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

If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then

Which of the following is incorrect?

The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is

The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is

Which of the following is correct?

Find the A.M. between:

 7 and 13 

Find the A.M. between:

12 and −8

Find the A.M. between:

(x − y) and (x + y).

Insert 4 A.M.s between 4 and 19.

Insert 7 A.M.s between 2 and 17.

Insert six A.M.s between 15 and −13.

If n A.M.s are inserted between two numbers, prove that the sum of the means equidistant from the beginning and the end is constant.

The vertices of the triangle are A(5, 4, 6), B(1, –1, 3) and C(4, 3, 2). The internal bisector of angle A meets BC at D. Find the coordinates of D and the length AD.

A point C with z-coordinate 8 lies on the line segment joining the points A(2, –3, 4) and B(8, 0, 10). Find its coordinates.

Show that the three points A(2, 3, 4), B(–1, 2 – 3) and C(–4, 1, –10) are collinear and find the ratio in which C divides AB. 

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

Find the ratio in which the line segment joining the points (2, –1, 3) and (–1, 2, 1) is divided by the plane x + y + z = 5. 

If the points A(3, 2, –4), B(9, 8, –10) and C(5, 4, –6) are collinear, find the ratio in which Cdivides AB.