A certain 12-hour digital clock displays the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) $12$-hour clock cycles through $12$ hours and $60$ minutes. $A$ full day consists of $24$ hours,or $1440$ minutes. First,identify the minutes in a

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(A) $12$-hour clock cycles through $12$ hours and $60$ minutes. $A$ full day consists of $24$ hours,or $1440$ minutes. First,identify the minutes in an hour where the digit $1$ appears: $01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51$. There are $15$ such minutes. In each hour,the clock shows the incorrect time for these $15$ minutes. Additionally,in hours $01, 10, 11, 12$,the clock shows the incorrect time for all $60$ minutes. Total incorrect minutes in a $12$-hour cycle: For the $8$ hours where $1$ does not appear in the hour digit $(02, 03, 04, 05, 06, 07, 08, 09)$,the clock is incorrect for $15$ minutes per hour: $8 	imes 15 = 120$ minutes. For the $4$ hours where $1$ does appear $(01, 10, 11, 12)$,the clock is incorrect for all $60$ minutes: $4 	imes 60 = 240$ minutes. Total incorrect minutes in $12$ hours = $120 + 240 = 360$ minutes. Since a day has two $12$-hour cycles,total incorrect minutes in a day = $360 	imes 2 = 720$ minutes. Total minutes in a day = $24 	imes 60 = 1440$ minutes. Correct minutes = $1440 - 720 = 720$ minutes. Fraction of the day showing correct time = $\frac{720}{1440} = \frac{1}{2}$.

$A$ certain $12$-hour digital clock displays the hour and the minute of a day. Due to a defect in the clock,whenever the digit $1$ is supposed to be displayed,it displays $7$. What fraction of the day will the clock show the correct time?

Similar Questions

There are $200$ individuals with a skin disorder. $120$ had been exposed to the chemical $C_{1}$,$50$ to chemical $C_{2}$,and $30$ to both the chemicals $C_{1}$ and $C_{2}$. Find the number of individuals exposed to chemical $C_{1}$ or chemical $C_{2}$.

The probabilities of three events $A, B$ and $C$ are given by $P(A)=0.6, P(B)=0.4$ and $P(C)=0.5$. If $P(A \cup B)=0.8, P(A \cap C)=0.3, P(A \cap B \cap C)=0.2, P(B \cap C)=\beta$ and $P(A \cup B \cup C)=\alpha$,where $0.85 \leq \alpha \leq 0.95$,then $\beta$ lies in the interval:

Let $A$ be a set containing $n$ elements. If $P$ and $Q$ are two subsets of $A$,then the number of ways of choosing $P$ and $Q$ such that $P \cap Q = \phi$ is:

In a class of $55$ students,$23$ study Mathematics,$24$ study Physics,$19$ study Chemistry,$12$ study Mathematics and Physics,$9$ study Mathematics and Chemistry,$7$ study Physics and Chemistry,and $4$ study all three subjects. Find the number of students who study exactly one subject.

$A$ market research group conducted a survey of $1000$ consumers and reported that $720$ consumers like product $A$ and $450$ consumers like product $B$. What is the least number of consumers that must have liked both products?

Vedclass Test Series

Exam Paper Generator

Online Exam Module