21. let r be a commutative ring with unity and let a be an ideal of r. then which one is tre ? (a) r/a is an integral domain ain prime ideal 8) ais prime ideal

21. Let R be a commutative ring with unity and let A be an ideal of R. Then which one is tre ? (A) R/A is an integral domain Ain prime ideal 8) Ais prime ideal R/A is an integral domain. (C) Both (AJant (B) (D) None of these 22. Let T:RRbe a lincar transformation given by: T(1,0,0)(1,0, 1)T0, 1,0)-(1,-1,0); T(0, 0, 1)-(0, 1,0) Then (a, b, c) for all (a, b, c) e R is: (A) (a-b, b-c,a) (B) (a+b-b+ c.a) (C)(a+b,b-ca) (D) None of these 23. Let T R R T()-(x+y.x-y,y)v(xy)eR?. Then dimension of range of T is: be linear transformation given by (A) 1 (B) 2 (C) 3 (D) None of these 24. Let U and V be vector spaces over the field F and let T be a linear transformation from U into V. Suppose that U is finite dimensional, then: (A) rank (T)+nullity (T)- dim (V) (B) rank (T)+ nullity (T)- dim (U) (C) rank (T)-nullity (1)-dim (U) (D) rank C)-nullity (T)-dim (V) 25 Let T: U V be a linear transformation. Then choose the correct statement (A) Tis one-one Ker (T)-(0) (B) Ker (T)- (0)T is one-one (C) Tis one-one s Ker (T)-{0) (D) None of these