NDA 1 2024 Maths, question 104

Topic: Statistics

Q104

Let $x+2y+1=0$ and $2x+3y+4=0$ are two lines of regression computed from some bivariate data. If $\theta$ is the acute angle between them, then what is the value of $488\tan 3\theta$ ?

(a) $191$ Correct answer
(b) $161$
(c) $131$
(d) $121$

Solution.

Answer: (a) $191$

The slopes are −1/2 and −2/3.
Thus tan θ = |(−2/3 + 1/2)/(1 + 1/3)| = 1/8.
The triple-angle formula gives tan 3θ = (3/8 − 1/512)/(1 − 3/64) = 191/488.
Multiplication by 488 gives 191.