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Category solved model papers

Solve system of equations by Gauss elimination method 3𝑥 + 𝑦 + 2𝑧 = 3, 2𝑥 − 3𝑦 − 𝑧 = −3, 𝑥 + 2𝑦 + 𝑧 = 4

9. B)Solve the system of equations by using the Gauss elimination method3𝑥 + 𝑦 + 2𝑧 = 3,2𝑥 − 3𝑦 − 𝑧 = −3,𝑥 + 2𝑦 + 𝑧 = 4…

Find the rank of the matrix [0 1 −3 −1][1 0 1 1][3 1 0 2][1 1 −2 0]

9. A)Find the rank of the matrix [0 1 −3 −1] [1 0 1 1] [3 1 0 2] [1 1 −2 0] Answer:-

Solve (1 + 𝑥)^2 𝑑^2𝑦/𝑑𝑥^2 + (1 + 𝑥)𝑑𝑦/𝑑𝑥+𝑦 = sin[2 log(1 + 𝑥)]

8. C)Solve (1 + 𝑥)2 𝑑2𝑦/𝑑𝑥2 + (1 + 𝑥)𝑑𝑦/𝑑𝑥+𝑦 = sin[2 log(1 + 𝑥)] Answer:-

Solve 𝑑^2𝑦/𝑑𝑥^2 + 4𝑑𝑦/𝑑𝑥+3𝑦 = 𝑠𝑖𝑛𝑥

8. B) Solve 𝑑2𝑦/𝑑𝑥2 + 4𝑑𝑦/𝑑𝑥+3𝑦 = 𝑠𝑖𝑛𝑥 Answer:-

Solve (𝑑^3𝑦/𝑑𝑥^3 − 5𝑑^2𝑦/𝑑𝑥^2 + 7𝑑𝑦/𝑑𝑥− 3𝑦) = 𝑒2𝑥

8. A)Solve ( 𝑑3𝑦/𝑑𝑥3 − 5𝑑2𝑦/𝑑𝑥2 + 7𝑑𝑦/𝑑𝑥− 3𝑦) = 𝑒2𝑥 Answer:-

Using the method of Variation of parameters, solve 𝑑2𝑦/𝑑𝑥2 − 6𝑑𝑦/𝑑𝑥+9𝑦 =𝑒3𝑥/𝑥2

7. C) Using the method of Variation of parameters, solve 𝑑2𝑦/𝑑𝑥2 − 6𝑑𝑦/𝑑𝑥+9𝑦 =𝑒3𝑥/𝑥2 Answer:-

Solve 𝑑2𝑦/𝑑𝑥2 +𝑑𝑦/𝑑𝑥= 𝑥2 + 2𝑥 + 4

7. B) Solve 𝑑2𝑦/𝑑𝑥2 +𝑑𝑦/𝑑𝑥= 𝑥2 + 2𝑥 + 4 Answer:-

Solve (4𝐷^4 − 8𝐷^3 − 7𝐷^2 + 11𝐷 + 6)𝑦 = 0

7. A) Solve (4𝐷4 − 8𝐷3 − 7𝐷2 + 11𝐷 + 6)𝑦 = 0 Answer:-

Find the general and singular solutions of 𝑥𝑝^2+𝑥𝑝−𝑦𝑝+1−𝑦=0

6. C) Find the general and singular solutions of 𝑥𝑝2 + 𝑥𝑝 − 𝑦𝑝 + 1 − 𝑦 = 0 Answer:-

Prove that the system of parabolas 𝑦^2= 4𝑎(𝑥 + 𝑎) are self-orthogonal

6. B) Prove that the system of parabolas 𝑦2 = 4𝑎(𝑥 + 𝑎) are self-orthogonal Answer:-