PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

Let (3, 4, –1) and (–1, 2, 3) be the end points of a diameter of a sphere. Then, the radius of the sphere is equal to 

The coefficient of x⁴ in \[\left( \frac{x}{2} - \frac{3}{x^2} \right)^{10}\] is

XOZ-plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio

What is the locus of a point for which y = 0, z = 0?

The coordinates of the foot of the perpendicular drawn from the point P(3, 4, 5) on the yz- plane are

If  \[T_2 / T_3\]  in the expansion of \[\left( a + b \right)^n \text{ and } T_3 / T_4\]  in the expansion of \[\left( a + b \right)^{n + 3}\]  are equal, then n =

The coordinates of the foot of the perpendicular from a point P(6,7, 8) on x - axis are 

The perpendicular distance of the point P (6, 7, 8) from xy - plane is

The coefficient of  \[\frac{1}{x}\]  in the expansion of \[\left( 1 + x \right)^n \left( 1 + \frac{1}{x} \right)^n\] is 

The length of the perpendicular drawn from the point P (3, 4, 5) on y-axis is 

The perpendicular distance of the point P(3, 3,4) from the x-axis is 

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