Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions

The coordinates of the mid-points of sides AB, BC and CA of  △ABC are D(1, 2, −3), E(3, 0,1) and F(−1, 1, −4) respectively. Write the coordinates of its centroid.

Write the coordinates of the foot of the perpendicular from the point (1, 2, 3) on y-axis.

Write the length of the perpendicular drawn from the point P(3, 5, 12) on x-axis.

What is the locus of a point for which y = 0, z = 0?

Find the ratio in which the line segment joining the points (2, 4,5) and (3, −5, 4) is divided by the yz-plane.

Find the point on y-axis which is at a distance of  \[\sqrt{10}\] units from the point (1, 2, 3).

Find the point on x-axis which is equidistant from the points A (3, 2, 2) and B (5, 5, 4).

The ratio in which the line joining (2, 4, 5) and (3, 5, –9) is divided by the yz-plane is

The ratio in which the line joining the points (a, b, c) and (–a, –c, –b) is divided by the xy-plane is

If the coefficient of x in \[\left( x^2 + \frac{\lambda}{x} \right)^5\]  is 270, then \[\lambda =\]

Let (3, 4, –1) and (–1, 2, 3) be the end points of a diameter of a sphere. Then, the radius of the sphere is equal to 

The coefficient of x⁴ in \[\left( \frac{x}{2} - \frac{3}{x^2} \right)^{10}\] is

XOZ-plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio

What is the locus of a point for which y = 0, z = 0?

The coordinates of the foot of the perpendicular drawn from the point P(3, 4, 5) on the yz- plane are

If  \[T_2 / T_3\]  in the expansion of \[\left( a + b \right)^n \text{ and } T_3 / T_4\]  in the expansion of \[\left( a + b \right)^{n + 3}\]  are equal, then n =

The coordinates of the foot of the perpendicular from a point P(6,7, 8) on x - axis are 

The perpendicular distance of the point P (6, 7, 8) from xy - plane is

The coefficient of  \[\frac{1}{x}\]  in the expansion of \[\left( 1 + x \right)^n \left( 1 + \frac{1}{x} \right)^n\] is 

The length of the perpendicular drawn from the point P (3, 4, 5) on y-axis is