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If you form a subset of integers chosen from between to , such that no two integers add up to a multiple of nine, what can be the maximum number of elements in the subset, including both and .
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Important Questions on Number Systems
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The series of numbers is taken. Now, two numbers are taken from this series (the first two) say . Then, the operation is performed to get a consolidated number. The process is repeated. What will be the value of the set after all the numbers are consolidated into one number?
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is a three-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the hundreds and the tens digits of K?
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is a three-digit number such that the ratio of the number to the sum of its digits is least. What can be said about the difference between the tens and the units digit?
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is a three-digit number such that the ratio of the number to the sum of its digits is least. For how many values of K will the ratio be the highest?
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A triangular number is defined as a number which has the property of being expressed as a sum of consecutive natural numbers starting with . How many triangular numbers less than , have the property that they are the difference of squares of two consecutive natural numbers?
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and are two positive integers. Then what will be the sum of the coefficients of the expansion of the expression ?
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What is the remainder when is divided by ?
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The remainder when the number is divided by is _____.
