Prove that: `((0. 6)^0-\ (0. 1)^(-1))/((3/8)^(-1)\ (3/2)^3+\ (-1/3)^(-1))=\ -3/2`

Evaluate: (0. 2)^3-\ (0. 3)^3+\ (0. 1)^3

Prove that: (1/4)^(-2)-3\ xx\ 8^(2/3)\xx\ 4^0+\ (9/(16))^(-1/2)=(16)/3

Prove that Lim_(x to 0) (root3((1+x))-root3((1-x)))/x = 2/3

without actually calculating , the cubes , find the valuse of (i) ((1)/(2))^(3)+((1)/(3))^(3)-((5)/(6))^(3) (ii) (0.2)^(3)-(0.3)^(3)+(0.1)^(3)

If A=[(3,-3,4),(2,-3,4),(0,-1,1)] , then A^(-1)=

Let A={0,\ 1,\ 2,\ 3} and R be a relation on A defined as R={(0,\ 0),\ (0,\ 1),\ (0,\ 3),\ (1,\ 0),\ (1,\ 1),\ (2,\ 2),\ (3,\ 0),\ (3,\ 3)} , is R reflexive? symmetric? transitive?

STATEMENT-1 : The centroid of a tetrahedron with vertices (0, 0,0), (4, 0, 0), (0, -8, 0), (0, 0, 12)is (1, -2, 3). and STATEMENT-2 : The centroid of a triangle with vertices (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_(3), z_(3)) is ((x_(1)+x_(2)+x_(3))/3, (y_(1)+y_(2)+y_(3))/3, (z_(1)+z_(2)+z_(3))/3)

Let (x_0, y_0) be the solution of the following equations: (2x)^(1n2)=(3y)^(1n3) 3^(1nx)=2^(1ny) The x_0 is 1/6 (b) 1/3 (c) 1/2 (d) 6

Prove that : Find the sum of the infinite series 1+(2)/(3).(1)/(2)+(2.5)/(3.6)((1)/(2))^(2)+(2.5.8)/(3.6.9)((1)/(2))^(3)+......oo

Find the matrix A such that : [(1 ,0 ),(0 ,1)]A=[(3 ,3 ,5 ),(1, 0 ,1)] (ii) A[(1, 2, 3 ),(4, 5 ,6)]=[(-7,-8,-9 ),(2, 4 ,6)]