To find out when the bells will next ring together, we need to find the least common multiple (LCM) of their individual ringing intervals. The LCM represents the smallest time duration after which all events (bells ringing) will coincide again.
Identify the given intervals: The bells ring at intervals of 16 minutes, 24 minutes, 36 minutes, and 42 minutes.
Find the prime factorization of each interval:
Calculate the LCM: The LCM is found by taking the highest power of all prime factors present in any of the numbers.
\[ \text{LCM}(16, 24, 36, 42) = 2^{\text{max}(4,3,2,1)} \times 3^{\text{max}(0,1,2,1)} \times 7^{\text{max}(0,0,0,1)} \] \[ \text{LCM}(16, 24, 36, 42) = 2^4 \times 3^2 \times 7^1 \] \[ \text{LCM}(16, 24, 36, 42) = 16 \times 9 \times 7 \] \[ \text{LCM}(16, 24, 36, 42) = 144 \times 7 \] \[ \text{LCM}(16, 24, 36, 42) = 1008 \]Interpret the result: The bells will next ring together after 1008 minutes.
Correct Option: D) 1008 minutes
When four terms are in proportion, it means that the ratio of the first term to the second term is equal to the ratio of the third term to the fourth term. We can set up an equation based on this definition and solve for the unknown third term.
Let the four terms in proportion be \(a, b, c, d\).
The definition of proportion states that the ratio of the first two terms is equal to the ratio of the last two terms:
\[ \frac{a}{b} = \frac{c}{d} \]Alternatively, this can be written as the product of the means equals the product of the extremes:
\[ a \times d = b \times c \]Given the first term \(a = 4\), the second term \(b = 22\), and the fourth term \(d = 33\). Let the third term be \(x\).
Substitute these values into the proportion equation:
\[ \frac{4}{22} = \frac{x}{33} \]To solve for \(x\), cross-multiply:
\[ 4 \times 33 = 22 \times x \]Calculate the product on the left side:
\[ 132 = 22x \]Divide both sides by 22 to find \(x\):
\[ x = \frac{132}{22} \]Perform the division:
\[ x = 6 \]Thus, the third term is 6.
Correct Option: B) 6
The question asks about the approximate orbital period of Halley's Comet. This is a factual question related to astronomy and general science, often tested in competitive exams. Recalling the specific period for this famous comet is key.
Correct Option: B) 76
This question tests general knowledge about Formula 1 racing, specifically the winner of a particular Grand Prix in a given year. To answer this, one needs to recall or know the results of the 2016 Formula-1 Rolex Australian Grand Prix.
Correct Option: C) Nico Rosberg won the 2016 Formula-1 Rolex Australian Grand Prix. This was the first race of the 2016 season, and Rosberg went on to win the World Championship that year.
The question asks about the number of cities where Maharaja Jai Singh II constructed Jantar Mantars. This is a factual recall question related to Indian history and architecture.
Correct Option: A) Five. Maharaja Jai Singh II built Jantar Mantar observatories in five different cities: Jaipur, Delhi, Varanasi, Ujjain, and Mathura.
This is an analogy question where we need to find the relationship between the first pair of words and apply the same relationship to the second pair to find the missing word.
Correct Option: D) Carpenter
The given series consists of Roman numerals. To find the next term, we need to identify the pattern in the values represented by these Roman numerals.
D) M is the correct option because it represents 1000, which follows the established pattern of alternating multiplications by 5 and 2 in the Roman numeral series.
A question and three statements labeled (I), (II) and (III) are given. You have to decide which statement(s) is/are sufficient to answer the question.
Question: How far is Sasa's mother's office from their home?
Statements:
I. Sasa is studying in standard 9.
II. Sasa's mother drops her first at school and then reaches her office.
III. Sasa's mother takes 1 hour and 30 minutes by cycle to reach her office.
Select the right option from the following.
I, II and III are sufficient.
Data insufficient.
I and II together are sufficient.
II and III together are sufficient.
To determine the distance to Sasa's mother's office, we need information about the speed and time taken for the journey. We will analyze each statement to see if it provides the necessary data or helps in deriving it.
This statement provides information about Sasa's academic status. It has no relevance to the distance, speed, or time of her mother's commute. Therefore, Statement I is insufficient.
This statement describes the route Sasa's mother takes. It indicates that the journey to the office is not directly from home but includes a stop at Sasa's school. While it gives context to the journey, it does not provide any numerical data (like distance, speed, or time) that can be used to calculate the distance to the office. It doesn't even state the distance from home to school or school to office. Therefore, Statement II is insufficient.
This statement provides the time taken for the journey to the office: 1 hour and 30 minutes, which is \(1.5\) hours. However, it does not provide any information about the speed at which she travels. Without speed, we cannot calculate the distance. Therefore, Statement III is insufficient.
Correct Option: B) Data insufficient.
The problem requires us to find the total number of apples given their weight and the weight of a known quantity of apples. We will first determine the weight of a single apple. Then, we will calculate the total weight of apples in all three boxes and finally divide the total weight by the weight of one apple to find the total number of apples.
C) 465 is the correct number of apples.
If & means '+', \$ means '−', # means '÷' and % means '×', then the value of
8 % 2 & 11 \$ 24 & 24 # 6
This problem involves substituting given symbols with mathematical operators and then evaluating the resulting expression using the order of operations (BODMAS/PEMDAS).
The expression is: 8 % 2 & 11 \) 24 & 24 # 6
Substituting the operators, we get:
\[ 8 \times 2 + 11 - 24 + 24 \div 6 \]The order is Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction.
D) 7 — By correctly substituting the symbols and applying the BODMAS rule, the value of the expression is found to be 7.