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(7 × 8)⁴ = 7⁴ × 8⁴ [∵(ab)^m = a^m x b^m]

p³ × q³ = (p × q)³

5² × 3²= (5 x3)² [∵ a^m × b^m = (ab)^m]

Given numbers are x , x + 2 , x + 4 , x + 6 , x + 8. 

Sum of numbers = x+(x+2) + (x+4) + (x+6) + (x+8) 

= 5x + 20 

Total Numbers = 5 

Now, Mean = (Sum of numbers) / (Total Numbers) 

= \(\frac{(5x+20)}{5}\)

= \(\frac{5(x + 4)}{5}\) 

= x + 4 

Mean = x + 4

The mean of the numbers is 27

The sum of 5 numbers = 5 * 27

= 135

If one number is excluded, then the new mean is 25

Therefore sum of new numbers = 4 * 25

= 100

Therefore, excluded number = 135 – 100

= 35

First five multiples of 3 are 3 , 6 , 9 , 12 , 15. 

Sum of numbers = 3+6+9+12+15

= 45

Total Numbers = 5 

Now, Mean = (Sum of numbers) / (Total Numbers) 

= \(\frac{45}{5}\)

= 9 

Mean = 9

The weights of 10 new born babies (in kg): 3.4 , 3 .6 , 4.2 , 4.5 , 3.9 , 4.1 , 3.8 , 4.5 , 4.4 , 3.6 

Sum of weights = 3.4 + 3.6 + 4.2 + 4.5 + 3.9 + 4.1 + 3.8 + 4.5 + 4.4 + 3.6

= 40 

Total number of babies = 10 

Now, Mean = (Sum of weights) / (Total number of babies) 

= \(\frac{40}{10}\) 

= 4 

Mean weight = 4 kg

The weight (in kg) of 10 new born babies = 3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6

Therefore, Mean \(=\frac{Sum\, of \, weight}{Total\,babies}\)

 \(=\frac{3.4 + 3.6 + 4.2 + 4.5 + 3.9 + 4.1 + 3.8 + 4.5 + 4.4 + 3.6}{10}\)

\(=\frac{40}{10}\)

= 4 kg

The mode of the data is 8 as it occurs the maximum times.

Correct answer is D.

D) 3.5 First of all we arrange the given data in increasing order.-3, -3, -1, 0, 2, 2, 2, 5, 5, 5, 5, 6, 6, 6 Now we count the no. of observations i.e. 14 which is even. So applying Median formula for even no.

of observation we get, median \(=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}}{2}\)

Where, x^th represent x^th term.

median \(=\frac{\frac{14}{2}^{th}+(\frac{14}{2}+1)^{th}}{2}\)

median \(=\frac{7^{th}+8^{th}}{2}\) \(=\frac{2+5}{2}\)

median = 3.5

Given that refractive index of air / water = 4/3

The height the bird would appear to fish = 4 + 4/3 × 3 = 4 + 4 = 8m

Correct option is  A) taller

Man will ultimately destroy the earth and eventually destroy himself.

Tigers, lions and some rare species are on the verge of extinction.

Our moral duty is to look after the things God has given us. We must learn to take care of the gifts of nature so that these are not destroyed or harmed. We must not use the gifts of nature for our selfish ends, but instead, work to preserve them.

The gifts of nature are ours to admire, use and preserve. So we should not destroy it.

Our school has a large area of open grounds in front and at the back of our school premises. The front area can be well used for planting trees in the borders. Each class can be allotted 10 beds to plant a sapling of shade-giving trees, prizes can be announced for the best maintainer. The last period of every day can be used for gardening work.

Read the following passage to your partner and write down suitable words in the blanks with his/her help.

Today the world is facing the problem of pollution. We are polluting Nature by our foolish acts. It is our duty to preserve the wonderful gifts of nature. We must leam to discipline our selves in preserving the gifts of Nature.

God has given us the most beautiful gift. The gift of Nature. Long ranges of mountains, oceans sprakling streams, dense forests, animals, birds, insects, colorful flowers, fruits and the earth and even the air we breathe are gifts of Nature. It our moral duty to protect and conserve these natural gifts.

Centuries ago, there were many more animals than there are today. Man has hunted them down for sport or food. Most animals species are extinct. Tigers and Lions and other rare species are now becoming endangered. If they are not protected and conserved we can see them only in pictures.

Oceans are endless expanse of water with countless fishes. Oceans are now becoming polluted by tons of refuse. When huge ships sink in bad weather the oil pollutes the oceans and kills the aquatic animals because they cannot breathe. We should preserve our oceans.

