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Soaps are sodium or potassium salts of long chain fatty acids. When soap is added to hard water, the Ca²⁺ and Mg²⁺ ions present in hard water react with soap. The sodium salts present in soaps are converted to their corresponding calcium and magnesium salts which are precipitated as scum. The insoluble scum sticks on the clothes and so the cleaning capacity of soap is reduced.
 
Ca²⁺ +  2RCOO^-Na⁺ → (RCOO)2Ca + 2Na⁺ 
 
Mg²⁺ + 2RCOO^-Na⁺ → (RCOO)2Mg + 2Na⁺
 
The salt of Ca and Mg is called as SCUM.

The uses of solar energy include solar electricity, solar water heating, solar heating, solar ventilation, solar lighting, portable solar (for personal electronic devices) and solar transportation (for electric vehicles).

(1) Anthropology. 

(2) Homo sapiens. 

(3) Homo habilus lived between 1.62 - 2.5 million years ago. 

(4) Africa. 

(a) Carbondioxide (CO₂) is necessary for the photosynthesis. 

(b) Wide mouthed bottle, split cork, KOH solution, Iodine, Potted plant. 

(c) KOH is used for the absorption of CO₂ in the bottle. 

(d) We should test two leaves of which one must be having the availability of CO₂ and other must not be having the availability of CO₂ to prove that CO₂ is essential for the photosynthesis.

(c) Both (a) and (b) 

(d) All the above. 

(c) Free goods

The Market price of all final goods and services produced in the domestic territory of a country in a year is known as G D P_MP .

The market value of all final goods and services produced in an economy over a year is called Gross Domestic Product.

In Perfect competition market AR= MR.

If for a country net factor income from abroad is negative then GDP > GNP.

The subject of the study of macroeconomics is the principle of national income.

Goods, which can alternatively be used are called Substitutes.

Net national income at factor cost is called National Income. 

Goods discrimination is Monopoly market.

General price level is studied in Macroeconomics.

General Price level is studied in Macroeconomics.

A consumer is said to be in equilibrium, when he is spending his given income on various goods in such a way that maximises his satisfaction. 

Condition of consumers equilibrium in case of a single commodity: consumers equilibrium in case of a single commodity is attained when the marginal utility of the commodity measured in terms of money equal to it’s price symbolically.

MUx = P_x

(1) Paddy in Kharif is more profitable for a small farmer in village - 2. 

(2) Small farmer in village - 1 is getting more net income on Rabi paddy, cotton and gingelly whereas small farmer in village - 2 is getting more income on Kharif paddy. In total, small farmers in village - 1 are getting more income than farmers in village - 2 as they are using water resources properly. 

(3) Cotton in place of paddy. 

(4) (1) Lack of awareness regarding sustainable use of natural resources like water. 

(2) Not adapting crops suitable for their condition.

1. To prove that sunlight is necessary for photosynthesis. 

2. The part of the leaf which is not exposed to sunlight present under cutout design did not change its colour in iodine test. 

3. To ensure that leaves are free from starch. So that it may not influence the result of the experiment. 

4. Potted plant, light screen, iodine solution, petridish, black paper.

Amplitude modulation provides an efficient way to shift an acoustic or speech signal to a desirable frequency.

Statistics:
Statistics is a study of presentation, analysis, collection, interpretation and organization of data

There are two main branches of statistics
- Inferential Statistic.
- Descriptive Statistic.

Inferential Statistics:
Inferential statistics used to make inference and describe about the population. These stats are more useful when its not easy or possible to examine each member of the population.

Descriptive Statistics:
Descriptive statistics are use to get a brief summary of data. You can have the summary of data in numerical or graphical form.

f_x(x) \(=\begin{cases}cx\,e^{-\frac x2},&x\geq0\\0,&x<0\end{cases}\)

∵ \(_0\int^\infty\) f_x(x) dx = 1

⇒ \(_0\int^\infty\,cx\,e^{-x/2}dx=1\)

⇒ \(c\left[-2x\,e^{-x/2}-\int-2e^{-x/2}dx\right]^\infty_0=1\)

⇒ \(c\left[-2x\,e^{-x/2}-4e^{-x/2}\right]^\infty_0=1\)

⇒ 4C = 1

⇒ C = 1/4

CDF = F_x(x) \(=\,_0\int^x\,f_T(t)\,dt\)

\(=\,_0\int^x\,t/4\,e^{-t/2}df\)

