The question asks about the fundamental principle governing a balanced chemical equation. This principle is based on the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. We need to identify the option that correctly reflects this law in the context of atoms and mass.
D) The total number of atoms for each element is the same on both sides of the equation. This statement accurately defines a balanced chemical equation, which adheres to the Law of Conservation of Mass. Atoms are rearranged, but their total count for each specific element remains unchanged from reactants to products.
To solve this problem, we need to track Manur's movements in the East-West and North-South directions separately. We will assign positive values for movement towards East and North, and negative values for movement towards West and South. Finally, we will calculate the net displacement from the starting point A to the final point P, and then determine the distance and direction needed to return to A.
So, Point P is 6 km North of Point A.
Since Point P is 6 km North of Point A, to reach Point A from Point P, Manur must drive 6 km towards the South.
C) 6 km to the South
The problem requires us to identify specific digits from a given set of four-digit numbers based on their magnitude (greatest, smallest) and then perform an addition operation. We need to list the numbers, sort them to find the second-greatest and smallest, extract the specified digits, and finally add them.
C) 8 — As per the step-by-step calculation, the resultant sum is 8.
We need to find the present ages of two people given two conditions: their age difference and a relationship between their ages six years ago. We can set up a system of two linear equations based on these conditions and solve for their present ages.
Let the present age of the older person be \(O\) years and the present age of the younger person be \(Y\) years.
Condition 1: The difference in their ages is 24 years.
Since \(O\) is the older person, we have:
Condition 2: 6 years ago, the older of the two was four times as old as the younger one.
6 years ago, the older person's age was \(O - 6\).
6 years ago, the younger person's age was \(Y - 6\).
According to the condition:
Simplify Equation 2:
\[ O - 6 = 4Y - 24 \]\[ O = 4Y - 24 + 6 \]\[ O = 4Y - 18 \quad \text{(Equation 2)} \]Now we have a system of two linear equations:
Substitute Equation 2 into Equation 1:
\[ (4Y - 18) - Y = 24 \]Solve for \(Y\):
\[ 3Y - 18 = 24 \]\[ 3Y = 24 + 18 \]\[ 3Y = 42 \]\[ Y = \frac{42}{3} \]\[ Y = 14 \text{ years} \]Now substitute the value of \(Y\) back into Equation 1 to find \(O\):
\[ O - 14 = 24 \]\[ O = 24 + 14 \]\[ O = 38 \text{ years} \]So, the present ages are 38 years and 14 years.
C) 14 and 38 years
A) 15 and 39 years: The difference is \(39 - 15 = 24\). 6 years ago, ages were 9 and 33. \(33 \neq 4 \times 9\). So, this is incorrect.
B) 12 and 36 years: The difference is \(36 - 12 = 24\). 6 years ago, ages were 6 and 30. \(30 \neq 4 \times 6\). So, this is incorrect.
D) 16 and 40 years: The difference is \(40 - 16 = 24\). 6 years ago, ages were 10 and 34. \(34 \neq 4 \times 10\). So, this is incorrect.
This question asks about the primary reason for a central bank to increase the reserve requirement ratio. We need to understand the concept of reserve requirements and their impact on commercial banks' lending capacity and the overall money supply in the economy.
A) To decrease the money supply in the economy — By increasing the reserve requirement ratio, commercial banks have less money to lend, which reduces the overall credit creation and thus decreases the money supply in the economy. This is a common monetary policy tool used to control inflation.
The question asks about fundamental properties of magnets. We need to evaluate each statement based on the basic principles of magnetism.
Correct Option: B) A magnet is a dipole with north and south poles.
This question asks about the outcome of a double displacement reaction between sodium chloride and silver nitrate. We need to identify the characteristic product formed in this specific reaction.
Correct Option: C) Formation of a precipitate
When sodium chloride and silver nitrate are mixed, a double displacement reaction occurs, producing sodium nitrate and silver chloride. Silver chloride is insoluble in water and thus forms a white precipitate. This is a classic example of a precipitation reaction.
To solve this problem, we need to perform the given arithmetic operations following the order of operations (BODMAS/PEMDAS). This means we first perform multiplication, then addition and subtraction from left to right.
The final value of the expression is \(12.59\).
Correct Option: D) 12.59
The question asks us to calculate the average of all natural numbers from 1 to 95. Since these numbers form an arithmetic progression (AP) with a common difference of 1, we can calculate their average using the formula for the average of the first and last terms.
Identify the given information:
The natural numbers from 1 to 95 are:
\[ 1,2,3,4,\ldots,95 \]Apply the average formula:
For consecutive natural numbers, the average is calculated as:
\[ \text{Average}=\frac{\text{First term}+\text{Last term}}{2} \]Substituting the values:
\[ \text{Average}=\frac{1+95}{2} \] \[ =\frac{96}{2} \] \[ \boxed{\text{Average}=48} \]Understand the result:
The numbers from 1 to 95 are equally spaced. Their middle value is 48, which is also their arithmetic mean.
Therefore, the average of all natural numbers from 1 to 95 is 48.
Correct Option: B) 48 — The natural numbers from 1 to 95 form an arithmetic progression. The average of an arithmetic progression is equal to the sum of its first and last terms divided by 2. Therefore, \(\frac{1+95}{2}=48\). Hence, Option B is the correct answer.
A) 49: This is incorrect because the average of the numbers from 1 to 95 is 48, not 49. The value 49 would be the average of consecutive natural numbers from 1 to 97.
C) 48.5: This is incorrect because the first and last terms are 1 and 95, whose average is exactly 48. The value 48.5 would be the average of the numbers from 1 to 96.
D) 47.5: This is incorrect because the average of the numbers from 1 to 95 is 48. The value 47.5 would be the average of the numbers from 1 to 94.
The question asks to identify the electrical appliance used for food preservation by maintaining low temperatures. We need to evaluate the primary function of each given option.
C) Refrigerator — A refrigerator is specifically designed to maintain low temperatures (typically between \(0^\circ \text{C}\) and \(5^\circ \text{C}\)) to slow down bacterial growth and enzymatic reactions, thereby preserving food and extending its shelf life.