Page 60 - ISC-12
P. 60
2Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal
π π
2. Let f 1 : R → R, f 2 : − , → R, f 3 : −1, e π/2 − 2 → R and f 4 : R → R be functions defined
2 2
by
√
(i) f 1 (x) = sin 1 − e −x 2 ,
| sin x|
if x 6= 0
−1
−1
(ii) f 2 (x) = tan x , where the inverse trigonometric function tan x assumes values
1 if x = 0
π π
in − , ,
2 2
(iii) f 3 (x) = [sin (log (x + 2))], where for t ∈ R, [t] denotes the greatest integer less than or equal
e
to t,
1
2
x sin if x 6= 0
x
(iv) f 4 (x) = .
0 if x = 0
List-I List-II
(P) The function f 1 is (1) NOT continuous at x = 0
(Q) The function f 2 is (2) continuous at x = 0 and NOT differentiable at
x = 0
(R) The function f 3 is (3) differentiable at x = 0 and its derivative is NOT
continuous at x = 0
(S) The function f 4 is (4) differentiable at x = 0 and its derivative is
continuous at 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; S → 3.
[JEE 2018]