\(=1/4[-2\,te^{-t/2}-\int-2e^{-t/2}df]^x_0\)

\(=1/4[-2t\,e^{-t/2}-4e^{-t/2}]^x_0\)

\(=1/4[-2x\,e^{-x/2}-4e^{-x/2}+4]\)

Hence, CDF of probability function is F_x(x) = -x/2 e^-x/2 - e^-x/2 + 1

A. False It should be urea-free to provide a high concentration gradient for urea loss. 

B. False It should be lower to favour loss of potassium, which is elevated in renal failure. 

C. False It should be higher to reduce extracellular fluid volume and hence blood pressure. 

D. False Fluid transfer is governed by hydrostatic pressure and crystalloid osmolality gradients, not by colloid osmotic pressure gradients. 

E. True It should be buffered to prevent large pH changes.

A. False It increases due to increased salt and water loss. 

B. False Body potassium rises since aldosterone normally increases its excretion. 

C. True Due to decreased sodium reabsorption. 

D. True Due to decreased extracellular fluid volume. 

E. False The viscosity increases as the haematocrit increases.

A. True Bladder pressure is measured while known volumes of fluid are run into it. 

B. True An example of receptive relaxation like that seen in the stomach. 

C. False The deflection usually occurs when around 500 ml is introduced. 

D. False The male urinary tract offers a higher ‘peripheral resistance’. 

E. True The increased work load causes muscular hypertrophy which allows generation of higher micturition pressures. 

A. False This is not a hormone. 

B. True For example, the globulin transcortin binds cortisol. 

C. True In both sexes they stimulate the growth of axillary and pubic hair. 

D. False After conjugation they are excreted mainly by the kidney. 

E. True Without replacement therapy, loss of adrenal cortical function results in death.

A. True It is formed in neurones whose cell bodies lie in the hypothalamus and whose axons transport it to the posterior pituitary gland. 

B. False The water retention it induces makes plasma osmolality fall. 

C. False It increases the permeability of the collecting ducts. 

D. False Secretion is affected by 1 per cent changes in osmolality; the sensitivity of the hypothalamic receptors to osmolar change accounts for the constancy of plasma osmolality. 

E. True Volume changes detected by vascular low-pressure receptors affect ADH secretion.

A. True Due to failure of the kidneys to reabsorb sufficient water. 

B. False Reabsorption of water in proximal tubules is normal since it depends on the active reabsorption of sodium; reabsorption in the collecting ducts is affected. 

C. False Both fluid compartments are depleted in volume. 

D. False It rises due to depletion of water but not salt. 

E. False Both compartments show the same raised osmolality; osmotic gradients are effective in moving water at cell membranes.

A. True Due to phasic or tonic release of adrenaline and/or noradrenaline. 

B. True Due to beta adrenoceptor stimulation by adrenaline. 

C. True Due to release of adrenaline. 

D. False α-receptor blockers typically lower the blood pressure. 

E. True This is a diagnostic feature.

A. False For example, parathyroid activity is not regulated by the pituitary. 

B. True Output can be increased and decreased by the action of prolactin-releasing hormone (PRH) or prolactin-inhibiting hormone (PIH) respectively. 

C. False ADH is secreted by the posterior pituitary in response to a rise in blood osmolality. 

D. True This may stimulate melanin production in human melanocytes. 

E. True The anterior pituitary is influenced by hormones arriving in portal-hypophyseal vessels and the posterior pituitary by impulses travelling in the hypothalamohypophyseal tract.

A. False Melanocyte-stimulating hormone is produced in the intermediate lobe of the pituitary; melatonin is produced mainly in the pineal gland. 

B. True The necessary enzymes are in the pineal parenchymal cells. 

C. False It has no role in regulation of human skin pigmentation. 

D. True Melatonin secretion has a pronounced circadian rhythm, low during the day and high by night. 

E. True Melatonin secreted in relation to prevailing conditions of light/darkness may adjust pituitary hormonal rhythms appropriately

