Q: Which of the following statements is not correct?
Solution: log (2 + 3) = log 5 log (2 x 3) = log 2 + log 3 log (2 + 3) ≠≠log (2 x 3)
Q: In a colony, there are 55 members. Every member posts a greeting card to all the members. How many greeting cards were posted by them?
Solution: First player can post greeting cards to the remaining 54 players in 54 ways. Second player can post a greeting card to the 54 players. Similarly, it happens with the rest of the players. The total numbers of greeting cards posted are 54 + 54 + 54 … 54 (55times) = 54 x 55 = 2970.
Q: Find the number of ways of arranging the letters of the words DANGER, so that no vowel occupies odd place.
Solution: The given word is DANGER. Number of letters is 6. Number of vowels is 2 (i.e., A, E). Number of consonants is 4 (i.e., D,N,G,R). As the vowels cannot occupy odd places, they can be arranged in even places. Two vowels can be arranged in 3 even places in 3P2 ways i.e., 6. Rest of the consonants can arrange in the remaining 4 places in 4! ways. The total number of arrangements is 6 x 4! = 144.
Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7, and 9, which are divisible by 5 and none of the digits is repeated?
Solution: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. Required number of numbers = (1 x 5 x 4) = 20.
Q: K is 4 times as fast as L and working together, they can complete a work in 24 days. In how many days can L alone complete the work ?
Solution: Given K=4L -->K+L = 4L+L = 5L These 5L people can complete the work in 24 days, which means L alone can do the work in (24 x 5)=120 days. Hence, K alone can do the work in 120/4= 30 days
Q: A and B can do a piece of work for Rs 1540. Find the difference between the wages of C and B for the same work If A can do the work in 12 days and B can do the same work in 8 days and with the help of C, A and B can do the same work in 2 days?
Solution: From the given data,
Day Capacity
A -> 12 2
B -> 8 3 2
A + B + C -> 2 12
=> Capacity of C = 12 - 5 = 7
Ratio of capacity of A : B : C = 2 : 3 : 7
Difference of wages of C & B = 4/5 x 1540
= 4 x 308 = Rs. 1232Q: A mother can do a certain job in x hours. Her daughter takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the mother take to do the job ?
Solution: The mother completes the job in x hours.So, the daughter will take 2x hours to complete the same job. In an hour, the mother will complete 1/x of the total job.In an hour, the daughter will complete 1/2x of the total job. So, if the mother and daughter work together, in an hour they will complete 1/x + 1/2x of the job.i.e., in an hour they will complete 3/2x of the job. The question states that they complete the entire task in 6 hours if they work together.i.e., they complete 1/6 th of the task in an hour. Equating the two information, we get 3/2x = 1/6By solving for x, we get 2x = 18 or x = 9. The mother takes 9 hours to complete the job.
Q: 10 women can do a piece of work in 6 days, 6 men can do same work in 5 days and 8 children can do it in 10 days. What is the ratio of the efficiency of a woman, a man and a child respectively?
Solution: 4 : 8 : 3
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