** **

**TERM END EXAMINATIONS**

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

**CALCULUS**

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

Note: – Attempt any 5 questions.

All questions carry equal marks.

**Q1.** Show that these evolute of these parabola x^{2} = 4ay is 4(y-2a)^{ 3} = 27 ax^{2}

**Q2**. Find these asymptotes of these curve x^{3}+2x^{2}y – xy^{2}- 2y^{3}+4y^{2} +2xy y–1 =0

**Q3. ** Find the coefficients of x^{n} in the expansion of e^{a+bx }

**Q4.** Find these envelope of x cos^{3 }a + y sin^{3} a = a where A is these parameter.

**Q5. **Obtain a fourier expansion for e^{x} in these interval –x<x<?

**Q6.** Find the radius of curvature of these curve xy^{2 }= a^{3} – x^{3} at these point (a, 0).

**Q7. ** Find the sum of first r coefficients of (1- x)^{-3}

Note: – The above sample/guess paper of B.Sc.Mathematics has been prepared to help students of B.Sc Mathematics preparing for Calculus. Above sample/guess paper is just an example of a question paper which is likely to come. But we recommend students to go through their syllabus and best prepare themselves.

All the Best