The question asks to identify the insect that is NOT beneficial. We need to evaluate each option based on its known interactions with humans and the environment, specifically whether it provides a useful product or service, or if it causes harm.
Correct Option: C) Termite is not a beneficial insect as it causes significant damage to wooden structures, crops, and other materials, making it a pest.
If the side of a square is \( \frac{1}{10} \) m, then how many such squares will get accommodated in a bigger square of side 4 m?
To find out how many smaller squares can fit into a bigger square, we need to calculate the area of both the small square and the big square. Then, we divide the area of the bigger square by the area of the smaller square.
Thus, 1600 such small squares can be accommodated in the bigger square.
Correct Option: D) 1600
This problem involves calculating distance given different speeds for the forward and return journeys and the total time taken. We can use the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\) and set up an equation based on the total time.
Convert total time to hours: The total journey took 5 hours 48 minutes. We need to convert 48 minutes into hours.
\[ 48 \text{ minutes} = \frac{48}{60} \text{ hours} = \frac{4}{5} \text{ hours} = 0.8 \text{ hours} \]So, the total time is \(5 + 0.8 = 5.8\) hours.
Define variables: Let \(D\) be the distance of the post-office from the village (in km).
Set up the equation: The total time is the sum of the time taken for the forward journey and the return journey.
\[ T_1 + T_2 = T_{\text{total}} \] \[ \frac{D}{25} + \frac{D}{4} = 5.8 \]Solve for D: Find a common denominator for the fractions, which is 100.
\[ \frac{4D}{100} + \frac{25D}{100} = 5.8 \] \[ \frac{4D + 25D}{100} = 5.8 \] \[ \frac{29D}{100} = 5.8 \]Now, multiply both sides by 100:
\[ 29D = 5.8 \times 100 \] \[ 29D = 580 \]Divide by 29 to find \(D\):
\[ D = \frac{580}{29} \] \[ D = 20 \]The distance is 20 km.
Correct Option: C) 20 km
The question asks to identify the pigment responsible for the green color in plants. This is a fundamental concept in biology, specifically related to photosynthesis.
Correct Option: D) Chlorophyll — Chlorophyll is the green pigment found in the chloroplasts of plant cells. It is essential for photosynthesis, the process by which plants convert light energy into chemical energy. The green color of plants is due to chlorophyll reflecting green light.
This problem involves relative speed and calculating the time taken for two entities to cover the same distance. We need to determine the time at which B overtakes A and C overtakes A. Since B and C overtake A at the same instance, we can equate the time taken by B and C to reach that point relative to A's start time. We will use the formula: \(\text{Distance} = \text{Speed} \times \text{Time}\).
Let \(t_A\) be the total time A travels until it is overtaken by B and C. Let \(t_B\) be the time B travels, and \(t_C\) be the time C travels.
Given speeds are: \(S_A = 60 \text{ km/h}\), \(S_B = 75 \text{ km/h}\), \(S_C = 80 \text{ km/h}\).
A starts 5 hours before B. So, \(t_A = t_B + 5\).
Let C start \(x\) hours after A. So, \(t_A = t_C + x\).
When B overtakes A, they have covered the same distance. Let this distance be \(D\).
\[ D = S_A \times t_A \]\[ D = S_B \times t_B \]Equating the distances for A and B:
\[ S_A \times t_A = S_B \times t_B \]\[ 60 \times (t_B + 5) = 75 \times t_B \]\[ 60t_B + 300 = 75t_B \]\[ 15t_B = 300 \]\[ t_B = \frac{300}{15} = 20 \text{ hours} \]Now we find \(t_A\):
\[ t_A = t_B + 5 = 20 + 5 = 25 \text{ hours} \]This means A travels for 25 hours, and B travels for 20 hours until they meet. The distance covered is:
\[ D = 60 \text{ km/h} \times 25 \text{ hours} = 1500 \text{ km} \]Since B and C overtake A at the same instance, C also covers 1500 km in \(t_C\) hours.
\[ D = S_C \times t_C \]\[ 1500 = 80 \times t_C \]\[ t_C = \frac{1500}{80} = \frac{150}{8} = \frac{75}{4} \text{ hours} \]Convert \(t_C\) to hours and minutes:
\[ t_C = 18 \frac{3}{4} \text{ hours} = 18 \text{ hours and } \left(\frac{3}{4} \times 60\right) \text{ minutes} = 18 \text{ hours and } 45 \text{ minutes} \]We need to find how much time after A did C start the journey, which is \(x\).
\[ x = t_A - t_C \]\[ x = 25 \text{ hours} - 18 \frac{3}{4} \text{ hours} \]\[ x = 6 \frac{1}{4} \text{ hours} \]Convert \(6 \frac{1}{4}\) hours to hours and minutes:
\[ x = 6 \text{ hours and } \left(\frac{1}{4} \times 60\right) \text{ minutes} = 6 \text{ hours and } 15 \text{ minutes} \]C) 6 hours 15 minutes is the correct answer, as calculated.
