If the mean of a and $\dfrac{1}{a}$ is x, then the mean of a³ and $\dfrac{1}{a^3}$ is :

1. x(4x² - 3)

2. x(x²- 2)

3. x² + 3

4. x²

There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be -3.5. The mean of the given numbers is :

1. 49.5

2. 53

3. 46.5

4. 56.5

There are 10 observations x₁, x₂, x₃, ….., x₁₀ in a data. The first five elements x₁, x₂, ….., x₅ are placed by x₁ + 5, x₂ + 5, ….., x₅ + 5 respectively. Also, the next five elements x₆, x₇, ….., x₁₀ are placed by x₆ - 5, x₇ - 5, …, x₁₀ - 5 respectively. Calculate the overall change in the mean of the data.

In an office, mean of salaries of employees is ₹1,00,000 and median is ₹80,000. An employee will be considered, Grade A officer if his income is at least ₹85,000. Based on the above information check the validity of the following statements.

(i) Number of Grade A officers is more than or equal to number of non Grade A officers.

(ii) Mean of salaries of Grade A officers is more than ₹1,00,000.