**Mathamatice (Subsidiary**/General)

**Mathamatice (Subsidiary**/General)

*Answer any one Assignment of the following about 2500-3000 words:*

**Question - 01**- State and Prove Leibnitzs theorem........Answer

- If y

^{1/m}+y

^{1/m }=2x , Prove that (x

^{2}-1) y

_{n+2 }+(2n +1) xy

_{n+1 }- (n

^{2}- m

^{2})y

_{n}= 0......Answer (YouTube Video)

- Discuss various methods for solving first order and first degree differential equations.....Answer

- Solve, the equation,
dy/dx + ytanx = y

^{3}secx.....Answer- Explain Principle of Virtual work......Answer

- State the convergence of the series ∑ 4.7 ...(3n+1)/1.2 ...n . Find .....Answer

- Find the common area
to the circles x

^{2}+ y^{2}= 4 and x^{2}+ y^{2}= 4x......Answer- State and Prove Keplar's law of planetary motion.....Answer

- Define
differentiation of vector point function and show that if r = acoswt +dr bsinwt
then r x dr/dt =wa x b and drt/dt =-w°r, where a, b and w are contant......Answer

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