PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

Find the equations to the altitudes of the triangle whose angular points are A (2, −2), B (1, 1) and C (−1, 0).

Find the equation of the line passing through the point (−3, 5) and perpendicular to the line joining (2, 5) and (−3, 6).

Find the equation of the straight lines passing through the following pair of point :

(0, 0) and (2, −2)

Find the equation of the straight lines passing through the following pair of point:

(a, b) and (a + c sin α, b + c cos α)

Find the equation of the straight lines passing through the following pair of point :

(0, −a) and (b, 0)

Find the equation of the straight lines passing through the following pair of point :

(a, b) and (a + b, a − b)

Find the equation of the straight lines passing through the following pair of point :

(at₁, a/t₁) and (at₂, a/t₂)

Find the equation of the straight lines passing through the following pair of point :

(a cos α, a sin α) and (a cos β, a sin β)

Find the equations of the sides of the triangles the coordinates of whose angular point is  respectively  (0, 1), (2, 0) and (−1, −2).

Find the equations of the medians of a triangle, the coordinates of whose vertices are (−1, 6), (−3, −9) and (5, −8).

Find the equations to the diagonals of the rectangle the equations of whose sides are x = a, x = a', y= b and y = b'.

By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.

Find the equation to the straight line which bisects the distance between the points (a, b), (a', b') and also bisects the distance between the points (−a, b) and (a', −b').

In what ratio is the line joining the points (2, 3) and (4, −5) divided by the line passing through the points (6, 8) and (−3, −2).

The vertices of a quadrilateral are A (−2, 6), B (1, 2), C (10, 4), and D (7, 8). Find the equation of its diagonals.

The length L (in centimeters) of a copper rod is a linear function of its celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.

The owner of a milk store finds that he can sell 980 litres milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.

Find the equations to the straight lines which go through the origin and trisect the portion of the straight line 3 x + y = 12 which is intercepted between the axes of coordinates.

Find the equation to the straight line cutting off intercepts 3 and 2 from the axes.

Find the equation to the straight line cutting off intercepts − 5 and 6 from the axes.