Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

Find the equation of the ellipse in the following case: 

Ends of major axis (± 3, 0), ends of minor axis (0, ± 2) 

Find the equation of the ellipse in the following case:  

Ends of major axis (0, ±\[\sqrt{5}\] ends of minor axis (± 1, 0) 

Find the equation of the ellipse in the following case: 

Length of major axis 26, foci (± 5, 0) 

Find the equation of the ellipse in the following case:  

Length of minor axis 16 foci (0, ± 6)

Find the equation of the ellipse in the following case:  

Foci (± 3, 0), a = 4

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ C

Each set X_r contains 5 elements and each set Y_r contains 2 elements and \[\bigcup\limits_{r=1}^{20} X_{r} = S = \bigcup\limits_{r=1}^{n} Y_{r}\] If each element of S belong to exactly 10 of the X_r’s and to exactly 4 of the Y_r’s, then n is ______.

Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}. Verify that L – (M ∪ N) = (L – M) ∩ (L – N)

Determine whether the following statement is true or false. Justify your answer.

For all sets A and B, (A – B) ∪ (A ∩ B) = A

Determine whether the following statement is true or false. Justify your answer.

For all sets A, B, and C, if A ⊂ B, then A ∩ C ⊂ B ∩ C

Determine whether the following statement is true or false. Justify your answer.

For all sets A, B, and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C

Determine whether the following statement is true or false. Justify your answer.

For all sets A, B, and C, if A ⊂ C and B ⊂ C, then A ∪ B ⊂ C

For all sets A and B, A ∪ (B – A) = A ∪ B

For all sets A and B, A – (A – B) = A ∩ B

For all sets A and B, A – (A ∩ B) = A – B

For all sets A and B, (A ∪ B) – B = A – B

If A and B are two sets, then A ∩ (A ∪ B) equals ______.

If X and Y are two sets and X′ denotes the complement of X, then X ∩ (X ∪ Y)′ is equal to ______.

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B = {2, 4, 6, 7} and C = {2, 3, 4, 8}. Then (B ∪ C)′ is ______.

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B = {2, 4, 6, 7} and C = {2, 3, 4, 8}. Then (C – A)′ is ______.