This is a syllogism problem. We will use Venn diagrams to represent the given statements and then check which conclusions logically follow from these representations.
Statement 1: All tablets are laptops.
This means the circle representing 'Tablets' is entirely inside the circle representing 'Laptops'.
Statement 2: No laptop is a desktop.
This means the circle representing 'Laptops' and the circle representing 'Desktops' are completely separate, with no overlap.
Statement 3: No laptop is a mobile.
This means the circle representing 'Laptops' and the circle representing 'Mobiles' are completely separate, with no overlap.
Evaluate Conclusion (I): No tablet is a desktop.
From Statement 1, all tablets are laptops. From Statement 2, no laptop is a desktop. Since tablets are a subset of laptops, and laptops have no relation with desktops, it logically follows that no tablet can be a desktop. This conclusion is definitely true.
Evaluate Conclusion (II): Some mobiles are desktops.
From Statement 2, no laptop is a desktop. From Statement 3, no laptop is a mobile. These statements tell us about the relationship of laptops with desktops and mobiles. However, there is no direct or indirect statement linking 'Mobiles' and 'Desktops'. They could overlap, or they could be entirely separate. We cannot conclude with certainty that some mobiles are desktops. This conclusion does not logically follow.
Correct Option: A) Only conclusion (I) follows.
This problem involves calculating the marked price of an item given its cost price, discount percentage, and profit percentage. We will first calculate the selling price using the cost price and profit percentage. Then, using the selling price and discount percentage, we can find the marked price.
The dealer purchased the washing machine for ₹1,301, which is the Cost Price (CP). He gains 41%.
\[ \text{Profit Percentage} = \frac{\text{Profit}}{\text{CP}} \times 100 \]\[ \text{SP} = \text{CP} + \text{Profit} \]\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]\[ \text{SP} = 1301 \times \left(1 + \frac{41}{100}\right) \]\[ \text{SP} = 1301 \times \left(\frac{100 + 41}{100}\right) \]\[ \text{SP} = 1301 \times \frac{141}{100} \]\[ \text{SP} = \frac{183441}{100} \]\[ \text{SP} = \text{₹}1834.41 \]A discount of 53% was allowed on the Marked Price (MP). The Selling Price (SP) is ₹1834.41.
\[ \text{Discount Percentage} = \frac{\text{Discount}}{\text{MP}} \times 100 \]\[ \text{SP} = \text{MP} - \text{Discount} \]\[ \text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount Percentage}}{100}\right) \]\[ 1834.41 = \text{MP} \times \left(1 - \frac{53}{100}\right) \]\[ 1834.41 = \text{MP} \times \left(\frac{100 - 53}{100}\right) \]\[ 1834.41 = \text{MP} \times \frac{47}{100} \]\[ \text{MP} = \frac{1834.41 \times 100}{47} \]\[ \text{MP} = \frac{183441}{47} \]\[ \text{MP} = \text{₹}3903 \]D) ₹3,903
The question asks to identify which option is NOT a valid method for moving selected text in MS Word. We need to evaluate each option based on its functionality in MS Word.
Correct Option: D) Format Painter is used to copy formatting, not to move text content. It does not facilitate the relocation of selected text.
The problem asks us to identify the letter-cluster that does not follow the same pattern as the others, based on the English alphabetical order. We need to find the positional values of the letters in each cluster and then look for a consistent mathematical or sequential relationship between them.
This is a coding-decoding problem where we need to find the code for a common word by comparing the given coded statements. We will identify the common word in the phrases and then find the common code associated with it.
The word common to both "rough and ready" and "road is rough" is 'rough'.
The common code in both sequences is 'km'.
Since 'rough' is the common word and 'km' is the common code, 'rough' is coded as 'km'.
Correct Option: D) km
The problem presents a series of letter-number clusters. To find the missing cluster, we need to identify the patterns in the letters and the numbers separately.
A) QIW 144 — This matches our derived pattern for letters (Q, I, W) and the number (144).
To find the greatest ratio, we need to convert each ratio into its decimal equivalent or compare them by finding a common denominator. Converting to decimals is often simpler for direct comparison.
Comparing these values, \(1\) is clearly the greatest.
Correct Option: C) 11 : 11
What is the mode of the data given below? [Give your answer correct to 2 decimal places.]
| Age in years | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| No. of patients | 16 | 21 | 14 | 34 | 37 | 32 | 13 |
To find the mode of grouped data, we first identify the modal class, which is the class interval with the highest frequency. Then, we use the formula for the mode of grouped data.
Identify the Modal Class:
The given data is:
| Age in years | No. of patients (Frequency, \(f\)) |
|---|---|
| 10-20 | 16 |
| 20-30 | 21 |
| 30-40 | 14 |
| 40-50 | 34 |
| 50-60 | 37 |
| 60-70 | 32 |
| 70-80 | 13 |
From the table, the highest frequency is 37, which corresponds to the class interval 50-60. Therefore, the modal class is 50-60.
Identify the values for the mode formula:
The formula for the mode of grouped data is:
\[ \text{Mode} = L + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h \]Substitute the values into the formula and calculate:
\[ \text{Mode} = 50 + \left( \frac{37 - 34}{2 \times 37 - 34 - 32} \right) \times 10 \]\[ \text{Mode} = 50 + \left( \frac{3}{74 - 34 - 32} \right) \times 10 \]\[ \text{Mode} = 50 + \left( \frac{3}{40 - 32} \right) \times 10 \]\[ \text{Mode} = 50 + \left( \frac{3}{8} \right) \times 10 \]\[ \text{Mode} = 50 + 0.375 \times 10 \]\[ \text{Mode} = 50 + 3.75 \]\[ \text{Mode} = 53.75 \]Round to two decimal places:
The calculated mode is 53.75, which is already in two decimal places.
B) 53.75 is the correct mode of the given data, calculated using the formula for grouped data.