49. the congruence x =1(mod p) has exactly s0lutions. (b) p-1 55 (a) p (d) nonc of these 50. the equation of the forn ar dy c, where a 0,b # 0 and c integers, i

49. The congruence x =1(mod p) has exactly S0lutions. (B) p-1 55 (A) P (D) Nonc of these 50. The equation of the forn ar Dy C, where a 0,b # 0 and c integers, is called a In two unknowns X and y. (A) Linear diophantine cquation (B) Quadratic equation (C) Non-linear diophantinc cquation D) None of these 51. The linear diophantine equation ax by = c; a, b, c being integers, has integer solutions if and only if de, where: (A) d g.c.d. of a and (C)d-8.c.d. of a and b and d-(a, b) (D) None of these (B) d-(a, b 52. The necessary and suflicicnt condition that a a b(mod m) is: (A) (B) a (C)b (D) None of these 53. Ifa=b (mod m) and 0 s 6sthen m is called the: (A) residue of a (mod m) (B) minimal residue of a (mod mi) (C) maximum residuc of a (mod nm) (D) None of these 54. The linear congruence ax = b (mod m) is solvable if and only if: (A) dlb (B) d=(a, m) (C) dib, where d= (a,m) (D) None of these