Define length (Magnitude) of a vector and hence find the length of following vectors, i. 2 i + 3j + 6k ii. i −2 j + 2k
[5 marks]Enlist types of matrixes with their example.
[5 marks]Solve the linear equations using matrix method: 2X + 3Y=1, Y- 4X=2
[5 marks]Find the roots of the equation x2 − x − 1 = 0.
[5 marks]If z=3+5i then find inverse of z.
[5 marks]What are logic gates? Explain OR, AND and NOR gate with their block diagram symbol and truth table.
[5 marks]Show that minimization of F1=A’BC+AB’C+ABC’+ABC F2=AB+BC+AC
[5 marks]Design logic circuit for Boolean expression A’+BC
[5 marks]Express the Boolean function F=x+yz as a product of maxterms
[5 marks]Y= Log (Sinx /1+Cosx) then find dy /dx.
[5 marks]∫ log x dx
[5 marks]X+Y=Sin(X+Y) then find dy /dx.
[5 marks]∫ (4x2 + 3x + 3)dx
[5 marks]Solve: 2dy/dx = y(x+2)/x
[5 marks]Form a differential equation from y= ax2 +bx
[5 marks]Y=Sin(lnx)/x then find dy /dx
[5 marks]Give two examples of differential equation of order 2 and degree 1
[5 marks]