To solve this problem, we need to translate the given word problem into a mathematical equation. We will represent the unknown number with a variable, form an equation based on the given conditions, and then solve for the variable.
Define the variable: Let the number be \(x\).
Translate the fractions of the number:
Formulate the sum: The sum of half, one-third, and one-fifth of the number is: \[ \frac{x}{2} + \frac{x}{3} + \frac{x}{5} \]
Set up the equation: The problem states that this sum exceeds the number by 12. This means: \[ \frac{x}{2} + \frac{x}{3} + \frac{x}{5} = x + 12 \]
Find a common denominator: The least common multiple (LCM) of 2, 3, and 5 is \(2 \times 3 \times 5 = 30\).
Multiply the equation by the LCM to clear denominators: \[ 30 \left( \frac{x}{2} + \frac{x}{3} + \frac{x}{5} \right) = 30(x + 12) \] \[ 15x + 10x + 6x = 30x + 360 \]
Simplify and solve for \(x\): \[ 31x = 30x + 360 \] Subtract \(30x\) from both sides: \[ 31x - 30x = 360 \] \[ x = 360 \]
Verify the answer: Half of 360 = 180 One-third of 360 = 120 One-fifth of 360 = 72 Sum = \(180 + 120 + 72 = 372\) Does \(372\) exceed \(360\) by 12? Yes, \(372 - 360 = 12\). The answer is correct.
Correct Option: C) 360
A student multiplied a number by \( \frac{3}{5} \) instead of \( \frac{5}{3} \). What is the percentage error in the calculation?
To find the percentage error, we need to determine the difference between the incorrect value and the correct value, and then express this difference as a percentage of the correct value. We will assume an arbitrary number to perform the multiplication to simplify calculations.
C) 64% is the calculated percentage error.
The question asks to identify the specific railway station in South Africa where Mahatma Gandhi was forcibly removed from a first-class compartment due to racial discrimination. This is a direct factual question related to a significant event in Gandhi's early life and the history of the anti-apartheid movement.
Correct Option: C) Pietermaritzburg
The problem states that the total number of students is 2401, and they are arranged in rows and columns such that the number of rows is equal to the number of columns. This means the arrangement forms a perfect square. To find the number of rows (or columns), we need to calculate the square root of the total number of students.
Let \(R\) be the number of rows and \(C\) be the number of columns.
According to the problem, the number of rows is equal to the number of columns, so \(R = C\).
The total number of students is given by the product of the number of rows and the number of columns. So, \(\text{Total Students} = R \times C\).
Substitute the given values into the equation:
\[ 2401 = R \times R \]\[ 2401 = R^2 \]To find \(R\), we need to calculate the square root of 2401:
\[ R = \sqrt{2401} \]We can find the square root by estimation or by prime factorization.
Thus, the number of rows \(R = 49\).
Correct Option: C) 49
The number of rows is 49, which is equal to the number of columns, and \(49 \times 49 = 2401\).
The radius of the circle in which a central angle of 60° intercepts an arc of length 35 cm is:
\(\frac{105}{\pi}\) cm
\(\frac{35}{\pi}\) cm
\(\frac{100}{\pi}\) cm
35π cm
To find the radius of the circle, we will use the formula relating the arc length, the radius, and the central angle. The central angle must be converted from degrees to radians before using the formula.
The formula for converting degrees to radians is:
\[ \text{Radians} = \text{Degrees} \times \frac{\pi}{180^\circ} \]\[ \theta = 60^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{3} \text{ radians} \]The formula for the arc length \(L\) of a circle with radius \(r\) and central angle \(\theta\) (in radians) is:
\[ L = r \theta \]A) \(\frac{105}{\pi}\) cm — This matches our calculated radius.