PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

If the coefficients of 2nd, 3rd and 4th terms in the expansion of \[\left( 1 + x \right)^n , n \in N\]  are in A.P., then n =

Constant term in the expansion of \[\left( x - \frac{1}{x} \right)^{10}\]  is

Calculate the mean deviation from the median of the following frequency distribution:

The number of telephone calls received at an exchange in 245 successive one-minute intervals are shown in the following frequency distribution:

Compute the mean deviation about median.

Calculate the mean deviation about the median of the following frequency distribution:

While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

Calculate the mean, variance and standard deviation of the following frequency distribution. 

The perpendicular from the origin to the line y = mx + c meets it at the point (−1, 2). Find the values of m and c.

Find the equation of the straight line which cuts off intercepts on x-axis twice that on y-axis and is at a unit distance from the origin.

For the ellipse 12x² + 4y² + 24x − 16y + 25 = 0

The equation of the ellipse with focus (−1, 1), directrix x − y + 3 = 0 and eccentricity 1/2 is

The equation of the circle drawn with the two foci of \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] as the end-points of a diameter is

The eccentricity of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] if its latus rectum is equal to one half of its minor axis, is

The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latus-rectum, is

The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci, is

The difference between the lengths of the major axis and the latus-rectum of an ellipse is

The eccentricity of the conic 9x² + 25y² = 225 is

The latus-rectum of the conic 3x² + 4y² − 6x + 8y − 5 = 0 is

The equations of the tangents to the ellipse 9x² + 16y² = 144 from the point (2, 3) are

The eccentricity of the ellipse 4x² + 9y² + 8x + 36y + 4 = 0 is