Question

Let $S=\{a\in N,a\le 100\}$. If the equation $\left[Ta{n}^{2}x\right]-Tanx-a=0$ has real roots then number of elements in S is (where [] is step functin).

• A. 10
• B. 8
• C. 9
• D. 0

Answer 1

The correct option is C

9

Given equation is true only when Tanx is an integer $Tanx=\frac{1\pm \sqrt{4a+1}}{2}=4a+1$ is perfect square and $4a+1\le 401$