Class 11 Mathematics Relations and Functions Relations Expert Level 27

\(\mathbb{R}\) पर (aRb) तभी जब \(a^3\leq b^3\)। यह relation किस relation के समान है?

On \(\mathbb{R}\), (aRb) if and only if \(a^3\leq b^3\). This relation is equivalent to which relation?

Explanation opens after your attempt
Correct Answer

A. \(a\leq b\)

Step 1

Concept

The function \(x^3\) is strictly increasing, so \(a^3\leq b^3\) is exactly equivalent to \(a\leq b\). Use monotonicity to identify relation properties quickly.

Step 2

Why this answer is correct

The correct answer is A. \(a\leq b\). The function \(x^3\) is strictly increasing, so \(a^3\leq b^3\) is exactly equivalent to \(a\leq b\). Use monotonicity to identify relation properties quickly.

Step 3

Exam Tip

Function \(x^3\) strictly increasing है, इसलिए \(a^3\leq b^3\) exactly \(a\leq b\) के बराबर है। Monotonicity से relation की property जल्दी पहचानें।

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\(\mathbb{R}\) पर (aRb) तभी जब \(a^3\leq b^3\)। यह relation किस relation के समान है? / On \(\mathbb{R}\), (aRb) if and only if \(a^3\leq b^3\). This relation is equivalent to which relation?

Correct Answer: A. \(a\leq b\). Explanation: Function \(x^3\) strictly increasing है, इसलिए \(a^3\leq b^3\) exactly \(a\leq b\) के बराबर है। Monotonicity से relation की property जल्दी पहचानें। / The function \(x^3\) is strictly increasing, so \(a^3\leq b^3\) is exactly equivalent to \(a\leq b\). Use monotonicity to identify relation properties quickly.

Which concept should I revise for this Mathematics MCQ?

The function \(x^3\) is strictly increasing, so \(a^3\leq b^3\) is exactly equivalent to \(a\leq b\). Use monotonicity to identify relation properties quickly.

What exam hint can help solve this Mathematics question?

Function \(x^3\) strictly increasing है, इसलिए \(a^3\leq b^3\) exactly \(a\leq b\) के बराबर है। Monotonicity से relation की property जल्दी पहचानें।