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

Which of the following statements are true and which are false? In each case give a valid reason for saying so.

s: If x and y are integers such that x > y, then –x < –y.

Which of the following statements are true and which are false? In each case give a valid reason for saying so.

t`sqrt11` is a rational number.

Check the validity of the statements given below by the method given against it.

p: The sum of an irrational number and a rational number is irrational (by contradiction method).

Check the validity of the statements given below by the method given against it.

q: If n is a real number with n > 3, then n² > 9 (by contradiction method).

Write the following statement in five different ways, conveying the same meaning.

p: If triangle is equiangular, then it is an obtuse angled triangle.

Find the mean and variance for the following frequency distribution.

Find the mean and variance for the following frequency distribution.

If the ordered pairs (x, −1) and (5, y) belong to the set {(a, b) : b = 2a − 3}, find the values of x and y. 

If a ∈ [−1, 2, 3, 4, 5] and b ∈ [0, 3, 6], write the set of all ordered pairs (a, b) such that a + b= 5.  

If a ∈ [2, 4, 6, 9] and b ∈ [4, 6, 18, 27], then form the set of all ordered pairs (a, b) such that a divides b and a < b.

Let A and B be two sets such that n(A) = 3 and n(B) = 2.
If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y, z are distinct elements.

State whether of  the statement is true or false. If the statement is false, re-write the given statement correctly:

 If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ B and y ∈ A.

A relation R is defined from a set A = [2, 3, 4, 5] to a set B = [3, 6, 7, 10] as follows:
(x, y) ∈ R ⇔ x is relatively prime to y
Express R as a set of ordered pairs and determine its domain and range.

Let A be the set of first five natural numbers and let R be a relation on A defined as follows:
(x, y) ∈ R ⇔ x ≤ y
Express R and R⁻¹ as sets of ordered pairs. Determine also (i) the domain of R⁻¹ (ii) the range of R.

Write the relation as the sets of ordered pairs:

(i) A relation R from the set [2, 3, 4, 5, 6] to the set [1, 2, 3] defined by x = 2y.

Write the relation as the sets of ordered pairs:

(ii) A relation R on the set [1, 2, 3, 4, 5, 6, 7] defined by (x, y) ∈ R ⇔ x is relatively prime to y.

Write the relation as the sets of ordered pairs:

(iii) A relation R on the set [0, 1, 2, ....., 10] defined by 2x + 3y = 12.

Write the relation as the sets of ordered pairs:

(iv) A relation R from a set A = [5, 6, 7, 8] to the set B = [10, 12, 15, 16,18] defined by (x, y) ∈ R ⇔ x divides y.

Let R be a relation in N defined by (x, y) ∈ R ⇔ x + 2y =8. Express R and R⁻¹ as sets of ordered pairs.

 Let A = {1, 2, 3} and\[R = \left\{ \left( a, b \right) : \left| a^2 - b^2 \right| \leq 5, a, b \in A \right\}\].Then write R as set of ordered pairs.