Find Dot product V ·Vwhere vectors Vand Vare i. V = 3i+2j+3k and V = i+3j+3k12 ii. V = i−2j+k and V = 4i+j+k12
[5 marks]If possible find a matrix multiplication AB, of matrix40 2 −2 A = [−1 5 ] and B = [ ]. −5 1 −4 3 −2
[3 marks]1 2 Find the inverse of the matrix [2 3 4].157
[5 marks](2+i)(1−2i) Find the complex conjugate and modulus of . 3−i
[5 marks]Find the roots of the equation x2 +2x +2 = 0.
[5 marks]Show that the minimization of F = x ·y·z+x ·y·z+x ·y∙z+x ∙y∙z is1 F = x·y+x ·z+y·z.2
[5 marks]What are logic gates? Explain NOT gate, AND gate and NAND gate with their block diagram symbol and the truth table.
[5 marks]Find the Boolean expression of the given logic circuit.
[5 marks]State and prove De-Morgan’s Law.
[5 marks]Find d (exsinx). dx
[5 marks]Find ∫(x3 −3x2 +x+1)dx
[5 marks]d sinx Find ( ). dx x
[5 marks]Find ∫x·ex dx1
[5 marks]Form a differential equation from y = c sinx +c cosx.
[5 marks]dy y Solve = . dx x+2
[5 marks]Find the order and degree of the following differential equations. i. d2y − ( dy )3 = 0 dx2 dx2 d3y d2y dy ii. ( ) + + + y = 0 dx3 dx2 dx
[5 marks]dy y Solve + = x. dx x
[5 marks]