1. Tardigrade
  2. Question
  3. Mathematics
  4. If a= displaystyle lim x arrow π / 2 √( tan x- sin ( tan -1( tan x))/ tan x+ cos 2( tan x)) and r=(1/λ prime) where λ is the least integral value for which three real normal can be drawn to the parabola y2=8 x from (λ, 0), then. Radius of the circle whose centre is (a, λ) which touches the line 3 x+4 y=4, is -

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Q. If $a=\displaystyle\lim _{x \rightarrow \pi / 2} \sqrt{\frac{\tan x-\sin \left(\tan ^{-1}(\tan x)\right)}{\tan x+\cos ^2(\tan x)}}$ and $r=\frac{1}{\lambda^{\prime}}$ where $\lambda$ is the least integral value for which three real normal can be drawn to the parabola $y^2=8 x$ from $(\lambda, 0)$, then.
Radius of the circle whose centre is $(a, \lambda)$ which touches the line $3 x+4 y=4$, is -

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Solution:

Correct answer is (b) 3