Match the following items of Column I with Column II –
Column-I | Column-II |
(i) If the range of the function f(x) = cos–1[5x] is {a, b, c} and a + b + c = , thenλ is equal to (where [.] denotes G.I.F.) | [A] 1 |
(ii) | [B] 2 |
(iii) The number of points at which g(x) = is not differentiable | [C] 4 |
(iv) The derivative of at at x = –1 is | [D] 3 |
Text Solution
Verified by Experts(i) [D]; (ii) [A]; (iii) [D]; (iv) [A]
Ans.
(i) [D]
(ii) [A]
(iii) [D]
(iv) [A]
Sol. (i) –1 ≤ [5x] ≤ 1 so [5x] = –1, 0, 1
so y = cos –1 (–1), cos –1 0, cos –1 1 y = π , π /2, 0
so a + b + c = 
so λ = 3.
(ii) 
= 
= 1
(iii) f(x) = 
= 
∀ x ≠ 0, –1
g(x) = 
= 
∀ x ≠ 
So g(x) is not differentiable at x = 0, –1, 
(iv) if y = 
⇒ 
= 
at x = –1 
= 1
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