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 gives the coded form of TYPEWRITTERS as PETYRWTEITSR and asks for the code of BRAINSTORMER. We need to find how the letters of the word are rearranged and apply the same rearrangement to BRAINSTORMER.
Identify the given information:
Split the word into two blocks of six letters:
TYPEWRITTERS splits into TYPEWR and ITTERS. The code PETYRWTEITSR splits into PETYRW and TEITSR.
Find the rearrangement within each block:
In TYPEWR (T1 Y2 P3 E4 W5 R6), the code PETYRW takes the letters in the order 3, 4, 1, 2, 6, 5.
In ITTERS (I1 T2 T3 E4 R5 S6), the code TEITSR also takes the letters in the order 3, 4, 1, 2, 6, 5. So, the rule is consistent.
Apply the rule to BRAINSTORMER:
The blocks are BRAINS and TORMER.
BRAINS (B1 R2 A3 I4 N5 S6) in the order 3, 4, 1, 2, 6, 5 gives AIBRSN.
TORMER (T1 O2 R3 M4 E5 R6) in the order 3, 4, 1, 2, 6, 5 gives RMTORE.
Therefore, the code is AIBRSNRMTORE.
Correct Option: A) AIBRSNRMTORE — In each block of six letters, the letters are written in the order 3, 4, 1, 2, 6, 5, which turns BRAINS into AIBRSN and TORMER into RMTORE. Hence, Option A is the correct answer.
B) AIBRSNOTERRM: This is incorrect because the second block TORMER must become RMTORE, not OTERRM; this code cannot be obtained from the given rule.
C) AIBRNSTOERRM: This is incorrect because it does not swap the 5th and 6th letters of BRAINS (it keeps NS instead of SN), and the second block is also wrong.
D) AIBRRMNSTORE: This is incorrect because it mixes letters across the two blocks; this code cannot be obtained from the given rule.
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.