The question asks about the tenure of non-permanent members of the UN Security Council. To answer this, one needs to recall the specific rules governing the election and term limits for these members as stipulated by the UN Charter and established practices.
C) 2 years — The non-permanent members of the UN Security Council are indeed elected by the General Assembly for a term of two years. This is a fundamental aspect of the UN Security Council's structure and function.
The question asks about the institution responsible for annually releasing the 'Ease of Doing Business Index' as of 2021. This requires knowledge of international reports and the organizations that publish them.
Correct Option: D) The 'Ease of Doing Business Index' was released annually by the World Bank Group. The World Bank Group published this report from 2003 until its discontinuation in September 2021. Therefore, as of 2021, it was still the publishing body.
This question tests the understanding of the relationship between measures of central tendency (mean, median, and mode) for different types of distributions, specifically a symmetric distribution.
A) Mean = Median = Mode
For a perfectly symmetric distribution, the data is evenly distributed around the center. This implies that the arithmetic mean (average), the median (the middle value when data is ordered), and the mode (the most frequently occurring value) all fall at the same central point. A classic example is the normal distribution.
The given series consists of numbers that follow a specific pattern involving multiplication and sequential integers. We need to identify this pattern to find the missing number.
Correct Option: C) 336
The question asks for the city where the first session of the Indian National Congress (INC) was held in 1885. This is a factual question related to the history of the Indian National Congress.
Correct Option: C) The first session of the Indian National Congress was held in Bombay (now Mumbai) in 1885.
This is a blood relations problem. We need to deduce the relationships between the individuals based on the given statements and then find the relationship between E and A. We will build a family tree or list relationships step-by-step.
Let's summarize the family structure:
Therefore, E is A's husband.
B) Husband — Based on the deductions, E is married to A, making E A's husband.
The question asks for the common name of mercury. This requires knowledge of common chemical names and their corresponding elements or compounds.
Correct Option: B) Quicksilver is the common name for mercury. The name "quicksilver" refers to its appearance as a silvery liquid that moves quickly, resembling liquid silver.
To find the time when A, B, and C will meet again at the starting point, we need to find the least common multiple (LCM) of the time taken by each person to complete one revolution. The LCM will represent the smallest time interval after which all three will have completed a whole number of revolutions and thus be back at the starting point simultaneously.
Correct Option: C) 252 s
The question asks for the headquarters of the National Stock Exchange of India (NSE). This is a factual question about a major financial institution in India. Knowledge of the financial geography of India is key to answering this.
Correct Option: D) Mumbai is the financial capital of India and hosts the headquarters of major financial institutions, including both the National Stock Exchange (NSE) and the Bombay Stock Exchange (BSE).
If x³ + \( \frac{1}{x^3} \) = 18, then what will be the value of x + \( \frac{1}{x} \)?
The problem provides an equation involving \(x^3 + \frac{1}{x^3}\) and asks for the value of \(x + \frac{1}{x}\). We can use the algebraic identity for the cube of a sum, \((a+b)^3 = a^3 + b^3 + 3ab(a+b)\), by substituting \(a=x\) and \(b=\frac{1}{x}\).
Let \(y = x + \frac{1}{x}\). Our goal is to find the value of \(y\).
Cube both sides of the equation \(y = x + \frac{1}{x}\):
\[ y^3 = \left(x + \frac{1}{x}\right)^3 \]Apply the algebraic identity \((a+b)^3 = a^3 + b^3 + 3ab(a+b)\) where \(a=x\) and \(b=\frac{1}{x}\):
\[ y^3 = x^3 + \left(\frac{1}{x}\right)^3 + 3 \cdot x \cdot \frac{1}{x} \cdot \left(x + \frac{1}{x}\right) \]Simplify the expression:
\[ y^3 = x^3 + \frac{1}{x^3} + 3 \cdot 1 \cdot \left(x + \frac{1}{x}\right) \]\[ y^3 = x^3 + \frac{1}{x^3} + 3\left(x + \frac{1}{x}\right) \]Substitute the given value \(x^3 + \frac{1}{x^3} = 18\) and \(y = x + \frac{1}{x}\) into the equation:
\[ y^3 = 18 + 3y \]Rearrange the equation to form a cubic equation:
\[ y^3 - 3y - 18 = 0 \]We need to find the integer roots of this cubic equation. We can test small integer values for \(y\).
Since \(y=3\) satisfies the equation, it is a root.
Thus, the value of \(x + \frac{1}{x}\) is 3.
C) 3 is the correct answer because substituting \(y=3\) into the derived cubic equation \(y^3 - 3y - 18 = 0\) yields \(27 - 9 - 18 = 0\), which is true.