Science (English Medium) Class 11 - CBSE Question Bank Solutions

One mapping is selected at random from all mappings of the set A = {1, 2, 3, ..., n} into itself. The probability that the mapping selected is one to one is

Three numbers are chosen from 1 to 20. The probability that they are not consecutive is

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:
 4x² + 9y² = 1

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

 5x² + 4y² = 1

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

 4x² + 3y² = 1

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

 25x² + 16y² = 1600.

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

Find the equation of the ellipse whose foci are (4, 0) and (−4, 0), eccentricity = 1/3. 

Find the equation of the ellipse in the standard form whose minor axis is equal to the distance between foci and whose latus-rectum is 10. 

Find the equation of an ellipse whose eccentricity is 2/3, the latus-rectum is 5 and the centre is at the origin.

Find the equation of an ellipse with its foci on y-axis, eccentricity 3/4, centre at the origin and passing through (6, 4). 

Find the equation of an ellipse whose axes lie along coordinate axes and which passes through (4, 3) and (−1, 4). 

Find the equation of an ellipse whose axes lie along the coordinate axes, which passes through the point (−3, 1) and has eccentricity equal to \[\sqrt{2/5}\] 

Write the centre and eccentricity of the ellipse 3x² + 4y² − 6x + 8y − 5 = 0. 

Write the eccentricity of an ellipse whose latus-rectum is one half of the minor axis.

If the distance between the foci of an ellipse is equal to the length of the latus-rectum, write the eccentricity of the ellipse.

For all sets A, B and C is (A ∩ B) ∪ C = A ∩ (B ∪ C)? Justify your statement.

Use the properties of sets to prove that for all the sets A and B 

A – (A ∩ B) = A – B

For all sets A, B, and C

Is (A – B) ∩ (C – B) = (A ∩ C) – B? Justify your answer.