1. Temperature in `.^(@)C` at which `H_(2)O` have density `1gm//mL=x`
2. Value of `mu` for `I(CN)_(2)^(-)=y`
3. Energy related to london forces `prop1/(r^(z))`
Calculate `(z-y)/x=?`

Find the centre and radius of sphere 2(x-5)(x+1)+2(y+5)(y-1)+2(z-2)(z+2)=7 .

Find the value of lambda for which the plane x+y+z=sqrt(3)lambda touches the sphere x^2+y^2+z^2-2x-2y-2z=6.

The value of a for which system of equation , a^3x+(a+1)^3y+(a+2)^3z=0, ax+(a+1)y+(a+2)z=0, x+y+z=0, has a non-zero solution is:

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

A point A is on the line vec r = (1- 3mu ) hat i + (mu - 1) hat j + (2 + 5 mu ) hat k. B(3,2,6) is a point of the plane . If the vector bar(AB) is parallel to the plane x-4y+3z = 1 then the value of mu is ............

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

Find the vaoue of each of the folllowing polynomials for the indicated value of variables: (i) p(x) = 4x ^(2) - 3x + 7 at x =1 (ii) q (y) = 2y ^(3) - 4y + sqrt11 at y =1 (iii) r (t) = 4t ^(4) + 3t ^(3) -t ^(2) + 6 at t =p, t in R (iv) s (z) = z ^(3) -1 at z =1 (v) p (x) = 3x ^(2) + 5x -7 at x =1 (vii) q (z) = 5z ^(3) - 4z + sqrt2 at z =2

Statement 1: The lines (x-1)/1=y/(-1)=(z+1)/1 and (x-2)/2=(y+1)/2=z/3 are coplanar and the equation of the plnae containing them is 5x+2y-3z-8=0 Statement 2: The line (x-2)/1=(y+1)/2=z/3 is perpendicular to the plane 3x+6y+9z-8=0 and parallel to the plane x+y-z=0