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

Given that N = {1, 2, 3, ..., 100}, then write the subset B of N, whose element are represented by x + 2, where x ∈ N.

State true or false for the following statement given below:

Let R and S be the sets defined as follows:
R = {x ∈ Z | x is divisible by 2}
S = {y ∈ Z | y is divisible by 3}
then R ∩ S = φ

State true or false for the following statement given below:

Q ∩ R = Q, where Q is the set of rational numbers and R is the set of real numbers.

Given that N = {1, 2, 3, ... , 100}. Then write the subset of N whose elements are even numbers.

Given that N = {1, 2, 3, ... , 100}. Then write the subset of N whose element are perfect square numbers.

If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by 4n

If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by n + 6

If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by `n/2`

If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by n – 1

If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

a ∈ Y but a² ∉ Y

If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

a + 1 = 6, a ∈ Y

If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

a is less than 6 and a ∈ Y

Suppose A₁, A₂, ..., A₃₀ are thirty sets each having 5 elements and B₁, B₂, ..., Bn are n sets each with 3 elements, let \[\bigcup\limits_{i=1}^{30} A_{i} = \bigcup\limits_{j=1}^{n} B_{j}\] = and each element of S belongs to exactly 10 of the A_i’s and exactly 9 of the B,’S. then n is equal to ______.

If X = {8ⁿ – 7n – 1 | n ∈ N} and Y = {49n – 49 | n ∈ N}. Then ______.

State True or False for the following statement.

If A is any set, then A ⊂ A.

State True or False for the following statement.

Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then B ⊄ M.

State True or False for the following statement.

The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.

State True or False for the following statement.

Q ∪ Z = Q, where Q is the set of rational numbers and Z is the set of integers.

Find x and y if: (4x + 3, y) = (3x + 5, – 2)

Find x and y if: (x – y, x + y) = (6, 10)