Define the following 1. Power set 2. Cartesian Product 3. Unit Matrix 4. Transpose of a matrix 5. Domain 6. De- Morgan’s laws 7. Infinite Set
[7 marks]1) Explain domain, Co-domain, and range with example. (3 MARKS)22 2) If A= [ ] , B= [8 3] Find AB 3 0 −511 if it is exist. (4 MARKS)
[7 marks]Let U={1,2,3,4,5,6,7,8,9,10,11,12,13} A = {1, 3, 5, 7} B = {5, 7, 9, 11} and C = {1, 3, 5, 7, 9, 11, 13} prove that: 1. (A∩ B) U (A ∩ C) = A ∩ (BU C) 2. (A U B)’ = A’ ∩ B’
[7 marks]1 0 0 1 1 1 If A = [0 1 1], B = [0 0 1], Find : (a) A∨B, (b) A∧B , (c) A ⊙ B.
[7 marks]Let U = {1,2,3,4,5,6,7,8,9,10}X = {1,2,4,5,6}Y = {2,4,5,7,8}Z = {2,7,9,10} Compute using Venn diagram. XZY, Y’X’, X-(Y Z).
[7 marks]Simplify Exponential function: a) 2x – 2x+1
[7 marks](4)3× (4)x+5 = (4)2x+12
[ marks]a +4 3b 2a +2 b+2 If [ ] = [ ] then find the value of (a-2b). 8 −6 8 a −8b
[7 marks]Define Rank of matrix .Find rank of following matrix. A = [4 5 7 ]2610
[7 marks]Aline passing through the point(1,2) with a slope of 4. Write equation.
[7 marks]Find the inverse of function. (i) f(x)=x+1/x (ii) f(x)=5x-7
[7 marks]Find x and y if 2x-3y=15 and x+5y = -18 using Cramer’s rule.
[7 marks]By using the section formula, find out the coordinates of the points Cthat divide the line segment joining the points A(8, -3) and B(16, 5) in the internal ratio 3:1.
[7 marks]Find the distance between the points A(-1, 2) and B(2, 3).
[7 marks]Simplify log (1/5) using logarithmic property.
[7 marks]Show that the points P( –1, 6, 6), Q(0, 7, 10) and R( –4, 9, 6) form an isosceles right triangle.
[7 marks]Find the area of the triangle in coordinate geometry by determinant method, whose vertices are: A(1,−2), B(−3,4), C(2,3)
[7 marks]If P (-2, 1), Q (2, 3) and R (-2, -4) are three points, find the angle between the straight lines PQ and QR.
[7 marks]