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

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_______.

Coordinate planes divide the space into ______ octants.

Three vertices of a parallelogram ABCD are A (3, –1, 2), B (1, 2, –4) and C (–1, 1, 2). Find the coordinates of the fourth vertex.

If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (–4, 3b, –10) and R (8, 14, 2c), then find the values of a, b and c.

Evaluate the following limit.

`lim_(x -> 3) x + 3`

Evaluate the following limit.

`lim_(x -> pi) (x - 22/7)`

Evaluate the following limit:

`lim_(r -> l) pir^2`

Evaluate the following limit.

`lim_(x -> 4) (4x + 3)/(x - 2)`

Evaluate the following limit.

`lim_(x-> -1) (x^10 + x^5 +1)/(x -1)`

Evaluate the following limit.

`lim_(x -> 0) ((x+1)^5 - 1)/x`

Evaluate the following limit.

`lim_(x- > 2) (3x^2 - x - 10)/(x^2- 4)`

Evaluate the following limit.

`lim_(x -> 3) (x^4 - 81)/(2x^2-5x - 3)`

Evaluate the following limit.

`lim_(x-> 0) (ax + b)/(cx + 1)`

Evaluate the following limit.

`lim_(z -> 1) (z^(1/3) - 1)/(z^(1/6) -1)`

Evaluate the following limit.

`lim_(x -> 1) (ax^2 + bx  + c)/(cx^2 + bx + a), a+b+c != 0`