Find the best approximation to the product 0.3333 × 0.25 × 0.499 × 0.125 × 24.
To find the best approximation of the given product, we should convert each decimal number into its closest fractional equivalent. This simplifies the multiplication and makes it easier to calculate the approximate value.
The expression becomes:
\[ \frac{1}{3} \times \frac{1}{4} \times \frac{1}{2} \times \frac{1}{8} \times 24 \]Multiply the numerators and the denominators:
\[ \frac{1 \times 1 \times 1 \times 1 \times 24}{3 \times 4 \times 2 \times 8} \]\[ \frac{24}{192} \]Divide both the numerator and the denominator by their greatest common divisor. We can see that \(24\) is a factor of \(192\) (\(192 = 24 \times 8\)).
\[ \frac{24}{192} = \frac{1}{8} \]Correct Option: C) 0.125 is the best approximation for the given product.
To identify an input device, we need to understand its function: an input device sends data to a computer system. Conversely, an output device receives data from a computer system and displays or presents it in some form. We will evaluate each option based on this definition.
Correct Option: B) Optical character reader
The question asks to identify the personality who coined the famous slogan 'Jai Jawan Jai Kisan'. This is a direct knowledge-based question related to Indian political history.
Correct Option: C) Lal Bahadur Shastri coined the slogan 'Jai Jawan Jai Kisan'.
The question asks to identify the region in Germany that is primarily responsible for a significant portion of its steel production. This requires knowledge of Germany's industrial geography and major industrial centers.
C) Ruhr — The Ruhr region is historically and currently the most significant industrial area in Germany, particularly known for its heavy industry, including coal mining and steel production. It accounts for a vast majority of Germany's steel output.
This problem involves analyzing statements and conclusions based on the principles of syllogism and Venn diagrams. We need to determine which conclusions logically follow from the given statements, assuming the statements are true.
C) Only conclusion 1 follows.
The question asks to identify the longest running train in the Indian railway network in terms of both distance and time. This requires knowledge of prominent Indian train services and their routes.
B) Vivek Express — The Vivek Express, running from Dibrugarh in Assam to Kanyakumari in Tamil Nadu, is the longest train route in India both in terms of distance (approximately 4,189 km) and journey time (around 82 hours and 30 minutes).
Find the missing frequency(p) for the following distribution whose mean is 8:
| x: | 3 | 5 | 7 | 9 | 11 | 13 |
| f: | 6 | 8 | 15 | p | 8 | 4 |
To find the missing frequency (p) when the mean of a distribution is given, we use the formula for the mean of a discrete frequency distribution. The mean is calculated as the sum of the product of each observation and its frequency, divided by the sum of all frequencies.
The distribution is given as:
| x | f |
|---|---|
| 3 | 6 |
| 5 | 8 |
| 7 | 15 |
| 9 | p |
| 11 | 8 |
| 13 | 4 |
The mean of this distribution is given as 8.
The formula for the mean (\(\bar{x}\)) is:
\[ \bar{x} = \frac{\sum fx}{\sum f} \]Given that the mean is 8, we can set up the equation:
\[ 8 = \frac{303 + 9p}{41 + p} \]Multiply both sides by \((41 + p)\):
\[ 8(41 + p) = 303 + 9p \]Distribute 8 on the left side:
\[ 328 + 8p = 303 + 9p \]Subtract \(8p\) from both sides:
\[ 328 = 303 + 9p - 8p \] \[ 328 = 303 + p \]Subtract 303 from both sides:
\[ p = 328 - 303 \] \[ p = 25 \]Correct Option: C) 25
The question asks for the location of the Keoladeo Ghana National Park. This requires knowledge of important national parks and their geographical locations in India.
Correct Option: C) Rajasthan. The Keoladeo Ghana National Park, also known as Bharatpur Bird Sanctuary, is a famous avifauna sanctuary that hosts thousands of birds, especially during the winter season. It is located in Bharatpur, Rajasthan, India. It is a UNESCO World Heritage Site.
This problem involves calculating the cost price of a single book given the selling price of a certain number of books and the profit made in terms of the cost price of some books. We will set up an equation relating the selling price, cost price, and profit.
Let the cost price of one book be \( \text{CP} \).
The cost price of 20 books will be \( 20 \times \text{CP} \).
The man sold 20 books for ₹1,800. So, the selling price of 20 books is ₹1,800.
The gain (profit) is equal to the cost price of 5 books. So, \(\text{Profit} = 5 \times \text{CP} \).
We know the formula: \(\text{Selling Price} = \text{Cost Price} + \text{Profit}\).
Substitute the values for 20 books into the formula:
\[ \text{Selling Price of 20 books} = \text{Cost Price of 20 books} + \text{Profit} \]Plug in the known values:
\[ 1800 = 20 \times \text{CP} + 5 \times \text{CP} \]Combine the terms involving \(\text{CP}\):
\[ 1800 = (20 + 5) \times \text{CP} \]\[ 1800 = 25 \times \text{CP} \]Solve for \(\text{CP}\):
\[ \text{CP} = \frac{1800}{25} \]\[ \text{CP} = 72 \]Therefore, the cost price of a book is ₹72.
D) ₹72 — The calculation shows that the cost price of one book is ₹72.