Match the following
Column-I | Column-II |
(i) | [A] 8 |
(ii) [.] denotes greatest integer function | [B] 0 |
(iii) where [.] denotes G.I. function | [C] 4 |
(iv) | [D] –1 |
Text Solution
Verified by Experts(i) [B]; (ii) [B]; (iii) [B]; (iv) [B]
Ans.
(i) [B]
(ii) [B]
(iii) [B]
(iv) [B]
Sol. (i) 
– 
= 0
(ii) 
+ 
× 
+ 
= – 10 + 10 = 0
(iii) Let f(x) = x 2 – sin x tan x
f '(x) = 2x – sin x sec 2 x – cosx tan x
f '(x) = 2x – sin x (sec 2 x + 1)
f "(x) = 2 – cos x (sec 2 x + 1) – sin x. 2 sec 2 x tan x
f "(x) = 2 – (secx + tan x) – 2 secx tan 2 x
So in neighbourhood of 0, sec x + cos x > 2
f "(x) < 0, f '(x) is decreasing f '(x) < f(0), x > 0
f '(x) < 0, f(x) is decreasing when x > 0
f(x) < f(0), x 2 < sin x + tanx, x > 0
0 < 
< 1
= 
= 0
(iv) 
= 
= 
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