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Question : 21
Total: 36
Section - B
Q. Nos. 21 to 26 carry 2 marks each.
Check if the relation
OR
Prove that:
Solution: 👈: Video Solution
Given,
A = { 1 , 2 , 3 , 4 , 5 , 6 }
R = { ( x , y ) : y is divisible by x }
(i)( 2 , 4 ) ∈ R { ∵ 4 is divisible by 2 }
But( 4 , 2 ) ∉ R { ∵ 2 is not divisible by 4}
∴ R is not symmetric.
(ii) Let( a , b ) ∈ R & ( b , c ) ∈ R
⇒ b = λ a and c = µ b
Now,c = µ b = µ ( λ a ) ⇒ ( a , c ) ∈ R
⇒ c is divisible by a
∴ R is transitive.
OR
L.H.S. =
−
s i n − 1
=
(
− s i n − 1
)
=
( cos − 1
) . . . . . ( 1 )
Now, letcos − 1
= x .
Then,cos x =
⇒ s i n x = √ 1 − (
) 2 =
∴ x = s i n − 1
⇒ cos − 1
= s i n − 1
∴ L.H.S. =
s i n − 1
= R.H.S.
(i)
But
(ii) Let
Now,
OR
Now, let
Then,
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