Recent questions tagged cat2003-1

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Let T be the set of integers $\{3, 11, 19,27, \dots ,451, 459, 467\}$ and S be a subset of T such that the sum of no two elements of S is $470.$ The maximum possible numb...
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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$$14$
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if $x,y,z$ are distinct positive real numbers then $\frac{x^2(y+z) + y^2(x+z) + z^2(x+y)}{xyz}$ would begreater than $4$greater than $5$greater than $6$None of these
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if $\log_3\left(2^x - 5\right), \: \log_3\left(2^x - \frac{7}{2}\right)$ are in arithmetic progression, then the value of $x$ is equal to$5$$4$$2$$3$