HSC Arts कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Find the equations of straight lines which are perpendicular to the line 3x + 4y − 6 = 0 and are at a distance of 4 units from (2, 1)

Find the equation of a straight line parallel to 2x + 3y = 10 and which is such that the sum of its intercepts on the axes is 15

Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from (−10, −2) to the line x + y − 2 = 0

If p₁ and p₂ are the lengths of the perpendiculars from the origin to the straight lines x sec θ + y cosec θ = 2a and x cos θ – y sin θ = a cos 2θ, then prove that p₁² + p₂² = a² 

Find the distance between the parallel lines
12x + 5y = 7 and 12x + 5y + 7 = 0

Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0

Find the family of straight lines perpendicular

Find the family of straight lines parallel to 3x + 4y – 12

If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then find the equation of the line in new position

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and it passes through the point (5, 3). Find the co-ordinates of the point A

A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq.units

Find the image of the point (−2, 3) about the line x + 2y − 9 = 0

A photocopy store charges ₹ 1.50 per copy for the first 10 copies and ₹ 1.00 per copy after the 10^th copy. Let x be the number of copies, and let y be the total cost of photocopying. Draw graph of the cost as x goes from 0 to 50 copies

A photocopy store charges ₹ 1.50 per copy for the first 10 copies and ₹ 1.00 per copy after the 10^th copy. Let x be the number of copies, and let y be the total cost of photocopying. Find the cost of making 40 copies

Find atleast two equations of the straight lines in the family of the lines y = 5x + b, for which b and the x-coordinate of the point of intersection of the lines with 3x − 4y = 6 are integers

Find all the equations of the straight lines in the family of the lines y = mx − 3, for which m and the x-coordinate of the point of intersection of the lines with x − y = 6 are integers

Choose the correct alternative:
The slope of the line which makes an angle 45° with the line 3x − y = −5 are

Choose the correct alternative:
The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are

Choose the correct alternative:
The equation of the line with slope 2 and the length of the perpendicular from the origin equal to `sqrt(5)` is

Choose the correct alternative:
A line perpendicular to the line 5x − y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq.units, then its equation is