Applied Mathematics I Question Bank PDF

Summary

This document contains a question bank for Applied Mathematics I. It covers various topics like series, arithmetic progressions, geometric progressions, quadratic equations, and solving linear equations.

Full Transcript

Applied Mathematics –I Question Bank 1. Find the 12 term of the series 7 , 11 , 15 , …………… 2. Find the sum of 14 term of the series 9 , 14 , 19 , ………….. 1 1...

Applied Mathematics –I Question Bank 1. Find the 12 term of the series 7 , 11 , 15 , …………… 2. Find the sum of 14 term of the series 9 , 14 , 19 , ………….. 1 1 1 3. If pth terms of an A.P is 𝑞 and qth terms is 𝑝 then prove that sum of pq terms is 2 (𝑝𝑞 + 1). 1 1 1 4. If 𝑎2 , 𝑏 2 , 𝑐 2 are in A.P then prove that 𝑏+𝑐 , 𝑐+𝑎 , 𝑎+𝑏 are in A.P 5. Find 10th term of the series 3 , 6 , 12 , ………….. 6. ̅̅̅̅. Find the value of 0.123 7. Find the sum of the following series. (i) 7 + 77 + 777 + … … … ….. 𝑛 𝑡𝑒𝑟𝑚𝑠. (ii) 0.5 + 0.55 + 0.555 + … … … 𝑛 𝑡𝑒𝑟𝑚𝑠. 1 1 1 8. If 𝑎𝑥 = 𝑏 𝑦 = 𝑐 𝑧 and a , b , c , are in G.P then prove that x , y , z , are in A.P 9. Solve by using quadratic formula 2𝑥 2 + 5𝑥 + 3 = 0. 10. Solving by using Cramer’s rule 2𝑥 + 𝑦 + 𝑧 = 1 𝑥 − 2𝑦 − 3𝑧 = 1 3𝑥 + 2𝑦 + 4𝑧 = 5 Find the degree of polynomial 𝑥 4 + 2𝑥 3 + 𝑥 2 − 4. 𝑦 5 − 𝑦 2 + 𝑦 + 3. 1 3 2 5 11. If 𝐴 = [ 4 2 ], 𝐵=[ 1 3 ] then find A+B. 12. Solve the linear equations of line 𝑥 + 𝑦 = 4 and 𝑥 − 𝑦 = 2. 3 2 13. Find the value of determinants | 1 3 | 14. Find the geometrical mean between 4 and 16. 1 2 3 2 1 2 15. Verify 𝐴𝐵 ≠ 𝐵𝐴 If 𝐴 = [2 4 1] 𝐵 = [1 2 1]. 3 1 4 3 1 2

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