The question asks to identify the option that is different from the rest. This is a classification type of question where we need to find a common characteristic among three options and identify the one that does not share that characteristic.
Correct Option: B) Indigo Airlines is the correct answer because it is the only airline among the given options that is currently operational. The other three airlines (Jet Airways, Air Deccan, and Kingfisher Airlines) are all defunct.
To determine the selling price per dozen for the remaining mangoes, we need to calculate the total cost, the desired profit, and the number of usable mangoes. Then, we can find the total selling price and divide it by the number of dozens of usable mangoes.
Correct Option: A) ₹78
The question asks to identify the pair that is NOT correctly matched among the given UNESCO World Heritage Sites and their respective locations. This requires knowledge of the locations of prominent Indian World Heritage Sites.
Based on the evaluation, the pair "Elephanta Caves - Karnataka" is not correctly matched.
Correct Option: B) Elephanta Caves - Karnataka
If \(\frac{x-y}{3}\) = \(\frac{x+y}{5}\) = \(\frac{xy}{8}\), then find the value of xy.
We are given a set of equal ratios involving \(x\) and \(y\). We can equate each part of the ratio to a constant \(k\) to express \(x\) and \(y\) in terms of \(k\). Then, we can substitute these expressions into one of the ratio equations to solve for \(k\) and subsequently find the value of \(xy\).
Let the given ratios be equal to a constant \(k\):
\[ \frac{x-y}{3} = \frac{x+y}{5} = \frac{xy}{8} = k \]From this, we can write three separate equations:
Add Equation 1 and Equation 2:
\[ (x-y) + (x+y) = 3k + 5k \] \[ 2x = 8k \] \[ x = 4k \]Substitute the value of \(x\) into Equation 2:
\[ 4k + y = 5k \] \[ y = 5k - 4k \] \[ y = k \]Now, substitute the values of \(x = 4k\) and \(y = k\) into Equation 3:
\[ xy = 8k \] \[ (4k)(k) = 8k \] \[ 4k^2 = 8k \]Solve for \(k\):
\[ 4k^2 - 8k = 0 \] \[ 4k(k - 2) = 0 \]This gives two possible values for \(k\): \(k=0\) or \(k=2\).
If \(k=0\), then \(x=4(0)=0\) and \(y=0\). In this case, \(xy = 0\), which is not among the options. Also, the original expression would involve division by zero if \(xy=0\) and \(8\) is in the denominator, but \(xy/8\) would be \(0/8=0\). However, if \(x=0\) and \(y=0\), then \((x-y)/3 = 0/3 = 0\) and \((x+y)/5 = 0/5 = 0\). So \(k=0\) is a valid solution for the equations, but it leads to \(xy=0\). Since \(xy/8\) is given, \(xy\) cannot be zero if we are looking for a non-zero value from the options.
Let's consider \(k=2\).
If \(k=2\), then:
\[ x = 4k = 4(2) = 8 \] \[ y = k = 2 \]Now, find the value of \(xy\):
\[ xy = (8)(2) = 16 \]D) 16
This problem involves calculating the sum of numbers given their mean and then using this information to find an unknown number. We will use the formula for the mean, which is the sum of all numbers divided by the count of numbers.
Calculate the sum of the initial 6 numbers:
The mean of 6 numbers is 18. The formula for the mean is:
So, the sum of the 6 numbers can be found as:
\[ \text{Sum}_6 = \text{Mean}_6 \times \text{Count}_6 = 18 \times 6 = 108 \]Calculate the sum of the 7 numbers after inclusion:
When one more number is included, the total count of numbers becomes 7, and their new mean is 20. The sum of these 7 numbers is:
Find the included number:
The new number included is the difference between the sum of 7 numbers and the sum of the initial 6 numbers.
Correct Option: B) 32
This problem can be solved using the empirical relationship between mean, median, and mode for a moderately skewed distribution. The formula is approximately:
\[ \text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean} \]B) 38 is the correct answer, calculated using the empirical formula.
The question asks for the specific year when Dadabhai Naoroji achieved the historic milestone of becoming the first Indian member of the British House of Commons. This requires knowledge of a key event in Indian political history and the timeline of prominent Indian leaders.
Correct Option: C) 1892
This is an analogy question where we need to find the relationship between the first pair of words and apply the same relationship to the third word to find the fourth word.
Correct Option: C) Depressed
The question asks to identify the world's first handwritten needle book from the given options. This is a factual question related to literary history, specifically focusing on unique forms of publication or artistic expression.
Correct Option: D) Madhushala is recognized as the world's first handwritten needle book. This unique form was created by artist Dr. Rajani Kant, who embroidered the entire text of Harivansh Rai Bachchan's famous poem "Madhushala" onto cloth using a needle, making it a distinctive piece of art and literature.