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Q.18 Let f₁: R → R, f2: (−½, ½-) → R‚ ƒ3: (−1, e7 − 2) → R and f4: R → R be functions
defined by
(i)
(ii)
(iii)
(iv)
f₁(x)
=
sin (√
√₂(x) = {
|sin x
tan-¹ x
1
assumes values in
LIST-I
P. The function f₁ is
Q. The function f₂ is
R. The function f3 is
S. The function f4 is
- e-
if x = 0, where the inverse trigonometric function tan-¹ x
if x = 0
(- / -/-),
f3(x) = [sin(loge (x + 2))], where, for t E R, [t] denotes the greatest integer
less than or equal to t,
f(x) = { x² sin() if x #0
0
if x = 0
The correct option is:
(A) P→ 2; Q→ 3; R→ 1; S→ 4
(B) P→ 4; Q → 1; R→ 2; S→ 3
(C) P→ 4; Q 2; R→ 1; S→ 3
(D) P→ 2; Q→ 1; R→ 4; S3
LIST-II
1. NOT continuous at x = 0
2. continuous at x = 0 and NOT
differentiable at x = 0
3. differentiable at x = 0 and its derivative
is NOT continuous at x = 0
4. differentiable at x = 0 and its derivative
is continuous at x = 0

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