To find the cost for 5 minutes 30 seconds, we first need to determine the cost per second. We will convert the given time into seconds, calculate the cost per second, and then use this rate to find the total cost for the new duration.
To find the fourth proportional to three given numbers, 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 proportional. We then solve for the unknown value.
Let the three given numbers be \(a = 12\), \(b = 18\), and \(c = 20\).
Let the fourth proportional be \(x\).
According to the definition of proportion, if \(a, b, c, x\) are in proportion, then the ratio of the first two is equal to the ratio of the last two:
\[ \frac{a}{b} = \frac{c}{x} \]Substitute the given values into the proportion:
\[ \frac{12}{18} = \frac{20}{x} \]To solve for \(x\), cross-multiply:
\[ 12 \times x = 18 \times 20 \]Calculate the product on the right side:
\[ 12x = 360 \]Divide both sides by 12 to find \(x\):
\[ x = \frac{360}{12} \]\[ x = 30 \]Thus, the fourth proportional to 12, 18, and 20 is 30.
A) 30 β This is the correct value calculated by setting up the proportion \(12/18 = 20/x\) and solving for \(x\).
The value of \(\frac{3.24 \times 4}{0.2}\) = ?
\( \frac{324}{25} \)
\( \frac{162}{25} \)
\( \frac{162}{5} \)
\( \frac{324}{5} \)
To solve this problem, we need to simplify the given expression by converting the decimal numbers into fractions and then performing the multiplication and division operations. Finally, we will simplify the resulting fraction to its lowest terms and compare it with the given options.
The given expression is:
\[ \frac{3.24 \times 4}{0.2} \]First, convert the decimal numbers to fractions:
\[ 3.24 = \frac{324}{100} \]\[ 0.2 = \frac{2}{10} \]Substitute these fractional forms back into the original expression:
\[ \frac{\frac{324}{100} \times 4}{\frac{2}{10}} \]Multiply the terms in the numerator:
\[ \frac{324}{100} \times 4 = \frac{324 \times 4}{100} = \frac{1296}{100} \]Now, divide the numerator by the denominator. Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ \frac{\frac{1296}{100}}{\frac{2}{10}} = \frac{1296}{100} \times \frac{10}{2} \]Cancel out common factors:
\[ \frac{1296}{100} \times \frac{10}{2} = \frac{1296}{10 \times 10} \times \frac{10}{2} \]Cancel one \(10\) from the denominator with the \(10\) in the numerator:
\[ \frac{1296}{10} \times \frac{1}{2} \]Now, multiply the remaining terms:
\[ \frac{1296 \times 1}{10 \times 2} = \frac{1296}{20} \]Divide both the numerator and the denominator by their greatest common divisor. Both are divisible by 4:
\[ \frac{1296 \div 4}{20 \div 4} = \frac{324}{5} \]D) \( \frac{324}{5} \) is the simplified value of the given expression.
The question asks to identify the key parameter used to assess the health of a water body. This requires knowledge of common water quality indicators and their significance.
Correct Option: A) Dissolved Oxygen
Dissolved Oxygen (DO) is a crucial indicator of water quality. Aquatic organisms, like fish, insects, and microorganisms, need dissolved oxygen to survive. A high level of dissolved oxygen indicates a healthy aquatic ecosystem capable of supporting diverse life forms. Conversely, low levels of dissolved oxygen (often caused by pollution, such as organic matter decomposition) can lead to stress or death for aquatic organisms, indicating an unhealthy or polluted water body.
The question asks to identify the gas known as 'Stranger' gas. This is a direct knowledge-based question related to the common names or etymology of elements, specifically noble gases.
A) Xenon β Xenon is derived from the Greek word 'xenos', meaning 'stranger' or 'foreign guest'. Therefore, it is commonly referred to as the 'Stranger gas'.
To determine Rashmi's rank, we need to know her position relative to others in the class. Rank is usually calculated from the top (highest score) or bottom (lowest score). The question implies a rank from the top. We need enough information to fix her exact position.
A) Both the statements together are needed. This is correct because by combining the total number of students (25) and the number of students who scored less than Rashmi (8), we can uniquely determine Rashmi's rank as 17th from the top.
The volume (in cu.cm.) of a right circular cylinder with radius 2 cm and height 2 cm is: (Take π = \( \frac{22}{7} \))
\( \frac{175}{7} \)
\( \frac{176}{21} \)
\( \frac{176}{7} \)
176
To find the volume of a right circular cylinder, we use the standard formula for the volume of a cylinder, which is the area of the base multiplied by its height. The base is a circle, so its area is \(\pi r^2\). We are given the radius and height, and a value for \(\pi\), so we can directly substitute these values into the formula.
The volume \(V\) of a right circular cylinder is given by:
\[ V = \pi r^2 h \]First, multiply the whole numbers:
\[ 4 \times 2 = 8 \]Now, multiply by \(\frac{22}{7}\):
\[ V = \frac{22}{7} \times 8 \]This gives:
\[ V = \frac{22 \times 8}{7} \]Calculate the numerator:
\[ 22 \times 8 = 176 \]So, the volume is:
\[ V = \frac{176}{7}\text{ cu.cm.} \]Correct Option: C) \(\frac{176}{7}\)
The question asks for the effective start date of the Jawahar Rozgar Yojana (JRY). This requires knowledge of key government schemes and their launch dates in India.
Correct Option: D) 1 April 1989 is the correct date when the Jawahar Rozgar Yojana (JRY) was started.
The question asks to identify the space agency that collaborated with the European Space Agency (ESA) on the 2016 ExoMars Trace Gas Orbiter mission. This requires knowledge of international space collaborations, specifically for the ExoMars program.
Correct Option: D) Roscosmos, Russia
The 2016 ExoMars Trace Gas Orbiter (TGO) mission was a joint venture between the European Space Agency (ESA) and the Russian space agency, Roscosmos. This mission aimed to study trace gases in the Martian atmosphere and to act as a data relay for future missions.