Rivers provide clean and useful water. We should aviod polluting our rivers. Trees are “Green gold” they are very valuable. We cannot live without Trees. Trees are necessary to build houses. So it is important for us to plant more trees to maintain ecological balance. We should plant saplings in parkes and road sides and protect them.

While trekking in the forests we must be careful to put off our campfires to avoid accidental forest fires, we should be careful and not pluck flowers in public gardens. Bees and butterflies carry pollen from place to place and perform an important function in nature. We should not kill them. We must learn to appreciate the beauty of nature and preserve this wonderful handiwork of God.

She gifts him the rose gardens of the quilt to tend for the rest of his life.

Maqbool is a gardener in the gardens of Mughal emperor Shah Jahan. His wife died long ago his sons were in the Emperor’s army and are away with their families in the Deccan. From then onwards the roses were his family. He named every rose like Gulbadan, Badal, Dilruba and Ghata.

One day he sent a rose ‘Subah’ well decorated in a basket to princess Jahanara through Dilruba the maid. In return the princess sent him a silk jacket. The next day when he was digging up a flower fed, another maid by name Panna comes and tells him that she is a maid to Princess Jahanara. Maqbool finishes his digging, sits down with a basket of golden marigolds and begins stringing a garland.

He tells that he is taking that to the Hanumanji mandir. Panna requests Maqbool to take her to the mandir. Maqbool agrees on the condition that he will not buy her anything. He took her to the bustling streets of Agra. Panna looked around in wonder and delight.

The girl walked slowly and stopped everywhere. Panna took the garland from Maqbool and placed it at the feet of the idol. She reached up and rang all the bells and then bent down low to do pranam. The priest gave them prasad and she immediately popped some into her mouth.

Then the two strolled through the bazaar. Panna sat and listened to a man singing on the masjid steps and stood giggling at a funny magician.

She bought roasted chana and sweet potatoes from a street vendor, she stood wide-eyed looking up at the sky, As she was looking at the kite flying high up, soldiers enter with their swords and said that the princess had been kidnapped. Panna revealed her disguise and the commander asked Maqbool to surrender. Princess Jahanara saves him and asks Maqbool to go back to his garden.

The next day Maqbool was sitting sadly in the garden and princess Jahanara came there. Maqbool said that the commander wanted him to leave for Sikandra immediately. Princess Jahanara rewarded Maqbool, the rose gardens of the Qila for the rest of his life and requested him to send her the prasadam whenever he went to the mandir.

The rose was a gift for princess Jhanara.

Maqbool’s wife died long ago. His sons were in the Emperor’s army and were away with their families in the Deccan. Then the roses were his family. Lovingly he calls each rose by names such as Gulbadan, Badal, Dilruba, and Ghata. He called the pink rose as ‘Subah’ and presented it with decoration to princess Jahanara.

Women seeing bangles or attar they will ask for it. Panna should not expect Maqbool to buy that for her as he had no money to buy anything.

When The Princess visited Agra, the roads were emptied for their visit. So she did not have a chance to see the crowded streets, people walking here Mid there. Now she looked around in wonder and delight. In the Hanuman temple, she rings the bell and eats the prasadam immediately. All this happened because of Maqbool. So she says that she had one of the most enjoyable days of her life.

Maqbool took princess Jahanara to the bustling streets of Agra, so he was asked to leave for Sikandra immediately. For taking Jahanara outside, Maqbool was punished and sent off to work at Akbar Badshah’s tomb at Sikandra.

The actual explanation is that the roads were emptied when the princess made a visit there. She explained that, she accompanied Princess Jahanara and then the roads were emptied.

Gastrin is Hormone.

Fat is largely digested in the small intestine. Bile salts of the bile break down fat droplets into many small ones by reducing the surface tension of fat droplets. This process is called emulsification. This increases lipases on fat.

Gall stones are formed in the gall bladder as a result of the precipitation of cholesterol or other substances. Some gall stones contain large amounts of calcium. Inflammation of gall bladder is called cholecystectomy.

(b) Gastro-intestinal hormone

Secretion of gastric juice is controlled by Gastrin.

Disorders of digestive system: 

(i) Jaundice : The liver is affected, skin and eyes turn yellow due to the deposit of bile pigment. 

(ii) Vomiting: It is the ejection of stomach contents through the mouth and controlled by the vomit centre in the medulla oblongata. 

(iii) Diarrhoea : Abnormal bowel movement and the faecal discharge with more liquidity, which leads to dehydration. 

(iv) Constipation : The feces are retained within the rectum due to irregular bowel movement. 

(v) Indigestion: Food is not properly digested leading to a feeling of fullness due to inadequate enzyme secretion, anxiety, food poisoning, over eating and spicy food.

