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

If the sum of the binomial coefficients of the expansion \[\left( 2x + \frac{1}{x} \right)^n\]  is equal to 256, then the term independent of x is

The length of the perpendicular drawn from the point P(a, b, c) from z-axis is 

The coefficient of x⁵ in the expansion of \[\left( 1 + x \right)^{21} + \left( 1 + x \right)^{22} + . . . + \left( 1 + x \right)^{30}\]

The coefficient of x⁸ y¹⁰ in the expansion of (x + y)¹⁸ is

If the coefficients of x² and x³ in the expansion of (3 + ax)⁹ are the same, then the value of a is

Find the slope of the lines which make the following angle with the positive direction of x-axis:

\[- \frac{\pi}{4}\]

Find the slope of the lines which make the following angle with the positive direction of x-axis:

\[\frac{2\pi}{3}\]

Find the slope of the lines which make the following angle with the positive direction of x-axis: 

\[\frac{3\pi}{4}\]

Find the slope of the lines which make the following angle with the positive direction of x-axis: \[\frac{\pi}{3}\]

Find the slope of a line passing through the following point:

 (−3, 2) and (1, 4)

Find the slope of a line passing through the following point:

\[(a t_1^2 , 2 a t_1 ) \text { and } (a t_2^2 , 2 a t_2 )\]

Find the slope of a line passing through the following point:

(3, −5), and (1, 2)

State whether the two lines in each of the following are parallel, perpendicular or neither.

Through (5, 6) and (2, 3); through (9, −2) and (6, −5)

State whether the two lines in each of the following are parallel, perpendicular or neither.

Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)

State whether the two lines in each of the following is parallel, perpendicular or neither.

Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)

State whether the two lines in each of the following is parallel, perpendicular or neither.

Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).

Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).

Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .

What is the value of y so that the line through (3, y)  and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?