| Detail | Information |
|---|---|
| Examination | RAJ. STATE AND SUB. SERVICES COMB. COMP. EXAM |
| Year | 2018 |
| Conducting Body | RPSC |
| Paper | Paper-1 |
| Question Type | Mixed |
This is the question paper for the Raj. State and Sub. Services Comb. Comp. (MAINS) Exam 2018, Paper-1, conducted by RPSC. This paper is crucial for candidates aiming to secure a position in the Rajasthan state services. Aspirants can use this previous year's paper to understand the exam structure, question difficulty, and the types of questions asked in the Mains examination. Familiarizing oneself with Paper-1 content is essential for effective preparation and to gauge performance against the competitive standards set by RPSC. This previous year RAJ. STATE AND SUB. SERVICES COMB. COMP. EXAM 2018 question paper (2018) is useful for Other Jobs aspirants preparing for Rajasthan government recruitment. The paper was conducted by RPSC and reflects the official exam pattern, marking scheme and difficulty level seen in recent cycles. Use it for timed practice, topic-wise revision and understanding how questions are framed in the real examination. Download the free PDF on QuizCurrent to read instructions, attempt MCQs and compare your answers with the study notes provided on this page. Key syllabus areas include RAJ. STATE AND SUB. SERVICES COMB. COMP. EXAM, Paper-1, RPSC, 2018 question paper, previous year paper, PDF download. Useful for RAJ. STATE AND SUB. SERVICES COMB. COMP. preparation. Helps understand the latest exam pattern. Useful for practice and self-assessment.
(c) Let G be a group and let H be a subgroup of G. Prove that if G is cyclic, then G/H is also cyclic.
(d) Let R be a commutative ring with unity. Show that an ideal I of R is a prime ideal if and only if for any a, b ∈ R, ab ∈ I implies a ∈ I or b ∈ I.
(e) Let F be a field. Show that the set of all polynomials in one variable over F, denoted by F[x], forms a Euclidean domain.
(a) Let V be a finite-dimensional vector space over a field F and let T: V → V be a linear transformation. Prove that dim(ker(T)) + dim( extIm(T)) = dim(V).
(b) Let G be a group. Show that the set of all inner automorphisms of G, denoted by ext{Inn}(G), is a normal subgroup of the group of all automorphisms of G, denoted by ext{Aut}(G).
(c) Let R be a commutative ring with unity. Show that if R is an integral domain, then the polynomial ring R[x] is also an integral domain.
(e) Let F be a field and let p(x) ∈ F[x] be a non-constant polynomial. Show that there exists an extension field K of F such that p(x) has a root in K.
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This is the question paper for the Raj. State and Sub. Services Comb. Comp. (MAINS) Exam 2018, Paper-1.
This question paper was released by RPSC (Rajasthan Public Service Commission).
The examination year for this paper is 2018.
The paper code mentioned is P-1.
This paper is for the MAINS stage of the examination.
Yes, this page provides access to the RPSC Rajasthan State Services Mains 2018 Paper-1 question paper.
