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

The maximum value of \[\sin^2 \left( \frac{2\pi}{3} + x \right) + \sin^2 \left( \frac{2\pi}{3} - x \right)\] is

If cos (A − B) \[= \frac{3}{5}\] and tan A tan B = 2, then

If tan 69° + tan 66° − tan 69° tan 66° = 2k, then k =

If \[\tan\alpha = \frac{x}{x + 1}\] and \[\tan\alpha = \frac{x}{x + 1}\], then \[\alpha + \beta\] is equal to

Express the following as the sum or difference of sines and cosines:

2 sin 3x cos x

Express the following as the sum or difference of sines and cosines:
2 cos 3x sin 2xa

Express the following as the sum or difference of sines and cosines:
2 sin 4x sin 3x

Express the following as the sum or difference of sines and cosines:
 2 cos 7x cos 3x

Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with the positive direction of x-axis is 15°.

Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle tan⁻¹ \[\left( \frac{5}{12} \right)\] with the positive direction of x-axi .

A line passes through a point A (1, 2) and makes an angle of 60° with the x-axis and intersects the line x + y = 6 at the point P. Find AP.

A line a drawn through A (4, −1) parallel to the line 3x − 4y + 1 = 0. Find the coordinates of the two points on this line which are at a distance of 5 units from A.

Find the distance of the point (2, 3) from the line 2x − 3y + 9 = 0 measured along a line making an angle of 45° with the x-axis.

Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to a line having slope 1/2.

Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to a line having slope 3/4.

Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to the line x − 2y = 1.

Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to the line 3x − 4y+ 8 = 0.

Find the distance of the line 2x + y = 3 from the point (−1, −3) in the direction of the line whose slope is 1.

The perpendicular distance of a line from the origin is 5 units and its slope is − 1. Find the equation of the line.