This is a logical reasoning problem involving seating arrangements or floor puzzles. We need to deduce the floor on which each person lives based on the given clues and then determine the number of people between C and E.
Identify the floors: There are 6 floors, numbered 1 to 6.
Clue 1: E lives on a floor which is a prime number.
The prime numbers between 1 and 6 are 2, 3, and 5. So, E can live on floor 2, 3, or 5.
Clue 2: The product of floors on which E and A live is 8.
Let E's floor be \(F_E\) and A's floor be \(F_A\). We have \(F_E \times F_A = 8\).
Possible pairs \((F_E, F_A)\) are:
Therefore, E lives on floor 2 and A lives on floor 4.
Clue 3: The sum of floors on which A and B live is 7.
We know A lives on floor 4. Let B's floor be \(F_B\). So, \(F_A + F_B = 7\).
\(4 + F_B = 7 \implies F_B = 3\).
So, B lives on floor 3.
Clue 4: C lives immediately above F.
This means C and F live on consecutive floors, with C on the higher floor. Possible pairs \((F_F, F_C)\) are (1,2), (2,3), (3,4), (4,5), (5,6).
Consolidate known positions:
The remaining floors are 1, 5, and 6.
Place C and F:
Since E, B, and A occupy floors 2, 3, and 4 respectively, the pairs (1,2), (2,3), (3,4), (4,5) are not available for (F, C) because floor 2, 3, and 4 are already occupied.
The only remaining consecutive floors are 5 and 6. So, F must live on floor 5 and C must live on floor 6.
Final arrangement:
Answer the question: How many people live between C and E?
C is on floor 6 and E is on floor 2.
The people living between floor 6 and floor 2 are F (floor 5), A (floor 4), and B (floor 3).
There are 3 people between C and E.
B) Three
The question asks about the material used for the famous sculpture of a bearded man (often referred to as the "Priest-King") found in Mohenjo-daro. This requires knowledge of the materials commonly used for sculptures during the Indus Valley Civilization.
D) Stone — The famous sculpture of the bearded man (often called the "Priest-King") from Mohenjo-daro is carved from steatite, a soft stone. This is a well-established fact in Indus Valley Civilization archaeology.
The question asks about the immediate effect of moving a file to the 'Trash' or 'Recycle Bin' in a GUI-based Operating System. This action is a common user interaction, and understanding its underlying mechanism is key. We need to evaluate what happens to the file's data and its entry in the file system.
D) The file is moved to a special directory, and its directory entry is updated, but the data remains on the storage device. This accurately describes the typical immediate effect. The file's entry is changed to point to the 'Trash' or 'Recycle Bin' directory, but the actual data blocks on the disk are not erased or overwritten immediately, allowing for recovery.
The question asks to identify the northernmost Himalayan range that contains the loftiest peaks. This requires knowledge of the major divisions of the Himalayas and their characteristics.
D) Himadri — The Himadri, or Great Himalayas, is indeed the northernmost range and contains the world's highest and most prominent peaks.
To determine the nature of the roots of a quadratic equation of the form \( ax^2 + bx + c = 0 \), we use the discriminant, denoted by \(\Delta\) or \(D\). The discriminant is calculated as \( \Delta = b^2 - 4ac \). The nature of the roots depends on the value of the discriminant:
Correct Option: A) Complex Roots (Imaginary Roots)
To find the new price, we need to apply the percentage decrease and then the percentage increase sequentially to the original price. First, calculate the price after the 12% decrease. Then, use this new price as the base for the 20% increase.
Original price \( = \text{₹}8,000 \)
Decrease percentage \( = 12\% \)
Amount of decrease \( = 12\% \text{ of } \text{₹}8,000 \)
\[ = \frac{12}{100} \times 8000 \]\[ = 12 \times 80 \]\[ = \text{₹}960 \]Price after decrease \( = \text{Original price} - \text{Amount of decrease} \)
\[ = 8000 - 960 \]\[ = \text{₹}7,040 \]Price after decrease \( = \text{₹}7,040 \)
Increase percentage \( = 20\% \)
Amount of increase \( = 20\% \text{ of } \text{₹}7,040 \)
\[ = \frac{20}{100} \times 7040 \]\[ = \frac{1}{5} \times 7040 \]\[ = \text{₹}1,408 \]New price \( = \text{Price after decrease} + \text{Amount of increase} \)
\[ = 7040 + 1408 \]\[ = \text{₹}8,448 \]D) 8,448 is the new price after applying a 12% decrease and then a 20% increase to the original price of ₹8,000.
Simplify: (\( \frac{36}{9} \)) × (74 + 12) + 99
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This stands for Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, and Subtraction. We will perform operations in this specific order.
The expression is \( (\frac{36}{9}) \times (74 + 12) + 99 \).
First, calculate the values inside the parentheses.
Substitute these values back into the expression:
\[ 4 \times 86 + 99 \]Next, perform the multiplication operation.
\[ 4 \times 86 = 344 \]Finally, perform the addition operation.
\[ 344 + 99 = 443 \]D) 443 is the correct answer after simplifying the expression following the order of operations.
To find the average weight of the whole class, we need to calculate the total weight of all students and divide it by the total number of students. This involves calculating the total weight for each section and then summing them up.
Correct Option: B) 36
This is a coding-decoding problem. We need to find the common word in the given phrases and then identify the common code associated with that word. This will allow us to determine the code for the word 'book'.
Correct Option: D) qr
If a : b = 3 : 4 and b : c = 4 : 7, then \(\frac{a+b+c}{c}\) is equal to:
The problem provides two ratios, \(a:b\) and \(b:c\). We need to find the value of the expression \(\frac{a+b+c}{c}\). The key is to combine the given ratios to find a common ratio for \(a:b:c\).
Identify the given ratios:
Combine the ratios:
Notice that the common term 'b' has the same value (4) in both ratios. This simplifies the combination significantly. If the values were different, we would find the least common multiple (LCM) of the 'b' values.
Since \(b\) is 4 in both ratios, we can directly write the combined ratio:
\[ a : b : c = 3 : 4 : 7 \]Represent \(a, b, c\) in terms of a common constant:
Let \(a = 3k\), \(b = 4k\), and \(c = 7k\) for some non-zero constant \(k\).
Substitute these values into the expression:
The expression to evaluate is \(\frac{a+b+c}{c}\).
Simplify the expression:
\[ \frac{3k + 4k + 7k}{7k} = \frac{(3+4+7)k}{7k} \]\[ \frac{14k}{7k} \]Cancel out the common term \(k\):
\[ \frac{14}{7} = 2 \]D) The calculated value of the expression is 2.