: chest or thorax region Q: abdominal region or between thoracic and sacral vertebrae b(i)Four observable differences between specimens L and Q. L(Thoracic vertebra) Q(Lumbar vertebra) presence of small centrum presence of large centrum Neural spine is long Neural spine is short Transverse process is long Transverse process is short Absence of anapophysis Anapophysis is present Demifacets are present Demifacets are absent (ii) Observable similarities between specimens L and Q. - Both thoracic and lumbar vertebrae have facet joints that articulate with adjacent vertebrae. - Both thoracic and lumbar vertebrae have a body. - Both thoracic and lumbar vertebrae have a spinous process that extends backward. - Both thoracic and lumbar vertebrae have transverse processes that extend laterally. - Both of them possess neural arch. c(i) Bones each that articulate with specimens M(humerus bone) and P(femur bone) M: scapula, ulna, cervical P: pelvic girdle, tibia (ii) One vertebra each that is located and after each of specimens L and Q in the vertebral column. Before After L: ...cervical vertebra.. ...Lumbar vertebra... Q: ....thoracic vertebra.. ....sacral vertebra.... (d) Specimen Features Neural canal Rounded head Neural spine Long shaft L(thoracic) ✔ X ✔ M(humerus bone) X ✔ X ✔ P(femur bone) ✔ X ✔ Q(Lumbar vertebra) ✔ X ✔

Carbon is the primary building block of life on Earth.Carbon can form stable, complex molecules with other elements, especially hydrogen, oxygen, and nitrogen. Carbon-based molecules are the basis for life in all living organisms, including humans. These molecules include nucleic acids, carbohydrates, lipids, cells, and proteins. It is considered the major building block of organisms because of its unique ability to form stable bonds with many different elements, including itself, allowing it to create complex, diverse, and large molecules necessary for life, like proteins, carbohydrates, and nucleic acids, which are the foundation of all living things.

The process by which plants lose water to the atmosphere is called transpiration. Transpiration is the process by which plants release water into the atmosphere as water vapour. It occurs through stomata, which are tiny pores on the surface of leaves that allow plants to exchange gases with the atmosphere. Transpiration also occurs through evaporation from the surfaces of leaves, stems, and flowers. Guttation also involves water loss but there is difference between the two. Transpiration is the process where plants lose water vapour through tiny pores called stomata on their leaves, while guttation is the release of liquid water droplets from specialized structures called hydathodes, usually located on the edges of leaves, occurring when the plant absorbs water faster than it can transpire, creating a pressure that forces the water out; essentially, transpiration is water loss as vapour, and guttation is water loss as liquid droplets. Translocation is the process by which plants move dissolved materials, like sugars and nutrients, throughout the plant. Evaporation" in plants refers to the process called transpiration, where water absorbed by the plant roots travels through the plant's vascular system and exits as water vapour through tiny pores on the leaves called stomata.

The housefly has a sponging and sucking type of mouthpart, meaning it absorbs liquid food by essentially "lapping" it up with its spongy labellum, not piercing to suck like a mosquito does. Grasshopper has a biting and chewing type of mouthpart, which is used to process solid foods like grass and leaves. Piercing and sucking mouth parts are found in insects such as mosquitoes, lice, fleas, bedbugs, and stinkbugs.These insects have mouth parts that are adapted for piercing the skin of animals and plants to suck up blood and plant juice. Major insect groups that have chewing mouthparts include the cockroaches and grasshoppers, most wasps, beetles, termites and caterpillars. Insects with piercing-sucking mouthparts include some flies (think mosquitoes), fleas, true bugs and their relatives.

The webbed feet of frogs and toads help them swim and move through water.The thin layer of skin that connects the toes of frogs and toads increases the surface area of their feet, allowing them to push against the water more effectively. This helps them move quickly through the water to chase food or escape predators.

The sacculus is a sensory organ located in the inner ear that primarily functions to detect vertical linear acceleration, meaning it senses movement in the up and down direction, like when you're in an elevator, and helps maintain balance by providing information about your head's position relative to gravity; essentially, it tells your brain if your head is tilting forward or backward. The cochlea is the part of the inner ear that is responsible for hearing. The cochlea is a snail-shaped organ filled with fluid that contains the organ of Corti, which is made up of tiny hair cells that line the cochlea. When sound enters the ear, it causes the fluid in the cochlea to vibrate, which makes the hair cells vibrate and send electrical impulses to the brain. The brain perceives these electrical signals as sound. The utriculus, located in the inner ear, functions as a sensory organ that detects linear acceleration and head position in the horizontal plane, essentially sensing side-to-side tilting movements of the head, contributing to our sense of balance by providing information about static equilibrium.The inner ear also contains the semicircular canals, which are responsible for balance. The semicircular canals are filled with fluid and have calcium crystals embedded in their lining. The function of the ampullae in the ear is to detect head rotation by sensing the movement of fluid within the semicircular canals, sending signals to the brain regarding angular acceleration and deceleration of the head, essentially contributing to balance perception.

Human evolution is the process by which humans evolved from ape-like ancestors over millions of years. This process resulted in the development of physical and behavioral traits that all humans share today. Organic evolution is the theory that all living organisms have evolved from pre-existing species, and that the differences between organisms are due to changes in their genetic makeup over generations. Organic evolution, also known as biological evolution, is the gradual process by which living organisms change over time. It's the theory that all species are descended from common ancestors, and that the differences between them are due to changes in their genetic makeup over generations. Physical evolution" refers to the process by which the physical characteristics of an organism change over generations, primarily due to changes in its genetic makeup, resulting in adaptations to its environment, often manifested in alterations to body shape, size, and function of different body parts; essentially, it's the observable physical manifestation of biological evolution at the organism level.

By crossing Rr x rr We obtain Rr , rr , rr , Rr ⇒ 50% = \(\frac{1}{2}\)

A lysosome functions as the "garbage disposal unit" of a cell, primarily responsible for breaking down and recycling waste materials within the cell by digesting old cell parts, extracellular debris, and invading pathogens using digestive enzymes, thus maintaining cellular homeostasis and contributing to important processes like programmed cell death (apoptosis). The primary function of a ribosome in a living cell is to synthesize proteins by translating the genetic code carried by messenger RNA (mRNA) into a sequence of amino acids, which then fold to form functional proteins; essentially acting as the site where protein synthesis occurs within the cell. Centrioles are barrel-shaped organelles in the cytoplasm of animal cells that help organize microtubules and form centrosomes, cilia, and flagella. They are found near the nuclear envelope. Centrioles are essential for the formation of cilia and flagella in living cells. It is a barrel-shaped organelles made of microtubules that play a central role in the formation of cilia, flagella, and centrosomes. Plastids, organelles found primarily in plant cells, are responsible for the synthesis and storage of important molecules like food, pigments, and other metabolites, with their primary function being photosynthesis, using sunlight to convert carbon dioxide into energy-rich compounds like glucose; they also play a role in the plant's color due to the pigments they store

Fat is the food nutrient with the highest energy value, providing 9 calories per gram, while carbohydrates and proteins provide 4 calories per gram. Fat is the body's most concentrated source of energy, providing more than twice as much potential energy as carbohydrates or proteins.However, carbohydrates burn fastest in metabolism. Fats are a type of lipid. Lipids are a group of organic compounds that are insoluble in water but soluble in organic solvents. Fats are solid at room temperature, while oils are liquid at room temperature. Therefore, the correct answer is option C.