The centroid of the triangle with vertices A(2, - 3, 3), B(5, - 3, - 4) and C(2, - 3, - 2) is the point :

• ( - 3, 3,  - 1)

• $\left(3, - 3, - 1\right)$

• (3, 1, - 3)

• $\left( - 3, - 1, - 3\right)$

What is the radius of the sphere x² + y² + z² - 6x + 8y - 1Oz + 1 = 0 ? 

• 5

• 2

• 7

• 3

The equation of the plane passing through the intersection of the planes 2x + y + 2z = 9, 4x - 5y - 4z = 1 and the point (3, 2, 1) is :

• 10x - 2y + 2z = 28

• 10x + 2y + 2z = 28

• 10x + 2y - 2z = 28

• 10x - 2y - 2z = 24

The distance between the parallel planes 4x - 2y + 4z + 9 = 0 and 8x - 4y + 8z + 21 = 0

• $\frac{1}{4}$

• $\frac{1}{2}$

• $\frac{3}{2}$

• $\frac{7}{4}$

A given quantity of metal is to be cast into a half cylinder (i.e., with a rectangular base and semi circular ends). If the total surface area is to be minimum, then the ratio of the height of the half cylinder to the diameter of the semicircular ends is

• $\mathrm{\pi } : \left(\mathrm{\pi } + 2\right)$

• $\left(\mathrm{\pi } + 2\right) : \mathrm{\pi }$

• 1 : 1

• None of the above

A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the triangle ABC ?

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 + {\mathrm{z}}^2 = {\mathrm{r}}^2$

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 + {\mathrm{z}}^2 = 4{\mathrm{r}}^2$

• $9\left({\mathrm{x}}^2 + {\mathrm{y}}^2 + {\mathrm{z}}^2\right) = 4{\mathrm{r}}^2$

• $3\left({\mathrm{x}}^2 + {\mathrm{y}}^2 + {\mathrm{z}}^2 \right) = 2{\mathrm{r}}^2$

If the three consecutive vertices of a parallelogram are (- 2, - 1), (1, 0) and (4, 3), then what are the coordinates of the fourth vertex ?

• (1, 2)

• (1, 0)

• (0, 0)

• (1, - 1)

The area bounded by the curve $\left|\mathrm{x}\right| + \left|\mathrm{y}\right| = 1$ is :

• 1 square unit

• $2\sqrt{2}$ square units

• 2 square units

• $2\sqrt{3}$ square units

Which one of the following is correct in respect of the graph of $\mathrm{y} = \frac{1}{\mathrm{x} - 1} ?$

• The domain is {x ∈ R | X ≠ 1} and the range is the set of reals

• The domain is {x ∈ R | X ≠ 1}, the range is {y ∈ R | y ≠ 0} and the graph intersects y-axis at (0, - 1).

• The domain is the set of reals and the range is the singleton set {0}

• The domain is {x ∈ R | X ≠ 1} and the range is the set of points on the y-axis