Verify the property: `x × y = y × x` by taking: (i) `x=-1/3, y=2/7` (ii) `x=(-3)/5, y=(-11)/(13)`

Find three different solutions of the each of the following equations. (i) 3x + 4y = 7 (ii) y = 6x (iii) 2x - y = 7 (iv) 13x - 12y = 25 (v) 10x + 11y = 21 (vi) x + y = 0

Verify (i) x ^(3) + y ^(3) = (x + y) (x ^(2) -xy + y ^(2)) (ii) x ^(3) -y ^(3) = (x-y) (x ^(2) +xy +y ^(2)) using some non-zone positive integers and check by actual multiplication. Can you call these as identities ?

Express each of the following equations in the form of ax + by + c = 0 and write the values of a, b and c. (i) 3x + 4y = 5 (ii) x - 5 = sqrt3y (iii) 3x = y (iv) x/2+y/2=1/6 (v) 3x - 7 = 0

If (5x - 3y) : (2x + 4y) = 11 : 12 , then find x : y .

If (7x+5y) :(3x + 9y) = 5 : 7 , then x : y =

Which of the following pair of graphs intersect ? (i) y = x^(2) - x and y = 1 (ii) y = x^(2) - 2x + 3 and y = sin x (iii) y = x^(2) - x + 1 and y = x - 4

Write each of the following in the form of ax + by + c = 0 and find the values of a, b and c (i) 2x = 5 (ii) y - 2 = 0 (iii) y/7=3 (iv) x= (-14)/13

If (x , y) is a variable point on the line y=2x lying between the lines 2(x+1)+y=0 and x+3(y-1)=0 , then x in (-1/2,6/7) (b) x in (-1/2,3/7) y in (-1,3/7) (d) y in (-1,6/7)

Verify that x ^(3) + y ^(3) + z ^(3) - 3xyz =1/2 (x + y + z) [(x-y)^(2) + (y-z) ^(2) + (z-x) ^(2) ]

Perpendiculars are drawn from points on the line (x+2)/2=(y+1)/(-1)=z/3 to the plane x + y + z=3 The feet of perpendiculars lie on the line (a) x/5=(y-1)/8=(z-2)/(-13) (b) x/2=(y-1)/3=(z-2)/(-5) (c) x/4=(y-1)/3=(z-2)/(-7) (d) x/2=(y-1)/(-7)=(z-2)/5