The question asks about the target for highway construction set by the Government of India for a specific financial year (FY21). This is a factual question related to government infrastructure targets and policies, often covered in economic surveys or budget documents.
A) 15000 Kms. The Government of India had set a target of building 15,000 Kms of national highways in Financial Year 2020-2021 (FY21). This information is often highlighted in government reports and economic reviews.
The question asks to identify the book written by Mahatma Gandhi in 1909 that discussed the idea of British rule ending if Indians withdrew their cooperation. This requires knowledge of Gandhi's early writings and their core themes.
Correct Option: A) Hind Swaraj is the correct answer. This book, written in 1909, contains Gandhi's seminal ideas on Swaraj and non-cooperation, arguing that British rule persisted due to Indian cooperation.
To find the maximum number of units that should be put into each packet such that both boxes A and B are filled to their full capacity, we need to find the largest number that divides both capacities exactly. This is equivalent to finding the Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of the two capacities.
Correct Option: C) 17 units per packet
The problem describes a coding pattern where a word is transformed into another. We need to identify this pattern and apply it to a new word. By comparing the original word "METHOD" with its coded form "DOHTEM", we can deduce the rule.
Original word: METHOD
Coded word: DOHTEM
Let's write the letters of "METHOD" and "DOHTEM" in order:
M E T H O D
D O H T E M
Observe that the coded word "DOHTEM" is simply the reverse of the original word "METHOD".
M (1st) <--> M (6th)
E (2nd) <--> E (5th)
T (3rd) <--> T (4th)
H (4th) <--> H (3rd)
O (5th) <--> O (2nd)
D (6th) <--> D (1st)
The coding rule is to reverse the order of the letters in the given word.
New word: CHOCOLATE
To code this word, we reverse its letters:
C H O C O L A T E
Reversed: E T A L O C O H C
C) ETALOCOHC is the correct option because it represents the word "CHOCOLATE" with its letters reversed, following the established pattern.
The question asks to identify which of the given options is NOT a file extension for a video file. This requires knowledge of common file extensions for different media types, specifically distinguishing between video and image formats.
Correct Option: C) .jpeg is an image file format, not a video file format. It stands for Joint Photographic Experts Group and is used for compressing digital images.
To find the profit percentage, we need to determine the cost price (CP), marked price (MP), and selling price (SP). We can assume a convenient cost price, calculate the marked price based on the given percentage above CP, then calculate the selling price after applying the discount on the marked price. Finally, we can find the profit and express it as a percentage of the cost price.
Let the Cost Price (CP) of the goods be Rs. 100.
The dealer lists his goods at 40% above the cost price.
\[ \text{Marked Price (MP)} = \text{CP} + (40\% \text{ of CP}) \]\[ \text{MP} = 100 + \left(\frac{40}{100} \times 100\right) \]\[ \text{MP} = 100 + 40 = \text{Rs. } 140 \]The dealer allows a discount of 20% on the Marked Price.
\[ \text{Discount Amount} = 20\% \text{ of MP} \]\[ \text{Discount Amount} = \frac{20}{100} \times 140 \]\[ \text{Discount Amount} = 2 \times 14 = \text{Rs. } 28 \]\[ \text{Selling Price (SP)} = \text{MP} - \text{Discount Amount} \]\[ \text{SP} = 140 - 28 = \text{Rs. } 112 \]Profit is the difference between the Selling Price and the Cost Price.
\[ \text{Profit} = \text{SP} - \text{CP} \]\[ \text{Profit} = 112 - 100 = \text{Rs. } 12 \]Profit percentage is calculated on the Cost Price.
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}} \times 100\right)\% \]\[ \text{Profit Percentage} = \left(\frac{12}{100} \times 100\right)\% \]\[ \text{Profit Percentage} = 12\% \]Correct Option: D) 12%
\(\sqrt{2}\) - \(\sqrt{3}\)is:
a whole number
an irrational number
a natural number
a rational number
To determine the nature of the expression \(\sqrt{2} - \sqrt{3}\), we need to understand the definitions of different types of numbers: natural numbers, whole numbers, rational numbers, and irrational numbers. We will evaluate the approximate values of \(\sqrt{2}\) and \(\sqrt{3}\) and then perform the subtraction to classify the result.
