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CAT 2003 | Question: 1-150

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go_editor asked Feb 10, 2016
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CAT 2003 | Question: 1-149
The number of positive integers $n$ in the range $12 \leq n \leq 40$ such that the product $(n-1)(n-2) \dots 3 \cdot 2 \cdot 1$ is not divisible by $n$ is $5$ $7$ $13$ $14$
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CAT 2003 | Question: 1-146
In a certain examination paper, there are n questions. For $j=1, 2, \dots,n,$ there are $2^{n-i}$ students who answered $j$ or more questions wrongly. If the total number of wrong answer is $4095,$ then the value of $n$ is $12$ $11$ $10$ $9$
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go_editor asked Feb 10, 2016
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CAT 2003 | Question: 1-139
If the product of $n$ positive real numbers is unity, then their sum is necessarily a multiple of $n$ equal to $n+\left(\frac{1}{n}\right)$ never less than $n$ a positive integer
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CAT 2003 | Question: 1-119
A positive whole number $\text{M}$ less than $100$ is represented in base $2$ notation, in base $3$ notation, and base $5$ notation. It is found that in all three cases the last digit is $1,$ while in exactly two out of three cases the leading digit is $1.$ Then $\text{M}$ equals $31$ $63$ $75$ $91$
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