Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.

The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.

Find the distance between P (x₁, y₁) and Q (x₂, y₂) when :

1. PQ is parallel to the y-axis,
2. PQ is parallel to the x-axis

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.

Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.

The slope of a line is double of the slope of another line. If tangent of the angle between them is `1/3`, find the slopes of the lines.

A line passes through (x₁, y₁) and (h, k). If slope of the line is m, show that k – y₁ = m (h – x₁).

If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`

Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?

Find the values of k for which the line (k–3) x – (4 – k²) y + k² –7k + 6 = 0 is 

1. Parallel to the x-axis,
2. Parallel to the y-axis,
3. Passing through the origin.

Find the equation of a line drawn perpendicular to the line `x/4 + y/6 = 1`through the point, where it meets the y-axis.

Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.

Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.

Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5),

(–3, –1, 6), (2, –4, –7).

The x-axis and y-axis taken together determine a plane known as_______.