Write the constant term of
(i) `3x^(2) + 5x + 8`
(ii) `2x^(2) - 9`
(iii) `4y^(2) - 5y + (3)/(5)`
(iv) `z^(3) - 2z^(2) + z - (8)/(3)`

If x = 1, y = 2 and z = 5, find the value of (i) 3x - 2y + 4z (ii) x^(2) + y^(2) + z^(2) (iii) 2x^(2) - 3y^(2) + z^(3) (iv) xy + yz - zx (v) 2x^(2) y - 5yz + xy^(2) (vi) x^(3) - y^(3) - z^(3)

Write the coefficient of (i) x in 13x (ii) y in - 5y (iii) a in 6ab (iv) z in - 7xz (v) p in - 2 pqr (vi) y^(2) in 8xy^(2)z (vii) x^(3) in x^(3) (viii) x^(2) in -x^(2)

Factors of (2x - 3y) ^(3) + ( 3y - 5z) ^(3) + ( 5z - 2x) ^(3) are:

Write the following in expanded form: (i) (9x+2y+z)^(2)( ii) (3x+2y-z)^(2)( iii) (x-2y-3z)^(2)( iv) (-x+2y+z)^(2)

Verify by substitution that the root of . (i) 3x-5=7 is x=4 . (ii) 3+2x=9 is x=3 . (iii) 5x-8=2x-2 is x=2 . (iv) 8-7y=1 is y=1 . (v) (z)/(7)=8 is z=56 .

Find the S.D. between the lines : (i) (x)/(2) = (y)/(-3) = (z)/(1) and (x -2)/(3) = (y - 1)/(-5) = (z + 4)/(2) (ii) (x -1)/(2) = (y - 2)/(3) = (z - 3)/(2) and (x + 1)/(3) = (y - 1)/(2) = (z - 1)/(5) (iii) (x + 1)/(7) = (y + 1)/(-6) = (z + 1)/(1) and (x -3)/(1) = (y -5)/(-2) = (z - 7)/(1) (iv) (x - 3)/(3) = (y - 8)/(-1) = (z-3)/(1) and (x + 3)/(-3) = (y +7)/(2) = (z -6)/(4) .

Show that the lines : (i) (x -5)/(7) = (y + 2)/(-5) = (z)/(1) " " and (x)/(1) = (y)/(2) = (z)/(3) (ii) (x - 3)/(2) = (y + 1)/(-3) = (z - 2)/(4) and (x + 2)/(2) = (y - 4)/(4) = (z + 5)/(2) are perpendicular to each other .

Subtract: (i) -8xy from 7xy (ii) x^(2) from -3x^(2) (iii) (x - y) from (4y - 5x) (iv) (a^(2) + b^(2) - 2ab) from (a^(2) + b^(2) + 2ab) (v) (x^(2) - y^(2)) from (2x^(2) - 3y^(2) + 6xy) (vi) (x -y + 3z) from (2z - x - 3y)

Simplify: (15x^(5)y^(-2)z^(4))/(5x^(3)y^(-3)z^(2))

Find the angle between the planes : (i) 3 x - 6y - 2z = 7 " " 2x + y - 2z = 5 (ii) 4 x + 8y + z = 8 " " and y + z = 4 (iii) 2 x - y + z =6 " " and x + y + 2z = 7 .