Consider the equation of a sphere x2 + y2 + z2 − 4x − 6y − 8z − 16 = 0.

Which of the following statements is/are correct ?

1. z-axis is tangent to the sphere.

2. The centre of the sphere lies on the plane x + y + z − 9 = 0.

Select the correct answer using the code given below :

A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?

Consider the following statements :

1. The direction ratios of y-axis can be <0, 4, 0>

2. The direction ratios of a line perpendicular to z-axis can be <5, 6, 0>

Which of the statements given above is/are correct?

Consider the following for the next three (03) items that follow

The Plane 6x + ky + 3z - 12 = 0 where k ≠ 0 meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x² + y² + z² - 2x - 3y - 4z = 0.

What is the value of k?