HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is equivalence

Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is reflexive

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is symmetric

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is transitive

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is equivalence

Let A = {a, b, c}. What is the equivalence relation of smallest cardinality on A? What is the equivalence relation of largest cardinality on A?

In the set Z of integers, define mRn if m − n is divisible by 7. Prove that R is an equivalence relation

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The relation R defined on a set A = {0, −1, 1, 2} by xRy if |x² + y²| ≤ 2, then which one of the following is true?

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Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer} Then which of the following is true?

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The number of relations on a set containing 3 elements is

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Let R be the universal relation on a set X with more than one element. Then R is

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Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is

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The rule f(x) = x² is a bijection if the domain and the co-domain are given by

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Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is

Solve for x: |3 − x| < 7

Solve for x: |4x − 5| ≥ −2

Solve for x: `|3 - 3/4x| ≤ 1/4`

Solve for x: |x| − 10 < −3

Solve `1/(|2x - 1|) < 6` and express the solution using the interval notation