Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions for Mathematics

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.

Let A, B and C be sets. Then show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Let P be the set of prime numbers and let S = {t | 2^t – 1 is a prime}. Prove that S ⊂ P.

From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student has passed in at least one of the subject, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 Mathematics and Chemistry and at most 20 Physics and Chemistry. What is the largest possible number that could have passed all three examination?