PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

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

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

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

Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x. 

Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.

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

By using the concept of slope, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.

A quadrilateral has vertices (4, 1), (1, 7), (−6, 0) and (−1, −9). Show that the mid-points of the sides of this quadrilateral form a parallelogram.

Find the equation of a straight line with slope 2 and y-intercept 3 .

Find the equation of a straight line  with slope − 1/3 and y-intercept − 4.

Find the equation of a straight line with slope −2 and intersecting the x-axis at a distance of 3 units to the left of origin.

Find the equations of the bisectors of the angles between the coordinate axes.

Find the equation of a line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.

Find the equation of the perpendicular to the line segment joining (4, 3) and (−1, 1) if it cuts off an intercept −3 from y-axis.

Find the equation of the strainght line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.

Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.