# B.Sc Mathematics Sample Paper for 1st year Number theory and Trigonometry

**BACHELOR OF SCIENCE**** (MATHEMATICS), YEAR-1**

**NUMBER THEORY AND TRIGONOMETRY**

**Time: 3 hours M.Marks:60**

Note: – Attempt any 5 questions.

All questions carry equal marks.

**Q1. **Show that a subgroup of a cyclic group is cyclic.

**Q2.** Show that (1,-1,1), (5,-5,4) (5,0,8) and (1,4,5) are these vertices of a rhombus.

**Q3. **State and prove Lagrange’s theorem on these order of a subgroup of a group.

**Q4.** If A and B are normal subgroups of a group G, Prove that AOB is also a, normal subgroup of G.

**Q5. **Find these image of (1,3,4) in these plane 2x-y+ z + 3=0

**Q6.** Show that a finite integral domain is a field.

**Q7. **If f (x) and v (x) in F [x] such that f (x) = u (x) q (x) + v (x) = 0 or else deg v (x) < deg g (x)

Note: Above B.Sc Mathematics Sample Paper for 1st year Number theory and Trigonometry has been prepared after reviewing few universities sample papers. We are not sure whether same or similar question papers pattern does your university has or not. We are just trying to help you by providing the possibilities. It is advisable to go thoroughly textbooks, teacher’s notes according to your syllabus for better preparation for your coming examination.

All the Best for your examination!!!

## Comments