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

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.

Find the ratio of the coefficients of x^p and x^q in the expansion of \[\left( 1 + x \right)^{p + q}\] .

If a and b are the coefficients of xⁿ in the expansion of  \[\left( 1 + x \right)^{2n} \text{ and }  \left( 1 + x \right)^{2n - 1}\]  respectively, find  \[\frac{a}{b}\]

If  \[\left( 1 - x + x^2 \right)^n = a_0 + a_1 x + a_2 x^2 + . . . + a_{2n} x^{2n}\] , find the value of  \[a_0 + a_2 + a_4 + . . . + a_{2n}\] .

If in the expansion of (1 + x)²⁰, the coefficients of rth and (r + 4)th terms are equal, then ris equal to

The coefficient of  \[x^{- 17}\]  in the expansion of \[\left( x^4 - \frac{1}{x^3} \right)^{15}\] is 

If P(0, 1, 2), Q(4, –2, 1) and O(0, 0, 0) are three points, then ∠POQ = 

If the extremities of the diagonal of a square are (1, –2, 3 and (2, –3, 5), then the length of the side is 

The points (5, –4, 2), (4, –3, 1), (7, 6, 4) and (8, –7, 5) are the vertices of 

In a three dimensional space the equation x² – 5x + 6 = 0 represents

Find out the following  sentence is a statement and is not. Justify your answer.

Listen to me, Ravi !