(c) (P – iv ) ( Q – iii ) ( R – ii) ( S – i)

(i) Microvilli are finger like projections of the mucosa of intestine. 

(ii) They increase the surface area of digestion and absorption.

(i) HCI activates the pepsinogen and prorenin and 

(ii) provides acidic medium for the action of pepsin.

(c) The process of preparation of incompletely digested acidic food through gastric juice.

Glands associated with alimentary canal are: 

(1) Salivary glands: A salivary gland may be defined as any cell or organ which discharges a secretion into the oral cavity. Human salivary glands are classified into two categories: major salivary glands and minor salivary glands. 

(a) Major Salivary glands: In man the major salivary glands are three pairs: parotid, sublingual and submandibular glands. 

(i) Parotid glands: These are the largest salivary glands which are situated near the ears. Their ducts open into the oral cavity near the upper second molars. The duct of parotid gland is called Stenson’s duct.

(ii) Sublingual glands: These are small-sized salivary glands which are located beneath the tongue and their ducts are called sublingual ducts or ducts of Rivinus. 

(iii) Submandibular glands: These are medium sized salivary glands which are located at the angles of the lower jaw. Their ducts open into the oral cavity near the lower central incisors. The duct of submandibular gland is called Wharton's duct. The parotid salivary glands secrete much of salivary amylase. 

(b) Minor salivary glands: There are numerous small glands situated in the mucous membrane of the lips (libial glands), Cheeks (buccal glands), tongue lingual glands) and palate (palatine glands). The secretions of these glands help to keep the mouth moist and provide a protective and lubricant coat of mucus. The fluids secreted by major and minor salivary glands constitute saliva. 

(2) Gastric glands: These are numerous microscopic, tubular glands formed by the epithelium of the stomach. The following types of cells are present in the epithelium of the gastric glands. 

(i) Peptic cells: (= chief or Zymogenic or Zymogen cells). They are usually basal in location and secrete gastric digestive enzymes as proenzymes or zymogens; pepsinogen and prorennin. 

(ii) Oxyntic cells: They are large and are most numerous on the side walls of the gastric glands They secrete hydrochloric acid and Castle’s intrinsic factor. 

(iii) Mucous cells: They are present between other types of cells and secrete mucus. 

(3) Liver: It is the largest gland of the body which secrete heparin (anticoagulant). It also produces bile. 

(4) Pancreas: It is a soft lobulated pinkish gland which secretes two major hormones:

 (i) Insulin, 

(ii) Glucagon.

(5) Intestinal gland: These are formed by the surface epithelium of small intestine. 

These are of two types: 

(i) Crypts of Lieberkuhn which secrete mucus and digestive enzymes. 

(ii) Brunner's gland found in duodenum which secretes mucus.

Alcoholic is a person who consumes lots of alcohol regularly. Alcohol is directly absorbed from the stomach by the blood capillaries. The alcohol is known to cause damage to the liver cells. Liver cells produce bile juice. If the liver cells are damaged, they would not be able to produce bile If the bile is not produced in required quantities, the emulsification and further digestion of fats is not possible. This would bring about disturbances in the digestion and adsorption of fats. The alcohol also hardens the stomach wall, which would reduce the churning of food in the stomach.

Carbohydrates are the major source of cellular fuel which provides energy.

To protect the intestinal mucosa from auto digestion, most of the proteases are activated only after they are released.

As their active form hydrolyse cellular and extracellular proteins of the organism itself, inactive enzymes are converted to their active form only at the site of action.

Crypts of Lieberkuhn are simple tubular intestinal glands which occur throughout small intestine between villi and secrete enzyme and mucus.

The semi-digested food mixed thoroughly with the acidic gastric juice of the stomach is called chyme.

Pancreatic duct in addition to bringing pancreatic juice brings bile juice also. 

(i) The pancreatic juice contains pancreatic lipase which is the principal enzyme for the digestion of fat. 

(ii) The bile juice helps in the emulsification of fats In the absence of these, the digestion of fats is seriously affected.

The villi of the small intestine are the absorbing units. They provide a large surface to absorb end products of digestion in the blood or lymph.

The eqestion of feces through the anal opening is called Defecation.

(d) They only participate ¡n digestion of fats.

Egestion is passing out of undigested food from the body.

The protein hydrolyzing enzymes are known as proteases. These proteases are secreted in inactive form and are called proenzymes. If these are secreted in active form these proenzymes would hydrolyze cellular and extra cellular proteins of the individual itself. Pepsin and rennin are secreted in inactive forms - pepsinogen and prorennin. These are activated at the sites of their action in stomach by optimal pH or by specific proteases.

The chylomicrons are transported into the within the intestinal villi Lacteals.