HSC Science (General) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Prove the following:

`(sin3x)/cosx + (cos3x)/sinx` = 2 cot 2x

Find the slope of the following line which passes through the points:

A(2, −1), B(4, 3)

Find the slope of the following line which passes through the points:

C(−2, 3), D(5, 7)

Find the slope of the following line which passes through the points:

E(2, 3), F(2, −1)

Find the slope of the following line which passes through the points:

G(7, 1), H(−3, 1)

If the X and Y-intercepts of lines L are 2 and 3 respectively then find the slope of line L.

Find the slope of the line whose inclination is 30°

Find the slope of the line whose inclination is `pi/4`

A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.

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

Find the slope of the line which makes angle of 45° with the positive direction of the Y-axis measured anticlockwise

Find the value of k for which points P(k, −1), Q(2, 1) and R(4, 5) are collinear.

Find the acute angle between the X-axis and the line joining points A(3, −1) and B(4, −2).

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

If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1

Select the correct option from the given alternatives:

If A is (5, −3) and B is a point on the x-axis such that the slope of line AB is −2 then B ≡

Select the correct option from the given alternatives:

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y−interecpt is

Select the correct option from the given alternatives:

The angle between the line `sqrt(3)x - y - 2` = 0 and `x - sqrt(3)y + 1` = 0 is 

Select the correct option from the given alternatives:

If kx + 2y − 1 = 0 and 6x − 4y + 2 = 0 are identical lines, then determine k

Answer the following question:

Find the value of k if the slope of the line passing through the points P(3, 4), Q(5, k) is 9