1-Number System, Approximation & Simplification

1.1-Classifications of Numbers

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When a number is divided by 84, it leaves a remainder of 27. If the same number is divided by 6, what will be the remainder?

1.2-Unit Digits

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Determine the value of the natural number \( n \) for which \( 4^n \) ends with the digit zero:

1.3-Factors

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What will come in the place of the question mark '?' in the following question? $40 \%$ of $750-?-450 \div 9 \times 4=40$

1.4-Remainder Concept

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Find the smallest four-digit number which is exactly divisible by 24,40 and 56.

1.5-Factorial

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If $\frac{(2 n)!}{3!(2 n-3)!}$ and $\frac{n!}{2!(n-2)!}$ are in the ratio $44: 3$, then $n$ is

1.6-HCF & L.C.M

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In how many hours will they come together again?

1.7-Surds & Indices

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Given the equation \((-7)^{2k+1}(-7)^5 = (-7)^{12}\), find the value of \(k\) from the following options:

1.8-Miscellaneous

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What will come in the place of the question mark '?' in the following question? $$ 13 \times 8 + 7 \times 22 = ? - 15 $$

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