A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM. The immediate next time that they will beep together is ________
Determine Next Simultaneous Beep Time
Watch X beeps every 30 seconds, and watch Y beeps every 32 seconds. They beeped together at 10 AM. We need to find the immediate next time they will beep simultaneously.
Calculate LCM of Beep Intervals
To find the next simultaneous beep time, we calculate the Least Common Multiple (LCM) of the beep intervals, which are 30 seconds and 32 seconds. The LCM gives the minimum time interval after which both watches will beep at the same moment.
Find the prime factorization for each interval:
- $30 = 2 \times 3 \times 5$
- $32 = 2^5$
Calculate the LCM using the highest power of each prime factor:
LCM$(30, 32) = 2^5 \times 3 \times 5 = 32 \times 15 = 480$ seconds.
Determine Next Beep Time
The watches will beep together again after 480 seconds.
Convert the LCM from seconds to minutes:
$480 \text{ seconds} = \frac{480}{60} \text{ minutes} = 8 \text{ minutes}$
They last beeped together at 10 AM. Add the calculated interval to find the next simultaneous beep time:
Next Beep Time = 10:00 AM + 8 minutes = 10:08 AM.
Important Questions from Numerical Computation
In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4th of the number of students who like other branches. The number of students who like both their core and other branches is 500.
The number of students who like their core branches is$A$ is an ($n \times n$) matrix. Consider the following two statements
Statement 1: Columns of matrix $A$ are linearly independent
Statement 2: Inverse of matrix $A$ exists
Which one of the following statements is TRUE?
- Consider the function $G(x, y, z) = 0$. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function $G(x, y, z)$ exist everywhere. Then, the value of $\left(\frac{\partial z}{\partial x} \times \frac{\partial x}{\partial y} \times \frac{\partial y}{\partial z}\right)$ is _________ (in integer)
- Levenshtein distance is used to measure the minimum edit distance between two strings by counting the minimum number of editing operations (such as, insertions, deletions, substitutions) required to transform one string to another. Consider an alternative version of the Levenshtein distance in which each insertion and each deletion has a cost of 1 and substitutions are not allowed.
Based on this alternative version, the Levenshtein distance between the strings, word and work is ______ (Answer in integer). - In a given collection of documents, let $N$ be the total number of documents and let $d$ be the number of documents in which the term $t$ occurs.
Which ONE of the following fractions is used to define the inverse document frequency (idf) of the term $t$?
