Mohan's Mother is three times as old as Mohan. After 6 years, his mother will be two times as old as he will be them, find the age of Mohan.

An equation of the type $y = kx$ (k $\neq$ 0) represents a line :

One says, "Give me a hundred rupees, friend! I shall then become twice as rich as you." The other replies, "If you give me ten rupees, I shall be six times as rich as you." What is the amount of their (respective) capital?

The pair of equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0 represents two lines, which are ?

Which of the following pair of linear equations is inconsistent?

(A) x - y = 5; 3x - 3y = 10

(B) 2x + 3y = 4; 4x + 6y = 8

(C) 9x + 6y = 6; 3x + 2y = 3

(D) 2x + 5y = 2; 6x - 15y = 4

Choose the correct answer from the options given below:

Which of the following pairs of linear equations is/are consistent?

A. x + y – 5 = 0, 3x + 2y – 10 = 0

B. 3x – 2y – 6 = 0, 6x – 4y – 12 = 0

C. x – y – 9 = 0, 3x – 3y – 27 = 0

D. x + y – 4 = 0 , 3x + 3y – 12 = 0

Choose the correct option from the given below:

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