To simplify the given expression, we can convert all decimal numbers into fractions or powers of 10, multiply the integer parts, and then account for the decimal places.
The given expression is \(5 \times 0.5 \times 0.05 \times 0.005 \times 500\).
So the expression becomes:
\[ 5 \times \frac{5}{10} \times \frac{5}{100} \times \frac{5}{1000} \times 500 \]Group the integer parts and the powers of 10 separately.
\[ (5 \times 5 \times 5 \times 5 \times 500) \times \left(\frac{1}{10} \times \frac{1}{100} \times \frac{1}{1000}\right) \]Cancel out the common zeros:
\[ \frac{312500}{1000000} = \frac{3125}{10000} \]Dividing by 10000 means moving the decimal point 4 places to the left.
\[ \frac{3125}{10000} = 0.3125 \]B) 0.3125 is the correct simplified value of the expression.
The question asks for the chemical formula of common salt. This requires knowledge of common chemical names and their corresponding formulas.
Correct Option: D) NaCl is the chemical formula for sodium chloride, which is commonly known as common salt.
The question asks to identify the Vice President of India as of October 2020. This requires knowledge of current affairs and political appointments during that specific period.
Correct Option: B) M Venkaiah Naidu
M. Venkaiah Naidu was the Vice President of India from August 11, 2017, to August 10, 2022. Thus, in October 2020, he held this office.
The question asks to identify the Chairman of NITI Aayog. This is a factual question related to the organizational structure of a key government body in India. Understanding the composition and leadership of such bodies is crucial for competitive exams.
B) The Prime Minister is the ex-officio Chairman of NITI Aayog. This ensures that the institution works in close coordination with the government's overall policy objectives and vision for the country's development.
The problem asks us to identify the number that is different from the rest among the given four options. This type of question usually involves finding a common property or pattern shared by three of the numbers, while the fourth number does not follow that pattern. We will examine each number for properties like divisibility, perfect squares, perfect cubes, or sum of digits.
D) 729 is the only number among the given options that is both a perfect square (\(27^2\)) and a perfect cube (\(9^3\)).
This is a circular arrangement puzzle. We need to deduce the seating positions of 8 people around a round table based on the given clues and then identify who is immediately to the right of G.
A) A is sitting immediately to the right of G, as determined by the step-by-step arrangement.
This problem involves calculating the combined work rate of multiple taps (inlets and outlets) to determine the total time required to fill a tank. We will calculate the individual filling/emptying rates as fractions of the tank filled/emptied per hour and then sum them up to find the net rate.
Tap A can fill the tank in 6 hours. So, in 1 hour, Tap A fills:
\[ \text{Rate of A} = \frac{1}{6} \text{ tank/h} \]Tap B can fill the tank in 8 hours. So, in 1 hour, Tap B fills:
\[ \text{Rate of B} = \frac{1}{8} \text{ tank/h} \]Tap C can empty the tank in 4 hours. So, in 1 hour, Tap C empties:
\[ \text{Rate of C} = \frac{1}{4} \text{ tank/h} \]The net rate will be the sum of the filling rates minus the emptying rate:
\[ \text{Net Rate} = \text{Rate of A} + \text{Rate of B} - \text{Rate of C} \]\[ \text{Net Rate} = \frac{1}{6} + \frac{1}{8} - \frac{1}{4} \]The least common multiple (LCM) of 6, 8, and 4 is 24.
\[ \text{Net Rate} = \frac{4}{24} + \frac{3}{24} - \frac{6}{24} \]If the net rate is \(\frac{1}{24}\) tank per hour, it means the tank will be filled in 24 hours.
\[ \text{Time} = \frac{1}{\text{Net Rate}} \]\[ \text{Time} = \frac{1}{\frac{1}{24}} = 24 \text{ h} \]D) 24 h
The question asks for the Chairman of the Fifteenth Finance Commission as of October 2020. This is a factual question related to Indian polity and current affairs. To answer this, one needs to recall the composition and leadership of the Finance Commissions, particularly the 15th one.
Correct Option: D) Nand Kishore Singh was appointed as the Chairman of the Fifteenth Finance Commission in November 2017 and continued in this role through October 2020, overseeing the submission of its reports.
