Jawaharlal Nehru Technological University Hyderabad 2010-1st Year B.Tech -\\Computer Science & Engineering\ regular\MATHEMATICs I set 1 - Question Paper

Trace the curve r = a (1 + cos 0)    [7+8]

Find the volume of Spherical cap of height h cut off from a sphere of radius a.

[8+7]

Solve the differential equation (D² + D + 1)y = x³ Solve the differential equation (D² + 1)y = sin x sin2x

Form the differential equation by eliminating arbitrary constants y = a x³ +bx²

Solve the differential equation x³ |f = y³ + y²\jy² x²

Find the orthogonal Trajectories of the family of curves x²+y² = a² [4+6+5] If u = x² 2y,v = x + y + z, w = x 2y + 3z find

Find the maximum and minimum values of f (x) = x³ + 3xy² 3x² 3y² + 4

[8+7]

Find the constants a and b so that the surface ax² byz = (a + 2) x will be orthogonal to the surface 4x²y + z³ = 4 at the point (-1,1,2).

Evaluate (yzdx + xzdy + xydz) over arc of a helix x = a cos t,y = a sin t,z =

e

kt as t varies from 0 to 2n    [8+7]

Find L

t

Solve the following differential equation using the Laplace transforms

df 2f + x = e^2t with x(0) = 2, f = 1 att = 0    [8+7]

(n!)²x²ⁿ

Test the convergence of the series ⁽ (2

V 5 l)

Test the convergence of the series ^vvra2+1

[7+8]

4

-k -k -k -k -k