Correct Option: B) an irrational number
Rationalising factor of \(\sqrt[3]{40}\) is:
\( 10^{\frac{1}{3}} \)
\( 5^{\frac{2}{3}} \)
\( 40^{\frac{1}{3}} \)
\( 2^{\frac{2}{3}} \)
To find the rationalizing factor of a surd like \(\sqrt[n]{x}\), we need to multiply it by another surd such that the product becomes a rational number. This means eliminating the radical sign. For \(\sqrt[3]{40}\), we need to find a factor that, when multiplied, results in an integer under the cube root.
First, we simplify \(\sqrt[3]{40}\) by finding its prime factors.
\[ 40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5 \]\[ \sqrt[3]{40} = \sqrt[3]{2^3 \times 5} = \sqrt[3]{2^3} \times \sqrt[3]{5} = 2 \times \sqrt[3]{5} \]The expression is now \(2 \times \sqrt[3]{5}\). To rationalize this, we need to eliminate the cube root from \(\sqrt[3]{5}\).
For \(\sqrt[3]{5}\) to become a rational number, we need to multiply it by a factor that will make the term inside the cube root a perfect cube. Since we have \(5^1\) inside the cube root, we need \(5^2\) to make it \(5^3\).
So, the rationalizing factor for \(\sqrt[3]{5}\) is \(\sqrt[3]{5^2}\).
\[ \sqrt[3]{5} \times \sqrt[3]{5^2} = \sqrt[3]{5 \times 5^2} = \sqrt[3]{5^3} = 5 \]The rationalizing factor is \(\sqrt[3]{5^2}\), which can be written as \(5^{\frac{2}{3}}\).
B) \(5^{\frac{2}{3}}\) is the rationalizing factor. When \(\sqrt[3]{40} = 2 \times \sqrt[3]{5}\) is multiplied by \(5^{\frac{2}{3}} = \sqrt[3]{5^2}\), the product is \(2 \times \sqrt[3]{5} \times \sqrt[3]{5^2} = 2 \times \sqrt[3]{5^3} = 2 \times 5 = 10\), which is a rational number.
This problem involves permutations, specifically the number of ways to assign distinct items to distinct positions. We need to calculate the number of permutations for Quantity A and Quantity B separately and then compare them.
Quantity A is the number of ways to assign a number from 1 to 5 (i.e., 5 distinct numbers) without repetition to each of four people. Here, \(n = 5\) (total numbers available) and \(k = 4\) (number of people to assign numbers to).
\[ \text{Quantity A} = P(5, 4) = \frac{5!}{(5-4)!} = \frac{5!}{1!} = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]Quantity B is the number of ways to assign a number from 1 to 5 (i.e., 5 distinct numbers) without repetition to each of 5 people. Here, \(n = 5\) (total numbers available) and \(k = 5\) (number of people to assign numbers to).
\[ \text{Quantity B} = P(5, 5) = \frac{5!}{(5-5)!} = \frac{5!}{0!} \]Recall that \(0! = 1\).
\[ \text{Quantity B} = \frac{5!}{1} = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]We found that Quantity A = 120 and Quantity B = 120.
Therefore, Quantity A is equal to Quantity B.
C) Both Quantities A and B are equal. As calculated, both Quantity A and Quantity B are 120.
This is a linear arrangement puzzle. We need to deduce the positions of five friends (G, H, I, J, K) in a row based on the given clues. We will use the clues to build the arrangement step by step.
Clue 2: G is at the left end.
Since there are five friends, the positions can be represented as 1 2 3 4 5 from left to right. G is at position 1.
Current arrangement: G _ _ _ _
Clue 3: K is the neighbour of both J and I.
This means K must be in the middle of J and I. So, the sequence must be either J K I or I K J.
Clue 1: The person in the middle is between J and I.
There are five positions, so the middle position is the 3rd position. This clue implies that the person at position 3 is between J and I. Combining this with Clue 3, it means K is at the middle position (position 3), and J and I are on either side of K.
So, the sequence J K I or I K J must occupy positions 2, 3, and 4.
Let's combine step 1 and step 3.
Case 1: If the sequence is J K I
G J K I _
Case 2: If the sequence is I K J
G I K J _
In both cases, one position remains vacant at the right end (position 5). The only friend left is H.
If Case 1: G J K I H
If Case 2: G I K J H
In both valid arrangements, H is at the right end.
Therefore, H is standing at the right end.
A) H is standing at the right end, as determined by the step-by-step deduction.