a)Unit 1Solve (1+y²)dx = (tan⁻¹y - x)dy
a)Unit 1
Solve (1+y²)dx = (tan⁻¹y - x)dy
b)Unit 1Solve (D²+3D+2)y = sin 3x
b)Unit 1
Solve (D²+3D+2)y = sin 3x
Previous Year Question Paper
BT-202 (GS) – Mathematics-II
December 2024•COMMON•SEMESTER-2
December 2024
Max Marks: 70
Duration: 3 Hours
Instructions:
• Attempt any five questions.
• All questions carry equal marks.
a)Unit 1Solve the simultaneous equations dx/dt - 7x + y = 0 and dy/dt - 2x - 5y = 0
a)Unit 1
Solve the simultaneous equations dx/dt - 7x + y = 0 and dy/dt - 2x - 5y = 0
b)Unit 2Solve by the method of variation of parameter (D²+1)y = x
b)Unit 2
Solve by the method of variation of parameter (D²+1)y = x
a)Unit 2Solve (1+x)²(d²y/dx²) + (1+x)(dy/dx) + y = cos log(1+x)
a)Unit 2
Solve (1+x)²(d²y/dx²) + (1+x)(dy/dx) + y = cos log(1+x)
b)Unit 2Show that Jₙ(-x) = (-1)ⁿ Jₙ(x) when n is positive or negative integer
b)Unit 2
Show that Jₙ(-x) = (-1)ⁿ Jₙ(x) when n is positive or negative integer
a)Unit 3Solve by Charpit's method, px + qy = pq
a)Unit 3
Solve by Charpit's method, px + qy = pq
b)Unit 3Solve the Partial differential equation (D³ - 4D²D' + 4DD'²)Z = cos(2x+y)
b)Unit 3
Solve the Partial differential equation (D³ - 4D²D' + 4DD'²)Z = cos(2x+y)
a)Unit 3Construct a partial differential equation from the relation f(x²+y²+z², z²-2xy) = 0
a)Unit 3
Construct a partial differential equation from the relation f(x²+y²+z², z²-2xy) = 0
b)Unit 4Show that u = e⁻ˣ(x sin y - y cos y) is Harmonic
b)Unit 4
Show that u = e⁻ˣ(x sin y - y cos y) is Harmonic
a)Unit 4Determine P such that f(z) = ½ log(x²+y²) + i tan⁻¹(px/y) be an analytic function
a)Unit 4
Determine P such that f(z) = ½ log(x²+y²) + i tan⁻¹(px/y) be an analytic function
b)Unit 4Evaluate using Cauchy's theorem ∮ z²e⁻ᶻ/(z-1)² dz where C is |z-1| = ½
b)Unit 4
Evaluate using Cauchy's theorem ∮ z²e⁻ᶻ/(z-1)² dz where C is |z-1| = ½
a)Unit 4Find the poles and residues at each pole of eᶻ/(z²+1)
a)Unit 4
Find the poles and residues at each pole of eᶻ/(z²+1)
b)Unit 5Find the directional derivative of φ = x²yz + 4xz² at (1, -2, -1) in direction of 2î - ĵ - 2k̂
b)Unit 5
Find the directional derivative of φ = x²yz + 4xz² at (1, -2, -1) in direction of 2î - ĵ - 2k̂
Unit 5Verify Green's theorem for ∮[(xy+y²)dx + x²dy] where C is the boundary by y=x and y=x²
Unit 5
Verify Green's theorem for ∮[(xy+y²)dx + x²dy] where C is the boundary by y=x and y=x²