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

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

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

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

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

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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

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The point on the line 2x − 3y = 5 is equidistance from (1, 2) and (3, 4) is

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If the two straight lines x + (2k − 7)y + 3 = 0 and 3kx + 9y − 5 = 0 are perpendicular then the value of k is

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If a vertex of a square is at the origin and its one side lies along the line 4x + 3y − 20 = 0, then the area of the square is

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If the lines represented by the equation 6x² + 41xy – 7y² = 0 make angles α and β with x-axis then tan α tan β =

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θ is acute angle between the lines x² – xy – 6y² = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`

Represent graphically the displacement of 45 cm, 30° north of east

Represent graphically the displacement of 80 km, 60° south of west