CDS || Math || Algebra || Linear_Equation || Quiz_2020

(x + y) : (x – y) = 3 : 5 and xy = positive imply that

If ax + by – 2 = 0 and ax.by = 1, where a ≠ 0, b ≠ 0, then what is (a²x + b²y) equal to?

Consider the following statements:

1) (a – b – c) in one of the factors of 3abc + b³ + c³ – a³

2) (b + c – 1) is one of the factors of 3bc + b³ + c³ – 1.

Which of the above statements is/are correct?

What is the lowest common multiple of ab (x² + 1) + x (a² + b²) and ab (x² – 1) + x (a² – b²)?

A certain number of two digits is three times the sum of its digits. If 45 is added to the number, the digits will be reversed. What is the sum of the squares of the two digits of the number?

Consider the following statements:

1. The equation 1990x – 173y = 11 has no solution in integers for x and y.

2. The equation 3x – 12y = 7 has no solution in integers for x and y.

Which of the above statements is/are correct?

What are the possible solutions of x of the equation , where x and n are positive integers?

Let A and B be finite non-empty sets with the number of elements in B = n. Let m > n. If for some integer k ÂÂ 1, the number of non-empty subsets of A = 2^k + the number of non-empty subsets of B, then which one of the following is correct?

If

then x³ + y³ + z³ - 3xyz is equal to

The number of pairs (x, y) where x, y are integers satisfying the equation 21x + 48y = 5 is: