Find the number of triplets (x, y, z) of integers satisfying the equations `x + y = 1 - z` and `x^(3) + y^(3) =1-z^(2)` (where `z ne 1`)

The number of ordered triplets (x,y,z) satisfy the equation (sin^(- 1)x)^2=(pi^2)/4+(sec^(- 1)y)^2+(tan^(- 1)z)^2

The number of integers solutions for the equation x+y+z+t=20 , where x,y,z t are all ge-1 , is

If x , y , z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x , y , z) that satisfy the equation is 0 (b) 1 (c) 2 (d) Infinite solutions

Find the equation of line of intersection of the planes 3x-y+ z=1 and x + 4 y -2 z =2.

Find the values of x ,\ \ y\ ,\ z if the matrix A=[0 2y z x y-z x-y z] satisfy the equation A^T\ A=I_3 .

Find the values of x,y,z if the matrix A=[[0,2y,z],[x,y,-z],[x,-y,z]] satisfy the equation A^T A=I_3

Find the angle between the planes 3x+y+2z=1 and 2x-y+z+3 = 0 .

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

Examine the consistency of the system of equations x + y + z = 1 2x + 3y + 2z = 2 a x + a y + 2a z = 4

Let x, y, z be positive real numbers such that x + y + z = 12 and x^3y^4z^5 = (0.1)(600)^3 . Then x^3+y^3+z^3 is