Question

A line - x/2 = f(t).y/t = t²z = λ is the perpendicular to the line of the intersection of the planes t.f(t)x + f(1/t²) z + f(-t) = 0 and ty + f (-t)z + f(t²)  = 0 where t ∈ R - {0}

f (t) is 

(A)  even function

(B)  odd function

(C)  neither even nor odd function

(D)  both even and odd function

If  t = tanθ , where θ ∈ R - {(2n +1)π/2,nπ};n ∈ I, then

(A)  f(tan θ)  = − tan(2θ) ⋅ f(cot² θ)

(B)  f(tanθ)  = −sin(2θ) ⋅ f(cot²θ)

(C)  f(tanθ)  = −sin(2θ).f (sec² θ)e

(D)  f(tan2θ)  = − tanθ ⋅ f(cotθ)

Answer 1

Correct option 16 (B),17  (A)

1. The normals to the planes and the given line are coplanar. Hence, applying the condition, the functional equation obtained is

Adding Eqs. (1) and (2) ⇒ f (t) is an odd function. 

2.  From Eqs. (1) and (2) of Solution 16, we have