If the HCF of two numbers is 6 and the product of the numbers is 2520, find their LCM.
This problem can be solved by using the fundamental relationship between the Highest Common Factor (HCF), the Least Common Multiple (LCM), and the product of two numbers. The relationship states that for any two positive integers, the product of the numbers is equal to the product of their HCF and LCM.
B) 420 — The LCM of the two numbers is 420, calculated by dividing the product of the numbers (2520) by their HCF (6).
To determine the rating of the fuse wire, we need to calculate the maximum current drawn by the electric kettle. The fuse wire rating should be slightly higher than this maximum operating current to prevent it from blowing during normal operation, but low enough to protect the appliance from overcurrents.
Since 1 kW = 1000 W, we have:
\[ P = 1.5 \text{ kW} = 1.5 \times 1000 \text{ W} = 1500 \text{ W} \]The relationship between power, voltage, and current is given by the formula:
\[ P = V \times I \]Where \(I\) is the current in Amperes. Rearranging the formula to find \(I\):
\[ I = \frac{P}{V} \]Substitute the values:
\[ I = \frac{1500 \text{ W}}{240 \text{ V}} = 6.25 \text{ A} \]The fuse rating should be equal to or slightly greater than the maximum operating current. In this case, the calculated current is 6.25 A. A fuse with a rating of 6.25 A would be appropriate. If 6.25 A is not available, the next standard higher rating would be chosen, but since 6.25 A is an option, it is the most precise choice.
Correct Option: C) 6.25 A
A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 950 gm for a kilogram. His gain per cent is:
4\( \frac{5}{19} \)%
5\( \frac{5}{19} \)%
7\( \frac{5}{19} \)%
6\( \frac{5}{19} \)%
This problem involves calculating the gain percentage of a dishonest dealer. The dealer claims to sell goods at cost price but uses a faulty weight. We need to find the profit made due to the reduced weight and express it as a percentage.
Correct Option: B) 5\( \frac{5}{19} \)% is the correct gain percentage.
The question asks to identify the state with the largest forest cover area-wise, according to the India State of Forest Report (ISFR) 2021. This requires knowledge of the key findings of the ISFR 2021 report.
Correct Option: D) Madhya Pradesh
The question asks about the specific right added to the Fundamental Rights by the 86th Amendment Act, which inserted Article 21(A) into the Indian Constitution. We need to identify which of the given options corresponds to this amendment.
Correct Option: A) Right to education
The 86th Amendment Act of 2002 inserted Article 21(A) into the Constitution, making the Right to Education a Fundamental Right for children between the ages of 6 and 14 years.
To determine the incorrect statement, we need to analyze the given chemical reaction, identify the oxidation states of the elements involved, and understand the definitions of oxidation and reduction.
D) Cl₂ is oxidised to HCl.
This statement is incorrect. In the reaction, \( \text{Cl}_2 \) is a product with an oxidation state of \(0\). If it were oxidized to \( \text{HCl} \), its oxidation state would have to decrease from \(0\) to \(-1\), which is a reduction, not an oxidation. In fact, \( \text{HCl} \) (specifically the chloride ion) is oxidized to \( \text{Cl}_2 \), as its oxidation state increases from \(-1\) to \(0\).
This is a basic direction sense question. We need to visualize the movement described and determine the final position of Ram relative to Raju.
Correct Option: C) North direction
In the word LIBRARY, how many letters are there which occupy the same position when counted from the front as well as from the back?
To solve this problem, we need to compare the position of each letter in the word "LIBRARY" when counted from the beginning with its position when counted from the end. We will list the letters and their positions from both directions and identify any letters that have the same position number.
D) One. There is only one letter ('R') in the word LIBRARY that occupies the same position when counted from the front as well as from the back.
This is a letter-cluster analogy question. We need to find the pattern or relationship between the letters in the first pair (EXA : HSH) and apply the same pattern to the second pair (LWQ : ORX) to confirm it. Once the pattern is identified and confirmed, we will apply it to the third given letter-cluster (KNO) to find the missing fifth letter-cluster.
A) NIV is the correct option because it follows the established pattern of \((+3, -5, +7)\) for each corresponding letter from KNO.
To find the modal weight from a given set of data, we need to identify the value that appears most frequently in the dataset. This is the definition of the mode in statistics.
Correct Option: B) 44.0 kg is the modal weight because it appears 3 times, which is the highest frequency among all the given weights.