| Directions: Assertion-Reason type questions. Each of these questions contains two statements: Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the codes [a], [b], [c] and [d] in the given below: |
| Statement I: If a + b + c = 12; (a, b, c > 0), then maximum value of abc is 64. |
| Statement II: Maximum value occurs when a = b = c. |
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; Statement II is a correct explanation for Statement I.
Correct Answer: D
Solution :
Since, \[AM\ge GM\] \[\therefore \] \[\frac{a+b+c}{3}\ge {{(abc)}^{1/3}}\] \[\Rightarrow \] \[\frac{12}{3}\ge {{(abc)}^{1/3}}\] \[\Rightarrow \]\[abc\le 64\] Also, maximum value of abc is 64 only when a = b = c Hence, option [d] is correct.
You need to login to perform this action.
You will be redirected in
3 sec
