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Find the pairs of natural numbers, the difference of whose squares is .
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Important Questions on Number Systems
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Which of these is the greatest?
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Is it possible for a common fraction whose numerator is less than the denominator to be equal to a fraction whose numerator is greater than the denominator?
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What digit should be put in the place of in to make it divisible by , , , and ?
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Find the HCF and LCM of the following numbers: , , , and .
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The last digit in the expansions of the three-digit number and are and , respectively. What can be said about the value of ?
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Amrit, a naughty boy, watches an innings of Sachin Tendulkar and acts according to the number of runs he sees Sachin scoring. The details of these are given below.
| run | Place an orange in the basket. |
| runs | Place a mango in the basket. |
| runs | Place a pear in the basket. |
| runs | Remove a pear and a mango from the basket. |
One fine day, at the start of the match, the basket is empty. The sequence of runs scored by Sachin in that innings are given as: . At the end of the above innings, how many more oranges were present inside the basket compared to mangoes?
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In the famous Bel Air Apartments in Ranchi, there are three watchmen meant to protect the precious fruits in the campus. However, one day a thief got in without being noticed and stole some precious mangoes. On the way out however, he was confronted by the three watchmen. The first watchman asked the thief to part with rd of the mangoes and more. The second watchman also asked the thief to part with rd of the remaining mangoes and more. The third watchman asked the thief to part with th of the mangoes and more. As a result, the thief had no mangoes left. What was the number of mangoes he had stolen?
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A -digit number is formed by writing the first "" natural numbers in front of each other as , and so on. Find the remainder when this number is divided by .
