Basic Mathematics — Summer 2024

If v 5iˆ4ˆj7k ˆ ,v iˆ2ˆjk ˆ then evaluate the following expressions,I)v 2v II)2v v

1 2 1 If Find A+2B , 3A-Bwhere A=[2 3 −1] and 1 −2 2132 B=[2 3 −1].122

Find the inverse of the given matrix by using the Gauss-Jordan 3 3 4   methodA 2 3   0 1 1  

Solve z2(5i)z8i0.

If and are the roots of 3x2 4x80, find , .

Explain any three logic gates with their block diagram symbol and the truth table.

Prove that xxy  xusing the truth table.

State De Morgna’s theorem for Boolean algebra. Also, write the complement of the following Boolean functions.

F  xyz xyz (b) F (x y)(xz)(yz)

Check whether Fis a minimization of F , where21 F xyzxyzxy and F xyxz.12

Find (2x3)2dx.

d Find  e3xsin3x  . dx

Find (3cosx4sinxsec2 x)dx.

Find derivative of function f x  x/x – 2.1

1 3 Find determinant |−3 −1 −3|.231

Find the order and degree of the following differential equations. d4y 2 d3ydy dy

     x3   0 (ii) xdy ydx0  dx4  dx3 dx dx

Solve 2xydxx2dy0.

dy Solve ye2x. dx