The problem presents a series of alphanumeric terms, each consisting of a number, a letter, and another number. We need to identify the pattern in the numbers and the letters separately to find the missing term.
The first numbers in the series are 2, 4, 8, 14.
The differences are 2, 4, 6. This is an arithmetic progression with a common difference of 2. The next difference should be \(6 + 2 = 8\). So, the next first number will be \(14 + 8 = 22\).
The letters in the series are A, E, I, O.
These are vowels in alphabetical order. The next vowel after 'O' is 'U'.
The second numbers in the series are 2, 6, 10, 16.
The differences are 4, 4, 6. This pattern seems to be increasing by 2 after the second term. So, the next difference should be \(6 + 2 = 8\). Therefore, the next second number will be \(16 + 8 = 24\).
Combining the next first number (22), the next letter (U), and the next second number (24), the next term in the series should be 22U24.
Let's re-examine the second number pattern as there might be a slight miscalculation or a different pattern. Let's look at the options.
The options are 20V22, 20U22, 22U20, 19U23.
Based on our first number and letter analysis, the term should start with 22 and have 'U' in the middle. This points to option C (22U20) or a variation.
Let's re-evaluate the first number pattern:
So the first number is 22.
Let's re-evaluate the letter pattern:
So the letter is U.
Let's re-evaluate the second number pattern:
The differences are 4, 4, 6. This means the next difference should be \(6+2 = 8\). So the next number would be \(16+8 = 24\).
This means the term should be 22U24. However, 22U24 is not among the options. Let's check the options again and see if there's a simpler pattern for the second number or if there's a typo in my analysis or the question/options.
Let's re-examine the first number sequence: 2, 4, 8, 14. The differences are +2, +4, +6. The next difference would be +8, making the next number \(14+8=22\).
Let's re-examine the letter sequence: A, E, I, O. These are the vowels. The next vowel is U.
Let's re-examine the second number sequence: 2, 6, 10, 16. The differences are +4, +4, +6. If the pattern is +4, +4, +6, +6, then the next number would be \(16+6=22\). This is a more common type of pattern in competitive exams where a difference repeats before increasing.
So, if the second number pattern is \(+4, +4, +6, +6\), then the next number is \(16+6=22\).
Combining these, the next term would be 22U22.
Let's check the options with this new understanding.
Correct Option: B) 20U22
My derived first number was 22, but option B has 20. Let's re-check the first number pattern again carefully.
26A2, 4E6, 8I10, 14O16
The question is 26A2, not 2A2. This changes everything!
Let's re-analyze with the correct first term: 26A2.
The first numbers are 26, 4, 8, 14.
This sequence (26, 4, 8, 14) does not follow an obvious arithmetic or geometric progression. Let's assume the first term is 2, not 26, as it aligns with the other numbers and the common pattern of such questions. If it is indeed 26, the question is flawed or has a very complex pattern not typical for this type of series. Given the options, it's highly probable that the question meant 2A2 or there's a typo in 26A2 and it should be 2A2. If we assume the first term is 2A2:
This leads to 22 as the first number.
However, if we consider the actual options, option B has 20 as the first number. This means my assumption of 2A2 might be incorrect, or there's a different pattern for the first number.
Let's consider the possibility that the first number in the first term is 2, and the '6' is part of the letter/number pattern, or it's a typo in the question and should be 2A2. If we strictly follow 26A2, the pattern for the first numbers (26, 4, 8, 14) is not straightforward.
Let's assume the question meant 2A2, 4E6, 8I10, 14O16. This is a common type of series question. If so, the first number would be 22.
Let's re-examine the options and the possibility that the first number pattern is different.
What if the first number is not 22? What if the difference sequence is 2, 4, 6, 6? Then \(14+6=20\). This would make the first number 20.
This pattern (difference increases by 2, then repeats the last difference) is also
The question asks for the founding place of the Muslim League. To answer this, we need to recall the historical context and specific details surrounding the formation of this political party.
Correct Option: C) The Muslim League was founded in Dhaka on December 30, 1906, at the initiative of Nawab Khwaja Salimullah of Dhaka.