Define length(Magnitude) of a vector and hence find the length of following vectors, i. 3i+2j+6k ii. i−j+2k
[5 marks]If possible find a matrix multiplication AB, of matrix 1 0 2 2 −1 0 A = [3 1 0] and B = [ 5 1 −1]. 5 −1 2 −2 0 0
[5 marks]1 1 Find the inverse of the given matrix [ 1 3 −3] −2 −4 −4
[5 marks](2+i)(1−2i) Find the real and imaginary term of . 3−i
[5 marks]Find the roots of the equation 5x2 −2x −6 = 0.
[5 marks]Design a Boolean function of1 A B C Dusing logic gates
[5 marks]Define logic gates. Explain different types of gates
[5 marks]Show that the minimization of F = x ·y·z+x ·y·z+x ·y is1 F = x·y+x ·z.2
[5 marks]Find the Boolean expression of the given logic circuit.
[5 marks]Find d (x2 +2x+3). dx
[5 marks]Find ∫(3x3 +2x +1)dx
[5 marks]d Find (xsinx). dx
[5 marks]Find ∫1·logxdx
[5 marks]1 1 Prove that the matrix [1 3 4] is symmetric.246
[5 marks]Find the order and degree of the following differential equations.1 d3y d2y2 i. − ( ) = 0 dx3 dx2 d3y d2y 2 dy ii. + ( ) + ( ) = 0 dx3 dx2 dx
[4 marks]Form a differential equation from y = c x2 +c x +c .
[5 marks]dy y+1 Solve = . dx x
[5 marks]