Applied Mathematics I.pdf

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