Category Archives: Class X

NCERT

Real Numbers: ClassX Mathematics SA1: CBSE

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Use Euclid’s lemma to show that square of any positive integer is of form 4m or 4m + 1 for some integer m. [CBSE-2011-560017, 560037; 2010-1040109-A1, 1040119-A2]

Sol. Let a be any integer. Let q be the quotient and r be the remainder, when a is divided by 4.

By Euclid’s division algorithm, we have : a = 4q + r, where r = 0, 1, 2, 3

 

For r = 0, a = 4q and a2 = 16q2 = 4(4q2), which is of the form 4m, where m = 4q2.

 

For r = 1, a = 4q + 1 and a2 = 16q2 + 8q + 1 = 4(4q2 + 2q) + 1, which is of the form 4m + 1, where m = 4q2 + 2q.

For r = 2, a = 4q + 2 and a2 = 16q2 + 16q + 4 = 4(4q2 + 4q + 1), which is of the form 4m, where m = 4q2 + 4q + 1.

For r = 3, a = 4q + 3 and a2 = 16q2 + 24q + 9 = 4(4q2 + 6q + 2) + 1, which is of the form 4m + 1, where m = 4q2 + 6q + 2.

Thus, a2 is either of the form 4m or 4m + 1 for some integer m.

Gulmohar English Reader

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Gulmohar English Reader
Chapter 9
Vet in the Forest

1.Who were in the team that went to Bishnupur forest?Why did they go there? Who joined them afterwards?

Ans: S C De, Chief Wildlife Warden of the State, Subrata Choudri, officer specialising in tranquillising animals and the author, Dhriti K Lahiri-Choudry. They had come to help the Wildlife Wing of the Forest Department to save a young, injured tusker. A veterinary officer.

2.We had just made a decision to inquire among the villagers.lnquire about what? Why was it necessary to inquire? Who had they inquired with earlier?

Ans:They wanted to inquire the whereabouts of an injured elephant as it was constantly moving with the herd and there was no exact information about its current location. They had earlier made enquiries with the local forest staff.

3.’We were enormously impressed’. What impressed them? Why was they impressive?

Ans: They were enormously impressed when they learnt that a young man from the local tribes had been feeding the injured elephant every day. His act surprised them as their fields were regularly ravaged by these elephants and yet he was kind enough to help one of them.

4.’We came back to camp’.Where were they camping? What mode of transport did they use?

Ans: rest house of Bishnupur forest. jeep.

5.(We)bumped across the forest tracks and fields to the spot’?
To what spot?What was the first problem they faced there?What was done to overcome it?

Ans: …to the spot where the injured elephant was. But the animal was in the middle of the herd and it would be impossible to separate the creature from the herd. The injured elephant was separated from the herd by chasing away the herd using crackers and a lot of noise by the villagers.

6.’Our next plan of action was to ask the enthusiastic villagers for help to locate our patient? Who was the patient? Why did they need help to locate him/it?Which word tells us that the villagers were very willing to help?

Ans: The injured elephant. They were new to the territory and the villagers were familiar with it. ‘Enthusiastic’ young men.

7.’He had therefore not thought of keeping syringes ready (10)
Why had he not thought of it?What made it necessary to have it ready in this situation? Did he not hasten to get it ready? How can you tell?What new problem resulted (for a short while )from not having it ready?

Ans: The veterinarian’s earlier experiences had been limited to langurs where he could take his own time to prepare the syringe. But here he was to deal with a wild elephant and time was of the essence. No, he took his own time. He behaved like he had ‘all the time in the world’. The frightened elephant got restless and began to limp away from them.

8.The animal quickened its pace. We quickened ours accordingly
What made the animal quicken its pace?Why did the men quickened theirs?When did both stop? Why did they stop?

Ans: The moment the dart pricked his body, the elephant foresaw danger and quickened its pace. They too quickened their steps to keep pace with it. They stopped as the animal gradually fell to the ground due to the effect of the tranquilliser.

9. Complete the sentences to show that the last problem encountered by team
a:The elephant did not ——–as a healthy elephant should have done.
b:It was not safe for ——- through the night.
a :come out of its drug-induced sleep
b :the team and the villagers to stay on the ground

10.Complete the list of different medicines given to the elephant
Ans.Antidote, Antibiotic and Tranquilizer