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Divisibility

Class 11 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsUsing digits (0,1,2,3,4,5,6) without repetition, (4)-digit numbers divisible by (5) are formed. Which count expression is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsUsing digits (1,2,3,4,5,6,7,8,9) without repetition, how many (5)-digit numbers divisible by (3) can be formed?Class 11Permutations and CombinationsPermutationsExpert MathematicsUsing digits (0,1,2,3,4,5,6) without repetition, how many (5)-digit numbers divisible by (5) can be formed?Class 11Permutations and CombinationsPermutationsExpert MathematicsHow many (4)-digit numbers can be formed from digits (2,3,4,5,6,7,8,9) without repetition and divisible by (25)?Class 11Permutations and CombinationsPermutationsExpert MathematicsHow many (5)-digit numbers can be formed from digits (0,1,2,3,4,5,6,7) without repetition and divisible by (4)?Class 11Permutations and CombinationsPermutationsExpert MathematicsHow many (4)-digit numbers divisible by (5) can be formed from digits (0,1,2,3,4,5) without repetition?Class 11Permutations and CombinationsPermutationsHard MathematicsWhat is the least (n) for which (n!) is divisible by (343)?Class 11Permutations and CombinationsFactorial notationExpert MathematicsWhat is the least (n) for which (n!) is divisible by (125)?Class 11Permutations and CombinationsFactorial notationExpert MathematicsWhat is the least (n) for which (n!) is divisible by (72)?Class 11Permutations and CombinationsFactorial notationExpert MathematicsWhat is the least natural (k) for which (k!) is divisible by (72)?Class 11Permutations and CombinationsFactorial notationMedium MathematicsUsing digits (0,1,2,3,4,5,6,7,8,9), how many (6)-digit numbers can be formed without repetition, divisible by (25), and containing the digit (7)?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsUsing digits (1,2,3,4,5,6,7,8,9), how many (5)-digit numbers can be formed without repetition and divisible by (9)?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsUsing digits (2,3,4,5,6,7,8), how many (5)-digit numbers can be formed without repetition and divisible by (4)?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsUsing digits (0,1,2,3,4,5,6), how many (4)-digit numbers can be formed without repetition and divisible by (3)?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsUsing the digits (0,1,2,3,4,5), how many (5)-digit numbers can be formed without repetition and divisible by (5)?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsIf the function \(f:\{1,2,3,4,5,6,7,8,9\}\to\{0,1\}\) is defined by \(f(n)=1\) when \(n\) is divisible by \(3\), and \(f(n)=0\) otherwise, what is \(f^{-1}(\{1\})\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeExpert MathematicsIf (f:\mathbb{Z}\to\mathbb{Z}) is given by (f(n)=\frac{n^5-n}{5}), which statement is correct?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf the function \(f:\{1,2,3,4,5,6,7,8\}\to\{0,1\}\) is defined by \(f(n)=1\) when \(n\) is divisible by \(4\), and \(f(n)=0\) otherwise, what is \(f^{-1}(\{1\})\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeExpert MathematicsIf (f:\mathbb{Z}\to\mathbb{Z}) is given by (f(n)=\frac{n^3-n}{3}), which statement is correct?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf \(f:\{1,2,3,4,5,6\}\to\{0,1\}\) is defined by \(f(n)=0\) when \(n\) is divisible by \(3\), and \(f(n)=1\) otherwise, what is \(f^{-1}(\{0\})\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeExpert