The problem requires us to interchange the mathematical operations '×' and '÷', and the digits '6' and '9' in each given equation. After performing these interchanges, we need to evaluate each modified equation to find which one holds true.
We will apply the given interchanges to each option and then calculate the result to check for correctness.
Original equation: \(69 \times 12 \div 96 = 552\)
Applying the interchanges:
Now, evaluate the modified equation:
\[ 96 \div 12 \times 69 \]\[ 8 \times 69 \]\[ 552 \]The left side equals \(552\), which matches the right side of the original equation. Thus, option C is correct.The question asks to identify the first Governor General of Independent India. This requires knowledge of the history of India's independence and the key figures involved in the transition of power.
Correct Option: D) Lord Mountbatten was the last Viceroy of British India and subsequently became the first Governor General of independent India, serving from 1947 to 1948.
The question asks to identify the article of the Indian Constitution that guarantees the 'Right to Life'. This is a fundamental right and is a core part of the Constitution's provisions for individual liberties.
Correct Option: A) Article 21 of the Constitution of India explicitly states, "No person shall be deprived of his life or personal liberty except according to procedure established by law." This article is widely interpreted by the Supreme Court to include a wide range of rights necessary for a dignified life, such as the right to live with human dignity, right to a livelihood, right to privacy, right to clean environment, right to health, right to free legal aid, and many others. It is the cornerstone of fundamental rights.
A man can complete a task in 7 days but with the help of his son, he can complete it in 4 days. In how many days can his son complete it alone?
7 \( \frac{2}{3} \) days
9 \( \frac{1}{3} \) days
8 \( \frac{1}{3} \) days
6 \( \frac{1}{3} \) days
This problem can be solved using the concept of work and time. We will calculate the individual work rates (amount of work done per day) of the man and the combined work rate of the man and his son. Then, we can find the son's individual work rate and, finally, the number of days the son would take to complete the task alone.
The man can complete the task in 7 days. This means his daily work rate is the reciprocal of the number of days he takes.
\[ \text{Man's daily work} = \frac{1}{7} \text{ of the task} \]With the help of his son, they can complete the task in 4 days. Their combined daily work rate is:
\[ \text{Combined daily work} = \frac{1}{4} \text{ of the task} \]The son's daily work rate can be found by subtracting the man's daily work rate from the combined daily work rate.
\[ \text{Son's daily work} = \text{Combined daily work} - \text{Man's daily work} \]\[ \text{Son's daily work} = \frac{1}{4} - \frac{1}{7} \]\[ \text{Son's daily work} = \frac{7 - 4}{28} \]\[ \text{Son's daily work} = \frac{3}{28} \text{ of the task} \]If the son completes \(\frac{3}{28}\) of the task per day, then the total number of days he takes to complete the entire task (which is 1 unit of work) is the reciprocal of his daily work rate.
\[ \text{Days taken by son alone} = \frac{1}{\text{Son's daily work}} \]\[ \text{Days taken by son alone} = \frac{1}{\frac{3}{28}} \]\[ \text{Days taken by son alone} = \frac{28}{3} \text{ days} \]Correct Option: B) 9 \( \frac{1}{3} \) days
The question asks to identify which of the given countries is NOT a member of the South Asian Association for Regional Cooperation (SAARC). To answer this, one needs to know the member countries of SAARC.
Correct Option: A) Iran is not a member of SAARC. SAARC is an organization of South Asian nations, and Iran is located in Western Asia.
This problem involves the concept of work and time. We need to calculate the total work units and then determine how many days the initial group of women worked before the additional women joined to complete the task within the revised deadline.
Calculate the total work: The total work can be expressed as the product of the number of workers and the time taken. If 25 women can complete a task in 60 days, the total work units are:
\[ \text{Total Work} = \text{Number of Women} \times \text{Days} = 25 \times 60 = 1500 \text{ units} \]Define variables for the two phases of work: Let \(x\) be the number of days after which 5 more women join.
The task needs to be completed in 55 days. So, the remaining days for Phase 2 will be \((55 - x)\) days.
Formulate the equation for total work: The work done in Phase 1 plus the work done in Phase 2 must equal the total work.
\[ (\text{Work in Phase 1}) + (\text{Work in Phase 2}) = \text{Total Work} \] \[ (25 \text{ women} \times x \text{ days}) + (30 \text{ women} \times (55 - x) \text{ days}) = 1500 \]Solve the equation for \(x\):
\[ 25x + 30(55 - x) = 1500 \] \[ 25x + 1650 - 30x = 1500 \] \[ 1650 - 5x = 1500 \] \[ 5x = 1650 - 1500 \] \[ 5x = 150 \] \[ x = \frac{150}{5} \] \[ x = 30 \]So, 5 more women should join after 30 days.
Correct Option: B) 30
The question asks to identify which of the given countries is a member of OPEC (Organization of the Petroleum Exporting Countries). This requires knowledge of the current member states of OPEC.
Correct Option: B) The Republic of the Congo is a member of OPEC. It joined the organization in 2018.
The question asks for the specific term used in page layout to describe the extra margin added to account for the space taken up by binding. Understanding common terminology in publishing and document design is key to answering this question.
D) Gutter margin is the correct term. It refers to the extra margin added to the inside edge of a page (near the spine) to ensure that text and images are not lost or obscured when the document is bound.
The question asks to identify the type of earthquake caused by the sliding of rocks along a fault plane. This phenomenon is directly related to the movement of tectonic plates.
D) Tectonic Earthquakes are produced due to the sliding of rocks along a fault plane. This is the most common type of earthquake and is a direct result of the movement and interaction of Earth's tectonic plates.
The sides of a triangle are in the ratio of \( \frac{2}{5} \) :\( \frac{1}{3} \) : \( \frac{3}{5} \) and its perimeter is 110 cm. The length of the shortest side is:
To find the length of the shortest side of the triangle, we first need to convert the given ratio of the sides into a simpler form with whole numbers. Then, we can use the perimeter to find the actual lengths of the sides and identify the shortest one.
Simplify the ratio of the sides:
The ratio of the sides is given as \[\frac{2}{5} : \frac{1}{3} : \frac{3}{5}\].
To convert this to a ratio of whole numbers, find the Least Common Multiple (LCM) of the denominators (5, 3, 5). The LCM of 5, 3, and 5 is 15.
Multiply each fraction in the ratio by the LCM (15):
\[ \left(\frac{2}{5} \times 15\right) : \left(\frac{1}{3} \times 15\right) : \left(\frac{3}{5} \times 15\right) \] \[ (2 \times 3) : (1 \times 5) : (3 \times 3) \] \[ 6 : 5 : 9 \]So, the sides of the triangle are in the ratio 6:5:9.
Represent the sides using a common multiple:
Let the sides of the triangle be \(6x\), \(5x\), and \(9x\) for some common multiple \(x\).
Use the perimeter to find the value of \(x\):
The perimeter of the triangle is given as 110 cm. The perimeter is the sum of the lengths of its sides.
\[ 6x + 5x + 9x = 110 \text{ cm} \] \[ 20x = 110 \text{ cm} \] \[ x = \frac{110}{20} \text{ cm} \] \[ x = 5.5 \text{ cm} \]Calculate the lengths of the sides:
Identify the shortest side:
Comparing the lengths 33 cm, 27.5 cm, and 49.5 cm, the shortest side is 27.5 cm.
A) 27.5 cm is the length of the shortest side, which corresponds to \(5x\).