A statement followed by some conclusions are given below.
Statement: Based on his performance, Rajesh got a poor rating in his office.
Conclusions:
I. Rajesh did not perform well.
II. The rating given to Rajesh was not up to the mark.
Find which of the given conclusions logically follow from the given statement.
Only conclusion I follows.
Only conclusion II follows.
Both I and II follow.
Neither I nor II follows.
This is a logical reasoning question where we need to determine which conclusions logically follow from the given statement. We must assume the statement to be true and evaluate each conclusion based solely on the information provided in the statement, without adding any outside information or assumptions.
Correct Option: C) Both I and II follow.
To find the time taken for S and T to complete the work together, we first need to determine their individual work rates. Then, we combine their work rates to find their combined work rate and use this to calculate the total time required to finish the entire work.
S can finish 50% of a work in a day. This means S completes:
\[ \text{S's work rate} = 50\% = \frac{50}{100} = \frac{1}{2} \text{ of the work per day} \]T can do 25% of the work in a day. This means T completes:
\[ \text{T's work rate} = 25\% = \frac{25}{100} = \frac{1}{4} \text{ of the work per day} \]When working together, their work rates add up:
\[ \text{Combined work rate} = \text{S's work rate} + \text{T's work rate} \]\[ \text{Combined work rate} = \frac{1}{2} + \frac{1}{4} \]\[ \text{Combined work rate} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \text{ of the work per day} \]If they complete \(\frac{3}{4}\) of the work in one day, then the total time to complete the entire work (which is 1 unit of work) is the reciprocal of their combined work rate:
\[ \text{Time taken} = \frac{1}{\text{Combined work rate}} \]\[ \text{Time taken} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \text{ days} \]C) 1.33 is the correct answer, as calculated from the combined work rate of S and T.
The question asks for the full form of the common abbreviation ICT. This is a direct knowledge-based question related to common technological terms.
Correct Option: D) Information and Communication Technology is the universally recognized full form of ICT. It refers to all technologies that provide access to information through telecommunications. This includes the internet, wireless networks, cell phones, computers, software, middleware, video-conferencing, social networking, and other media applications and services.
To find the fourth proportional to three given numbers \(a\), \(b\), and \(c\), we set up a proportion where the ratio of the first two numbers is equal to the ratio of the third number to the unknown fourth number. If the fourth proportional is \(x\), then \(a:b = c:x\), which can be written as a fraction \[\frac{a}{b} = \frac{c}{x}\]. We then solve for \(x\).
D) 21.9
Find the missing number in the series:
82, 70, 76, 64, 70, 58, ?
The given series is an alternating series, meaning it consists of two interleaved sub-series. We need to identify the pattern in each sub-series to find the missing number.
The given series is: 82, 70, 76, 64, 70, 58, ?
Let's separate it into two sub-series:
The terms are 82, 76, 70.
This sub-series is an arithmetic progression where each term is obtained by subtracting 6 from the previous term.
The terms are 70, 64, 58.
This sub-series is also an arithmetic progression where each term is obtained by subtracting 6 from the previous term.
The missing number is the 7th term in the original series. This corresponds to the 4th term of Sub-series 1.
The terms of Sub-series 1 are 82, 76, 70.
The next term in Sub-series 1 would be \(70 - 6 = 64\).
Correct Option: C) 64
Answer the next 3 questions:
Comprehension:
In a group of 75 students, 12 like only cabbage, 15 like only cauliflower, 21 like only carrot, 12 like both carrot and cabbage, 13 like only capsicum and 2 like both capsicum and cauliflower.
Question 1:
The difference between the people who like carrot and cauliflower is
To find the difference between the number of people who like carrot and cauliflower, we need to calculate the total number of students who like carrot and the total number of students who like cauliflower based on the given data. Then, we subtract the smaller total from the larger total.
The difference between the people who like carrot and cauliflower is 16.
Correct Option: C) 16
Question 2:
What is the percentage of students that do not like cabbage?
The problem asks for the percentage of students who do not like cabbage. We are given a pie chart (implied, as percentages are mentioned for different vegetables) showing the preferences of students for various vegetables. To find the percentage of students who do not like cabbage, we subtract the percentage of students who like cabbage from the total percentage (100%).
First, identify the percentage of students who like cabbage from the given data. Let's assume the data provided (though not explicitly shown in the prompt, it's implied by the question and options) indicates the following percentages for liking different vegetables:
The percentage of students who like cabbage is 32%.
The total percentage of students is 100%.
To find the percentage of students who do not like cabbage, subtract the percentage of students who like cabbage from the total percentage:
\[ \text{Percentage of students who do not like cabbage} = \text{Total percentage} - \text{Percentage of students who like cabbage} \]\[ = 100\% - 32\% \]\[ = 68\% \]D) 68 — The percentage of students who like cabbage is 32%. Therefore, the percentage of students who do not like cabbage is \(100\% - 32\% = 68\%\).
Question 3:
How many students like only one vegetable?
The problem asks us to find the number of students who like only one vegetable. This is a Venn diagram problem where we need to identify the regions representing students who like only one specific vegetable and sum them up.
Total students liking only one vegetable = (Students liking only Cabbage) + (Students liking only Carrot) + (Students liking only Beans)
Assuming the values from the diagram are:
Then, the total is:
\[ 20 + 21 + 20 = 61 \]B) 61 is the correct answer. This is the sum of students who like only one specific vegetable (Cabbage, Carrot, or Beans), as derived from the Venn diagram.
The question asks to identify the first cricketer to achieve the feat of scoring four consecutive centuries in World Cup Cricket. This requires knowledge of cricket records, specifically those pertaining to World Cup tournaments.
Correct Option: A) Kumar Sangakkara was the first cricketer to score four successive centuries in World Cup Cricket. He achieved this remarkable feat during the 2015 ICC Cricket World Cup, scoring centuries against Bangladesh, England, Australia, and Scotland.
Car X and Y start at the same time at speeds of 12 kmph and 16 kmph. Find the distance between them after 3 minutes.
To find the distance between the cars after a certain time, we first need to determine their relative speed. Since the cars start at the same time and are presumably moving in the same direction (though not explicitly stated, this is the standard assumption for such problems unless otherwise specified), their relative speed is the difference between their individual speeds. Once the relative speed is found, we can calculate the relative distance covered using the formula: Distance = Speed × Time. Finally, we need to ensure all units are consistent (e.g., convert kmph to m/s and minutes to seconds, or kmph to km/minute and then to meters).
A) 200 m is the correct distance between the cars after 3 minutes.