Q16 of 46 Page 1

Prove the following:


OR


Prove the following:



LHS:





=RHS


Hence proved


OR


To prove


As we know that


⇒


⇒


Now taking LHS:


⇒


⇒


⇒


⇒


Hence proved.


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14

Using elementary row operations, find the inverse of the following matrix :

 15

Let Z be the set of all integers and R be the relation on Z defined as R = {(a, b) ; a, b ∈ Z, and (a - b) is divisible by 5.} Prove that R is an equivalence relation.

 17

Show that the function f defined as follows, is continuous at x = 2, but not differentiable:


OR


Find if

18

Evaluate :

OR


Evaluate :