This problem involves calculating the combined work rate of two pipes: one filling and one draining. We need to find the effective filling rate and then determine the time taken to fill the remaining half of the cistern.
Calculate the filling rate of the first pipe:
The first pipe fills the cistern in 4 hours. So, in 1 hour, it fills \(\frac{1}{4}\) of the cistern.
Calculate the draining rate of the second pipe:
The second pipe drains the cistern in 10 hours. So, in 1 hour, it drains \(\frac{1}{10}\) of the cistern.
Calculate the net filling rate when both pipes are open:
Since one pipe fills and the other drains, their effects are opposite. The net filling rate is the difference between the filling rate and the draining rate.
\[ \text{Net filling rate} = \text{Filling rate} - \text{Draining rate} \]
\[ \text{Net filling rate} = \frac{1}{4} - \frac{1}{10} \]
To subtract these fractions, find a common denominator, which is 20.
\[ \text{Net filling rate} = \frac{5}{20} - \frac{2}{20} = \frac{3}{20} \text{ of the cistern per hour} \]
Determine the amount of cistern to be filled:
The cistern was half-empty, which means it was half-full. Therefore, the remaining portion to be filled is \[1 - \frac{1}{2} = \frac{1}{2}\] of the cistern.
Calculate the time taken to fill the remaining half:
Time taken = (Amount to be filled) / (Net filling rate)
\[ \text{Time} = \frac{\frac{1}{2}}{\frac{3}{20}} \]
\[ \text{Time} = \frac{1}{2} \times \frac{20}{3} \]
\[ \text{Time} = \frac{20}{6} = \frac{10}{3} \text{ hours} \]
Convert the time to hours and minutes:
\[ \frac{10}{3} \text{ hours} = 3 \frac{1}{3} \text{ hours} \]
To convert \(\frac{1}{3}\) of an hour to minutes:
\[ \frac{1}{3} \times 60 \text{ minutes} = 20 \text{ minutes} \]
So, the total time is 3 hours and 20 minutes.
Correct Option: B) 3 hours 20 minutes
The question asks to identify the substance used for disinfecting drinking water from the given options. We need to recall the common chemicals used for water purification and disinfection.
B) Bleaching powder is widely used for disinfecting drinking water. Its active ingredient, chlorine, effectively kills bacteria and other microorganisms, making the water safe for consumption.
In the following Venn diagram the total number of students who play all the three games is: 
To determine the number of students who play all three games, we need to identify the region in the Venn diagram where all three sets (Kabaddi, Football, and Cricket) overlap.
Correct Option: A) S
To find the radius of the inscribed circle (inradius) in a right-angled triangle, we can use the formula relating the inradius to the sides of the triangle. First, we need to find the length of the hypotenuse using the Pythagorean theorem.
Correct Option: C) 3 cm
The question asks to identify which of the given options is NOT a combined form of carbon. A combined form of carbon means carbon chemically bonded with other elements. We need to distinguish between pure forms of carbon and compounds containing carbon.
Correct Option: D) Diamond is a pure allotropic form of carbon, meaning it consists only of carbon atoms. It is not a compound where carbon is combined with other elements.
The question asks to identify an essential component that every shirt must possess. We need to consider the fundamental definition and characteristics of a "shirt" to determine which option is universally true.
Correct Option: D) fabric
This problem involves the volume of a cube. We are given information about how the volume changes when the edge length is increased. We need to set up an equation based on the volume formula for a cube and solve for the original edge length.
Correct Option: A) 8 cm
Choose the correct mirror image of the following figure if the mirror is held at AB line. 
To find the correct mirror image of the given figure, we need to visualize how the figure would appear if reflected across the line AB. The mirror image will flip horizontally across this line.
Correct Option: D) The figure in option D correctly shows the trapezoidal shape with the circular shape above it, and the small circle is now on the left side, matching the mirror image.
How many atoms will one mole of Carbon (C-12) contain?
6.02 × 1023
60.20 × 1026
8.06 × 1020
6.02 × 1026
The question asks for the number of atoms in one mole of Carbon (C-12). This is a direct application of Avogadro's number, which defines the number of constituent particles (atoms, molecules, ions, etc.) in one mole of any substance.
Correct Option: A) 6.02 × 10 23
The question asks for the fundamental equation for Force, as defined by Newton's Second Law of Motion. We need to identify the expression that correctly represents this law.
This equation is a cornerstone of classical mechanics and is used to calculate the force required to accelerate an object of a given mass, or to determine the acceleration of an object when a known force is applied.
Correct Option: A) ma
This option correctly represents Newton's Second Law of Motion, where \(F\) is force, \(m\) is mass, and \(a\) is acceleration.