| Assertion (A): The length of the minute hand of a clock is \[\text{7 cm}\]. The n the area swept by the minute hand in 5 minutes is \[12\frac{5}{6}c{{m}^{2}}\] |
| Reason (R): The length of an arc of a sector of angle \[\theta \] and radius r is given by \[l=\frac{\theta }{360}\times 2\pi r\] |
A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
C) Assertion (A) is true but Reason (R) is false
D) Assertion (A) is false but Reason (R) is true
Correct Answer: B
Solution :
| [b] Area swept by minute hand in 5 minutes |
| \[=\frac{\theta }{360}\times \pi {{r}^{2}}=\frac{30}{360}=\frac{22}{7}\times 7\times 7\] |
| \[=\frac{77}{6}=12\frac{5}{6}c{{m}^{2}}\] |
| (Angle is 5 minutes by minute hand is \[30{}^\circ \]) |
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