The question asks for the Governor of Andhra Pradesh and Telangana as of 2018. This requires knowledge of the political appointments during that specific period.
Correct Option: C) ESL Narasimhan
The question asks for the date on which World Environment Day is celebrated. This is a factual question related to important international days, which are common in competitive exams.
A) 5 June is the correct answer. World Environment Day is celebrated annually on 5 June to encourage worldwide awareness and action for the protection of our environment.
A separating funnel is a laboratory apparatus used to separate immiscible liquids. Immiscible liquids are those that do not mix and form distinct layers when combined. The principle behind using a separating funnel is the difference in densities of the two immiscible liquids.
Correct Option: C) oil and water
Oil and water are immiscible liquids. When mixed, they form two distinct layers because oil is less dense than water and does not dissolve in it. This makes them perfectly separable using a separating funnel. The oil will float on top of the water, and the water can be drained off from the bottom.
This problem requires us to find the median of a dataset given its mode and mean. We can use the empirical relationship between mean, median, and mode for a moderately skewed distribution, which is given by the formula: \( \text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean} \).
Thus, the median of the observations is 9.
Correct Option: A) 9 is the correct answer, derived from the empirical relationship between mode, median, and mean.
The problem presents a statement describing a situation and two proposed courses of action. We need to evaluate which action(s) logically follow from the statement, considering the statement to be true. This involves identifying appropriate and practical responses to the given problem.
D) Only 1 follows. Action I is a logical and constructive response to the water crisis faced by the construction industries. The government's intervention to solve the crisis is expected and necessary.
The problem requires us to decode a word based on a given coding pattern. We need to identify the rule applied to transform the letters of the word "WEAK" into "DVZP" and then apply the same rule to the word "MEAT".
A) NVZG is the correct code for MEAT, following the established pattern where each letter is replaced by its corresponding letter from the opposite end of the alphabet.
The question asks to identify the individual who coined the term 'atom'. This requires knowledge of the historical development of atomic theory and the contributions of various scientists and philosophers.
Correct Option: D) Democritus is credited with coining the term "atom" (from the Greek "atomos") to describe the fundamental, indivisible particles of matter.
The median of a set of observations is the middle value when the observations are arranged in ascending or descending order. If the number of observations is odd, the median is the \(\left(\frac{n+1}{2}\right)^{\text{th}}\) observation. If the number of observations is even, the median is the average of the two middle observations. When a constant is added to some observations, it's important to understand how this affects the position and value of the median.
We are given 11 distinct observations. Let these observations, when arranged in ascending order, be \(x_1, x_2, \ldots, x_{11}\).
Since \(n = 11\) (an odd number), the median is the \(\left(\frac{11+1}{2}\right)^{\text{th}}\) observation, which is the \(6^{\text{th}}\) observation.
So, the initial median is \(x_6 = 12.5\).
The last five observations are \(x_7, x_8, x_9, x_{10}, x_{11}\).
When 11 is added to each of these, they become \(x_7+11, x_8+11, x_9+11, x_{10}+11, x_{11}+11\).
The first six observations \(x_1, x_2, x_3, x_4, x_5, x_6\) remain unchanged.
Since the observations are distinct and arranged in ascending order, we know that \(x_6 < x_7\).
Even after adding 11 to \(x_7\), the new value \(x_7+11\) will still be greater than \(x_6\), because \(x_7+11 > x_7 > x_6\). The same applies to \(x_8+11, \ldots, x_{11}+11\).
Therefore, the relative order of the observations remains the same. The first six observations are still \(x_1, x_2, x_3, x_4, x_5, x_6\), and the next five observations are \(x_7+11, x_8+11, x_9+11, x_{10}+11, x_{11}+11\).
The total number of observations is still 11. The median will still be the \(6^{\text{th}}\) observation in the ordered set.
The \(6^{\text{th}}\) observation is \(x_6\).
Since \(x_6\) was not among the observations to which 11 was added, its value remains unchanged.
Thus, the new median is \(x_6 = 12.5\).
C) 12.5 — The median is the 6th observation. Since 11 is added only to the last five observations (7th to 11th), the 6th observation remains unchanged, and its value is still 12.5.
Rahil had 15\( \frac{5}{8} \) litres of petrol in the vehicle's tank at the beginning of the journey. At the end of the journey only 3\( \frac{1}{8} \) litres of petrol was left in the fuel tank. What part of the initial quantity of petrol was consumed during the journey?
\( \frac{3}{4} \)
\( \frac{9}{10} \)
\( \frac{5}{6} \)
\( \frac{4}{5} \)
To find the part of the initial quantity of petrol consumed, we first need to calculate the total amount of petrol consumed. This is done by subtracting the remaining petrol from the initial petrol. Then, we express the consumed petrol as a fraction of the initial petrol quantity.
Initial quantity of petrol:
\[ 15\frac{5}{8} \text{ litres} = \frac{(15 \times 8) + 5}{8} = \frac{120 + 5}{8} = \frac{125}{8} \text{ litres} \]Petrol left at the end of the journey:
\[ 3\frac{1}{8} \text{ litres} = \frac{(3 \times 8) + 1}{8} = \frac{24 + 1}{8} = \frac{25}{8} \text{ litres} \]Petrol consumed = Initial quantity - Petrol left
\[ \text{Petrol consumed} = \frac{125}{8} - \frac{25}{8} = \frac{125 - 25}{8} = \frac{100}{8} \text{ litres} \]Part consumed = \[\frac{\text{Petrol consumed}}{\text{Initial quantity of petrol}}\]
\[ \text{Part consumed} = \frac{\frac{100}{8}}{\frac{125}{8}} = \frac{100}{8} \times \frac{8}{125} = \frac{100}{125} \]Divide both the numerator and the denominator by their greatest common divisor, which is 25.
\[ \frac{100 \div 25}{125 \div 25} = \frac{4}{5} \]D) \(\frac{4}{5}\) is the correct answer, as calculated in the step-by-step solution.
What will be the next term of the given series?
9T, 11R, 14P, 18N,?
To find the next term in the series, we need to identify the pattern in both the numerical and alphabetical parts of each term.
Correct Option: C) 23L