#natural numbers

Sets, Relations and Functions

Let ‘*’ be defined on the set N. Which of the following are both commutative and associative?

The trick is using formula we get a * b = a + b. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get a * b = a + b.

Ref: NCERT Mathematics Class XI — Sets, Relations and Functions

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General Mathematics 3

If f: N→N, g: N→N and h: N→R is defined f(x) = 3x - 5, g(y) = 6y2 and h(z) = tan⁡z, find ho(gof).

Understanding this is easy: using formula we get tan⁡(6(3x - 5)²). Calculation gives this directly, check steps: apply rule, substitute values, simplify to get tan⁡(6(3x - 5)²).

Ref: NCERT Mathematics Class XI and XII

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Sets, Relations and Functions

Let R be a relation in the set N given by R=(a,b): a+b=5, b>1. Which of the following will satisfy the given relation?

The trick is solving fully: apply relevant formula, put numbers, compute. Result comes as (2,3) ∈ R. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XI — Sets, Relations and Functions

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General Mathematics 3

Let ‘*’ be a binary operation on N defined by a * b =a - b + ab², then find 4 * 5.

Look at it this way: after simplifying, 99 is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XI and XII

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Matrices and Determinants 2

If A =bmatrix 1 & 2 3 & 4 bmatrix and B =bmatrix a & 0 0 & b bmatrix , where a, b and natural numbers, then which one of

Let's break it down: using formula we get There exist infinitely many B's such that AB = BA. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get There exist infinitely many B's such that AB =

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Sets, Relations and Functions

Let N be the set of natural numbers and f : N → N be a function given by f (x) = x + 1 ∀ x ∈ N. Which one of the followi

We can see that solving fully: apply relevant formula, put numbers, compute. Result comes as f is one - one but not onto. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XI — Sets, Relations and Functions

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Sets, Relations and Functions

Suppose A = X| X ∈ N, -1 < X < 8 and B = Y| Y ∈ N, -1 < Y < 1 then find A × B.

We know that using formula we get Ⴔ. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get Ⴔ.

Ref: NCERT Mathematics Class XI — Sets, Relations and Functions

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