PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

Find the equations of the lines through the point of intersection of the lines x − 3y + 1 = 0 and 2x + 5y − 9 = 0 and whose distance from the origin is \[\sqrt{5}\].

Write the area of the triangle formed by the coordinate axes and the line (sec θ − tan θ) x + (sec θ + tan θ) y = 2.

If the diagonals of the quadrilateral formed by the lines l₁x + m₁y + n₁ = 0, l₂x + m₂y + n₂ = 0, l₁x + m₁y + n₁' = 0 and l₂x + m₂y + n₂' = 0 are perpendicular, then write the value of l₁² − l₂² + m₁² − m₂².

Write the integral values of m for which the x-coordinate of the point of intersection of the lines y = mx + 1 and 3x + 4y = 9 is an integer.

If a, b, c are in G.P. write the area of the triangle formed by the line ax + by + c = 0 with the coordinates axes.

If a, b, c are in A.P., then the line ax + by + c = 0 passes through a fixed point. Write the coordinates of that point.

Write the equation of the line passing through the point (1, −2) and cutting off equal intercepts from the axes.

Find the locus of the mid-points of the portion of the line x sinθ+ y cosθ = p intercepted between the axes.

The equation of the straight line which passes through the point (−4, 3) such that the portion of the line between the axes is divided internally by the point in the ratio 5 : 3 is

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

If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point

If the point (5, 2) bisects the intercept of a line between the axes, then its equation is

The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 is

The inclination of the straight line passing through the point (−3, 6) and the mid-point of the line joining the point (4, −5) and (−2, 9) is

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

B ∪ C

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

B ∪ D

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ B ∪ C

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ B ∪ D

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

B ∪ C ∪ D

Choose the correct alternative.

The equation of tangent to the curve y = x² + 4x + 1 at (-1, -2) is