1.

The solution of the differential equation condition y = 1 when t = 0, is Select one: O a. y = Inkt O b. y2 = 2t +k O c. y = sin kt O d. y= e (kt) O e. None of theseThe ratio of interior angles of a triangle is 1:3:5. The shortest side is 10m. Find the perimeter of the triangle Select one: O a. 63.1m O b. 62.1m O c. 64.1m O d. None of these Oe. 61.1mWhat is the area bounded by the parabola x^2 = 4ay, its latus rectum and the y-axis? Select one: O a. 2/3 a^2 O b. 4/3 a^2 O c. 3/4 a^2 O d. 3/2 a^2 O e. None of theseFind the area bounded by the curve (y curve) 3x + 3 = 0 and then x = 4. Select one: O a. 12 O b. 8 O c. 16 O d. None of these O e. 9The centroid of the triangle having vertices at A(3, 12), B(7, y) and C(-1, 0) is at (3, 4). The orthocenter of the triangle is at (x, 2). Find the value of x if the line x + 4y - 10 = 0 passes through the orthocenter. Select one: O a. 3 O b. None of these O c. 1 O d. 2 Oe. 4Find the centroid of the volume generated by revolving about the y-axis the area bounded by the curve y^2 = 4ax in the first quadrant and the line x = a. Select one: O a. None of these O b. 4/5 a O c. 3/5 a O d. 5/6 a Oe. 3/4 aDetermine the coordinates of the point which is 3/5 of the way from the point (2, -5) to the point (-3, 5). Select one: O a. (1, -2) O b. (4, -1) O c. None of these O d. (-1,1) O e. (-2,3)Solve the differential equation dy - xdx = 0 if the curve passes through (1, 0). Select one: O a. None of these O b. 2x^2 + 2y - 2 = 0 O c. 2y + x42 - 1 = 0 O d. x^2 - 2y - 1 = 0 O e. 3x^2 + 2y - 3 = 0Solve for the general solution of the differential equation (D + 3)(D2 + 3D + 2)y = 0, where D is the differential operator d/dx, where x = 1. Determine y in terms of the constant of integration. Select one: O a. 0.368C1 + 0.135C2 + 20.086C3 O b. 0.368C1 + 0.135C2 + 0.0503 O c. 2.718C1 + 7.389C2 + 20.086C3 O d. 0.368C1 + 7.389C2 + 20.086C3 O e. None of theseSolve the differential equation dex/dt2 + 4x = 0. With initial condition x(0) = 10, x(0) = 0 Select one: O a. x(t) = 10 sin 2t O b. x(t) = 10 cos 2t O c. x(t) = 10 cos 2t + 10 sin 2t O d. None of these O e. x(t) = 10 cost +10 sintThe property described in cleat f(t)} = F(s-a) is Select one: O a. First Shifting Property O b. second Shifting Property O c. Change of Scale Property O d. Linearity Property O e. None of theseThis is the method used to represent a periodic function by a series of sinusoids to any desired to any desired degree of accuracy. Select one: O a. Maclaurin's series O b. Taylor's series O c. None of these O d. Laplace transforms O e. Fourier seriesDetermine the equation of the line normal to the graph x +3xy +y =5 at the point (1,1) Select one: O a. x-y = 1 O b. None of these Oc. x+y=0 O d. x-y=0 Oe. x+y = 1