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]3 −1 1 Find the inverse of the given matrix [0 0 1] by using the 5 −2 Gauss-Jordan method
[2 marks](2i)(13i) Find the complex conjugate and modulus of . 32i
[5 marks]Find the roots of the equation 5x2 −2x −6 = 0.
[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]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]Express the Boolean function F x yzas a sum of minterms.
[5 marks]Find d (ex(x2 +3x +8)). dx
[5 marks]Find ∫(3x2 +2x +3)dx OR1
[5 marks]d sinx Find ( ). dx x
[5 marks]Find ∫x·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 i. d3y − ( dy )2 = 0 dx3 dx d3y d2y 3 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]