Recent questions tagged cat2005

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65
Let $g(x)$ be a function such that $g(x+1) +g(x-1) = g(x)$ for every real $x.$ Then for what value of $p$ is the relation $g(x+p)=g(x)$ necessarily true for every real $x...
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66
Let $x=\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-}}}} \dots$ to infinity. Then $x$ equals$3$$\frac{\sqrt{13} -1}{2}$$\frac{\sqrt{13} +1}{2}$$\sqrt{13}$
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67
Let $\text{S}$ be a positive integer such that every element $n$ of $\text{S}$ satisfies the conditions$1000 \leq n \leq 1200$every digit in $n$ is oddThen how many elem...
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71
In the $\text{X-Y}$ plane, the area of the region bounded by the graph $|x+y| + |x-y| =4$ is$8$$12$$16$$20$
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73
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74
If $x \geq y$ and $y 1$ then the value of the expression $\log_x\left(\frac{x}{y}\right) + \log_y\left(\frac{y}{x}\right)$ can never be$-1$$-0.5$$0$$1$
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76
The rightmost non-zero digit of the number $30^{2720}$ is ______$1$$3$$7$$9$
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78
If $a_1 =1$ and $a_{n+1}-3a_n +2 = 4n$ for every positive integer n then $a_{100}$ equals$3^{99} - 200$$3^{99} + 200$$3^{100} - 200$$3^{100} + 200$