| Direction: Assertion- Reaction type. Each of these contains tow statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below: |
| Statement I: If f(x) is odd function and g(x) is even function, then f(x)+ g(x) is neither even no odd. |
| Statement II: Odd function is symmetrical at in opposite quadrants and even function is symmetrical about the y-axis. |
A) Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I
B) Statement I is true; Statement II is false.
C) Statement I is false; Statement II is true.
D) Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
Correct Answer: A
Solution :
Since, f (x) is odd. \[\therefore \]\[f(-x)=-f(x)\]and g(x) is even \[\Rightarrow \] g(-x) = g(x) Let \[F(x)=f(x)+g(x)\] \[\therefore \]\[F(-x)=f(-x)+g(-x)=-f(x)+g(x)\] \[\therefore \] F(x) is neither even nor odd. Hence, Statements I, II both are true, but Statement II is not the correct explanation of Statement I.
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