Match the following
Column I | Column II |
(i) The value of 2 +(cot 17º – 1) (cot 28º – 1) is | [A] 3 |
(ii) Area of the parallelogram formed by the lines 2x ± y ±=0, is- | [B] 4 |
(iii) The number of five digit numbers in which every digit excedes the immediately preceding digit is | [C] 5 |
(iv) In interval (0, π) number of solutions of sin x. tan 4x = cos x is | [D] 126 |
Text Solution
Verified by Experts(i) [B]; (ii) [A]; (iii) [D]; (iv) [C]
Ans.
(i) [B]
(ii) [A]
(iii) [D]
(iv) [C]
Sol. (i) 1 = cot (17º + 28º) = 
⇒ (cot 17º – 1) (cot 28º – 1) = 2
2 + (cot 17º – 1) (cot 28º – 1) = 4
(ii) Area = 
= 
= 
= 3
(iii) Required selecting 5 digits out of 9
= 
= 126
(iv) sin x tan 4x = cos x
sin x . 
– cos x = 0
sin x. sin 4x – cos x cos 4x = 0, where cos 4x ≠ 0
∴ the solution set is 5x = m π + 
i.e. x = 
+ 
The solutions are 
, 
, 
, 
, 
There are 5 solutions
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