The distance between the point (1, - 5, - 10) and the point of intersection of the plane x - y + z = 5 and the line $\frac{\mathrm{x} - 2}{3} = \frac{\mathrm{y} + 1}{4} = \frac{\mathrm{z} - 2}{12}$, will be

• 10

• 11

• 12

• 13

A point is in motion along the curve 12y = x³. The x-coordinate, changes faster than y-coordinate, if

• $\mathrm{x} \in \left[- 2, 2\right]$

• $\mathrm{x} \in \left[- \infty , - 2\right] \cup \left[2, \infty \right]$

• $\mathrm{x} \in \left[- 2, \infty \right]$

• $\mathrm{x} \in \left[- \infty , 2\right] \cup \left[2, \infty \right]$

The ratio in which yz-plane divides the line joining (2, 4, 5) and (3, 5, 7) is

• - 2 : 3

• 2 : 3

• 3 : 2

• - 3 : 2

The y - coordinate of a point P on the line joining A(7, 2,1) and B(10, 5, 7) is 4. Then, x and z - coordinates of the point are

• x = 9, z = 5

• x = 3, z = 7

• x = 2, z = 3

• None of these

If point D divides the base BC of a $∆$ABC in the ratio n : m, then the value of mBD² + nCD² + (m + n)AD² is

• mAC² + nAB²

• (m + n)(AC² + AB²)

• nAC² + mAB²

• None of these

The graph of the equation y² + z² = 0 in three dimensional space is

• YZ-plane

• Z-axis

• Y-axis

• X-axis

The centroid of the triangle formed by the lines x + y = 1, 2x + 3y = 6 and 4x - y = - 4 lies in the quadrant

• I

• II

• III

• IV

All the points on the X-axis have

• x = 0

• y = 0

• x = 0, y = 0

• y = 0, z = 0

For all values of a and b the line (a + 2b)x + (a - by + (a + 5b) = 0 passes through the point.

• (- 1, 2)

• (2, - 1)

• (- 2, 1)

• (1, - 2)

50.

The incentre of triangle formed by the lines x + y = 1, x =1, y = 1 is

• $\left(1 - \frac{1}{\sqrt{2}}, 1 - \frac{1}{\sqrt{2}}\right)$

• $\left(1 - \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

• $\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

• $\left(\frac{1}{\sqrt{2}}, 1 - \frac{1}{\sqrt{2}}\right)$