Mathematics Tes...

If z is a complex number such that |z| + z = 3 + 4i then z is equal to

If z and w are two complex number satisfying |z – 1| = 2 and |w – 5| = 3, then the maximum value of |z – 4w| is

Equation of plane through the intersection of the planes x + y + z = 1 and 2x + 3y – z + 4 = 0 which is parallel to x-axis is

A plane passes through the point (1, –2, 3) and is parallel to the plane 2x – 2y + z = 0. The distance of the point (–1, 2, 0) from the plane is

A point z moves such that |z – 3 – i| + |z – 1 – 3i| = 3, then locus of z is -

If z₁, z₂ are two non-zero complex numbers such that |19z₁ – 31z₂|² = |19z₁|² + |31z₂|² then

Two lines L₁ : x = 5,  and L₂ : x = α,  are coplanar. Then α can take value(s)

A line ℓ passing through the origin is perpendicular to the lines

ℓ₁ : (3 + t)î + (–1 + 2t)ĵ + (4 + 2t), –∞ < t < ∞
ℓ₂ : (3 + 2s)î + (3 + 2s)ĵ + (2 + s), –∞ < s < ∞

Then, the coordinate(s) of the point(s) on ℓ₂ at a distance of  from the point of intersection of ℓ and ℓ₁ is(are) -

Consider planes P₁ & P₂ given by P₁ : x + y + z = 3 and P₂ : x – 2y + z = 3.

Line of intersection of P₁ & P₂ is given by -

Consider planes P₁ & P₂ given by P₁ : x + y + z = 3 and P₂ : x – 2y + z = 3.

Equation of a plane which is perpendicular to P₁ and parallel to the line of intersection of P₁ & P₂ is given by -