A. False It is negative due to muscle wasting. 

B. False It rises due to liberation of calcium from bone. 

C. True Beta adrenoceptor blocking drugs relieve such features, e.g. tachycardia. 

D. True Heat intolerance is due to the increased heat production. 

E. False The protein levels are normal but they bind more thyroxine.

A. False Typically it will be reduced by about 80 per cent. 

B. False It should fall to the normal value of about 1 ml/minute. 

C. False It should rise to about 600–900 mosmol/litre, 2–3 times normal plasma osmolality (300 mosmol/litre). 

D. False ADH does not interfere with salt regulation. 

E. True Due to greater stability of the body fluids.

A. True Early stunting cannot be compensated for later in childhood. 

B. False This leads to increased height due to delayed closure of the epiphyses. 

C. True The sex hormones promote early closure of the epiphyses. 

D. True Thyroid hormones are essential for normal growth. 

E. True Adrenal hormones also are essential for normal growth.

A. False Increased metabolism leads to peripheral vasodilation. 

B. True The frequency of defaecation increases in hyperthyroidism. 

C. True Thyroid hormones uncouple oxidation from phosphorylation so that more energy appears as heat.

D. False The reverse is true. 

E. True This suggests a direct action on cells in the sinoatrial node.

A. False Glucocorticoids inhibit mitotic activity in lymphocytes. 

B. False Glucocorticoids inhibit fibroblastic activity; this may allow chronic infections to spread since they are not walled off effectively by fibrous scarring. 

C. False They are catabolic; released amino acids are converted to glucose. 

D. True Decreased bone formation and increased resorption may cause osteoporosis. 

E. True This blocks release of histamine and lysosomal enzymes in allergic responses.

A. True This is a prime feature of ketoacidosis. 

B. True The excess H⁺ ions compete with K⁺ ions for excretion in the distal tubules. 

C. True Due to the dissolved glucose. 

D. False This falls due to osmotic diuresis and vomiting. 

E. False Hyperventilation reduces P_CO2 to compensate the metabolic acidosis.

A. False This reduces aldosterone secretion. 

B. False This increases adrenocortical hormone (ADH) secretion. 

C. True K⁺ has a direct stimulatory effect on the adrenal cortex. 

D. True This leads to formation of angiotensin II which stimulates the cortex. 

E. True Though the main action of ACTH is on glucocorticoid secreting cells; it has some action on mineralocorticoid secreting cells.

A. True This is a central feature of tetany. 

B. True Due to severe convulsions. 

C. False Calcium levels do not fall below the levels needed for haemostasis. 

D. True This is the acute treatment of choice, e.g. calcium gluconate. 

E. True This acts by increasing intestinal calcium absorption.

A. False Insulin is required mainly in response to meals. 

B. False The disease is not usually due to rapid insulin breakdown. 

C. True Abnormal binding may occur in diabetes mellitus. 

D. True Obese patients usually show increased insulin resistance. 

E. False Exercise reduces insulin requirements. 

A. True The waking catabolic state changes to an anabolic state. 

B. True Insulin secretion occurs mainly in association with meals. 

C. True Adrenaline secretion is associated with stress. 

D. False This rises as plasma osmolality rises; water is lost but not replaced during sleep. 

E. False This increases, allowing growth and anabolic repair of tissue wear and tear.

A. False They are distinct hormones with different actions. 

B. False Breast growth depends on oestrogens and progestogens. 

C. True This mediates hypothalamic regulation of prolactin levels. 

D. True This is responsible for the maintenance of lactation in the puerperium. 

E. False Milk ejection is a consequence of oxytocin secretion.

A. False It is the time it takes for the initial concentration to fall by half. 

B. False It is much shorter (about five minutes); this allows more precise and continuous regulation of the blood glucose level. 

C. True It is much longer since moment to moment regulation of its level is less critical. 

D. True It is more highly protein-bound which appears to prolong its life. 

E. True Acetylcholine is broken down almost immediately by cholinesterase.

A. True In alkalosis, the calcium-binding power of the plasma proteins increases. 

B. False Like calcium, magnesium ions tend to prevent tetany. 

C. False The pituitary is not involved in calcium homeostasis. 

D. False The acidosis in respiratory failure reduces calcium binding by protein. 

E. False The acidosis in renal failure also reduces calcium binding by protein.

A. False It contains two peptide chains. 

B. False Minor differences occur but these differences do not affect insulin action. 

C. False Its peptide structure is broken down by digestive proteases in the gut. 

D. True In 1964 by Katsoyannis. 

E. True Using recombinant DNA.

A. False It is stored as thyroglobulin in the follicles. 

B. True By increasing the basal metabolic rate. 

C. True Deficiency in infancy causes mental retardation (cretinism). 

D. True Thyroxine deficiency can cause anaemia. 

E. False T₃ acts within a day, thyroxine within 2–3 days. 

(C) मनुष्य का आर्थिक कार्य