A father said to his child, "I was as old as you are at the time of your birth". If the father's age is 48 years now, the child's age six years back was:

Which one of the following pair of linear equations is/are inconsistent?

A. x – y = 8, 6x – 6y = 32

B. x + y = 5, 4x + 4y = 20

C. 4x– 6y = 16, 8x – 12y = 18

D. 4x – 4y – 4 = 0, 8x – 8y – 10 = 0

Choose the correct answer from the options given below:

If $2^{(x+y)} = 64$ and $128^{(x-y)} = 2$, then what is the value of x?

The sum of digits of a two-digit number is 14 and the difference between the two digits of the number is 2. The product of the two digits of the number is:

Which of the following pair of linear equations has / have many infinite solutions?

A. $9x + 3y + 12 = 0$; and $18x + 6y + 24 = 0$

B. $2x - 3y = 13$; and $7x - 2y = 20$

C. $x + y = 5$; and $2x + 2y = 10$

D. $3x + y - 3 = 0$; and $2x + \dfrac{2}{3}y = 2$

Choose the correct answer from the options given below:

Linear equations $3x + 5y = 19$ and $10x - 3y = 24$ have solution $x = \frac{\alpha}{3}$ and $y = \frac{\beta}{2}$, then the value of $\alpha + \beta$ is:

The product of two positive numbers is 189 and their quotient is $\frac{3}{7}$. Find the sum of these numbers.