Science (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Find the locus of the point, the sum of whose distances from the points A(4, 0, 0) and B(–4, 0, 0) is equal to 10.

Show that the points A(1, 2, 3), B(–1, –2, –1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram ABCD, but not a rectangle.

Write the sum of the coefficients in the expansion of \[\left( 1 - 3x + x^2 \right)^{111}\]

Find the equation of the set of the points P such that its distances from the points A(3, 4, –5) and B(–2, 1, 4) are equal.

If a and b denote respectively the coefficients of x^m and xⁿ in the expansion of \[\left( 1 + x \right)^{m + n}\], then write the relation between a and b.

If a and b are coefficients of xⁿ in the expansions of \[\left( 1 + x \right)^{2n} \text{ and } \left( 1 + x \right)^{2n - 1}\] respectively, then write the relation between a and b.

If a and b denote the sum of the coefficients in the expansions of \[\left( 1 - 3x + 10 x^2 \right)^n\]  and \[\left( 1 + x^2 \right)^n\]  respectively, then write the relation between a and b.

Find the ratio in which the sphere x² + y² + z² = 504 divides the line joining the points (12, –4, 8) and (27, –9, 18).

The term without x in the expansion of \[\left( 2x - \frac{1}{2 x^2} \right)^{12}\] is 

Show that the plane ax + by + cz + d = 0 divides the line joining the points (x₁, y₁, z₁) and (x₂, y₂, z₂) in the ratio \[- \frac{a x_1 + b y_1 + c z_1 + d}{a x_2 + b y_2 + c z_2 + d}\]

Write the distance of the point P (2, 3,5) from the xy-plane.

Write the distance of the point P(3, 4, 5) from z-axis.

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