This problem involves work and time, where some entities contribute positively (builders) and others negatively (destroyers). We need to determine the number of destroyers given the total number of individuals, their individual work rates, and the net time taken to complete the task.
Define variables:
Calculate individual work rates:
Calculate combined work rate:
Use the given total time:
Substitute \(N_B\) in terms of \(N_D\):
Solve for \(N_D\):
Verify the answer:
A) 4 is the correct number of destroyers.
The question asks to identify the quantity that possesses only magnitude and no direction. This refers to the definition of a scalar quantity in physics. We need to evaluate each option to determine if it is a scalar or a vector.
Correct Option: C) Work has only magnitude and no direction, making it a scalar quantity.
The question asks to identify the organ responsible for synthesizing testosterone, a male sex hormone. This requires knowledge of the male reproductive system and the specific functions of its components.
Correct Option: B) Testicle
The question asks to identify the Mughal emperor who introduced the Mansabdari system to strengthen the army. This requires knowledge of the administrative and military reforms undertaken by various Mughal rulers.
Correct Option: C) Akbar started the system of Mansabdari to strengthen the army. He introduced this system in 1571. It was a grading system used by the Mughals to fix the rank, salary, and military responsibilities of officers. Each Mansabdar was required to maintain a specified number of cavalrymen, and this system helped in organizing the army and administration efficiently.
The question asks to identify the process in plants that facilitates the absorption and upward movement of water and minerals from roots to leaves. We need to evaluate each given option based on its role in plant physiology.
Correct Option: D) Transpiration — Transpiration is the process of water vapor loss from the leaves through stomata. This loss creates a negative pressure (transpirational pull) in the xylem, which draws water and dissolved minerals from the roots up to the leaves, thus facilitating absorption and uptake activity.
The question asks us to simplify a numerical expression involving negative integers, division, multiplication, and brackets. We need to apply the BODMAS rule by simplifying the innermost brackets first, followed by division and multiplication.
Write the given expression:
\[ (-8)[30\div\{7-(-3)\}] \]Simplify the innermost brackets:
Subtracting a negative number is equivalent to adding the positive number.
\[ 7-(-3)=7+3=10 \]Therefore, the expression becomes:
\[ (-8)[30\div10] \]Perform the division:
\[ 30\div10=3 \]Therefore:
\[ (-8)\times3 \]Perform the multiplication:
According to the rules of integer multiplication, a negative number multiplied by a positive number gives a negative result.
\[ (-8)\times3=\boxed{-24} \]Therefore, the value of the given expression is −24.
Correct Option: A) −24 — First, simplify the innermost brackets: \(7-(-3)=10\). Then divide 30 by 10 to get 3. Finally, multiply −8 by 3 to obtain −24. Hence, Option A is the correct answer.
B) 60: This is incorrect because the correct simplification gives \((-8)\times3=-24\), not 60. The negative sign must be retained during multiplication.
C) 24: This is incorrect because multiplying a negative number by a positive number gives a negative result. Therefore, the answer is −24, not +24.
D) −60: This is incorrect because the expression inside the brackets simplifies to \(30\div10=3\). Multiplying −8 by 3 gives −24, not −60.
The question asks about the nature of elements that are electro-positive. Electro-positivity refers to the tendency of an element to lose electrons and form positive ions (cations). We need to identify which category of elements exhibits this characteristic most prominently.
Correct Option: B) Metals
Kaveri bought a toy for Rs. 280 and sold it for Rs. 315. How much profit did she get?
To find the profit percentage, we first need to calculate the actual profit in rupees. Profit is the difference between the selling price and the cost price. Once we have the profit, we can calculate the profit percentage by dividing the profit by the cost price and multiplying by 100.
B) The profit percentage is 12.5%.
To find the length of the train, we need to use the relationship between speed, distance, and time. When a train crosses a platform, the total distance covered by the train is the sum of its own length and the length of the platform. We will first convert the speed from km/hr to m/s, then use the formula \(\text{Distance} = \text{Speed} \times \text{Time}\) to find the total distance, and finally subtract the platform's length to get the train's length.
Given speed of the train is \(78 \text{ km/hr}\). To convert km/hr to m/s, we multiply by \(\frac{5}{18}\).
\[ \text{Speed} = 78 \times \frac{5}{18} \text{ m/s} \]\[ \text{Speed} = \frac{13 \times 6 \times 5}{3 \times 6} \text{ m/s} \]\[ \text{Speed} = \frac{13 \times 5}{3} \text{ m/s} \]\[ \text{Speed} = \frac{65}{3} \text{ m/s} \]The time taken to cross the platform is \(27 \text{ seconds}\). The total distance covered by the train is its speed multiplied by the time.
\[ \text{Total Distance} = \text{Speed} \times \text{Time} \]\[ \text{Total Distance} = \frac{65}{3} \text{ m/s} \times 27 \text{ s} \]\[ \text{Total Distance} = 65 \times 9 \text{ m} \]\[ \text{Total Distance} = 585 \text{ m} \]The total distance covered is the sum of the length of the train and the length of the platform.
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Platform} \]\[ 585 \text{ m} = \text{Length of Train} + 450 \text{ m} \]\[ \text{Length of Train} = 585 \text{ m} - 450 \text{ m} \]\[ \text{Length of Train} = 135 \text{ m} \]Correct Option: B) 135 m
To find the Least Common Multiple (L.C.M.) of a set of numbers, we can use the prime factorization method. This involves finding the prime factors of each number and then multiplying the highest powers of all common and uncommon prime factors.
Correct Option: B) 336