Commerce (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point

If the point (5, 2) bisects the intercept of a line between the axes, then its equation is

The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 is

The inclination of the straight line passing through the point (−3, 6) and the mid-point of the line joining the point (4, −5) and (−2, 9) is

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

B ∪ C

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

B ∪ D

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

A ∪ B ∪ C

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

A ∪ B ∪ D

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

B ∪ C ∪ D

If X and Y are subsets of the universal set U, then show that Y ⊂ X ∪ Y

If X and Y are subsets of the universal set U, then show that X ∩ Y ⊂ X

If X and Y are subsets of the universal set U, then show that X ⊂ Y ⇒ X ∩ Y = X

If A and B are subsets of the universal set U, then show that A ⊂ A ∪ B

If A and B are subsets of the universal set U, then show that A ⊂ B ⇔ A ∪ B = B

If A and B are subsets of the universal set U, then show that (A ∩ B) ⊂ A

A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20} B = {3, 6, 9, 12, 15}, C = {5, 10, 15, 20} and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.

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

In a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics and 70 study Chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 none of these subjects. Find the number of students who study all the three subjects.

In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B, 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers. Find the number of families which buy newspaper A only.

In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B, 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers. Find the number of families which buy none of A, B and C