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

Fill in the blank:

If f(x) = x - 3x² + 3x - 100, x ∈ R then f''(x) is ______

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

The set (A ∩ B′)′ ∪ (B ∩ C) is equal to ______.

If A = {1, 3, 5, 7, 9, 11, 13, 15, 17} B = {2, 4, ..., 18} and N the set of natural numbers is the universal set, then A′ ∪ (A ∪ B) ∩ B′) is ______.

Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets A, B and C can be ______.

For all sets A and B, A – (A ∩ B) is equal to ______.

Match the following sets for all sets A, B, and C.

State True or False for the following statement.

If (x – 2, y + 5) = `(-2, 1/3)` are two equal ordered pairs, then x = 4, y = `(-14)/3`

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

If ⁿP_r = 840, ⁿC_r = 35, then r = ______.