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cubic-plus-linear MCQ Questions for Class 12

cubic-plus-linear se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

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3 questions tagged with cubic-plus-linear.

Question 1/3 Hard Mathematics Relations and Functions One-one function Class 12 Level 23

फलन \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=x-3+x) के बारे में सही कथन कौन-सा है?

Which statement is correct about the function \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=x-3+x)?

Explanation opens after your attempt
Correct Answer

A. एकैकी हैOne-one

Step 1

Concept

Assume (a>b).

Step 2

Why this answer is correct

Then \(a^3>b^3\) and (a>b), so \(a^3+a>b^3+b\).

Step 3

Exam Tip

A strictly increasing function is one-one. चरण 1: मान लें (a>b)। चरण 2: \(a^3>b^3\) और (a>b), इसलिए \(a^3+a>b^3+b\)। चरण 3: यदि फलन सख्ती से बढ़ता है, तो वह एकैकी होता है।

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Question 2/3 Medium Mathematics Relations and Functions One-one function Class 12 Level 24

यदि \(f:\mathbb{R}\to\mathbb{R}\) और (f(x)=x-3+x) है, तो (f) के बारे में सही निष्कर्ष क्या है?

If \(f:\mathbb{R}\to\mathbb{R}\) and (f(x)=x-3+x), what is the correct conclusion about (f)?

Explanation opens after your attempt
Correct Answer

A. एकैकी हैOne-one

Step 1

Concept

Consider the function \(x^3+x\).

Step 2

Why this answer is correct

It is strictly increasing on \(\mathbb{R}\) because both terms increase with (x).

Step 3

Exam Tip

A strictly increasing function is one-one, so different inputs cannot give the same value. चरण 1: मान लें (f(a)=f(b))। चरण 2: फलन \(x^3+x\) पूरे \(\mathbb{R}\) पर लगातार बढ़ता है क्योंकि (x) बढ़ने पर दोनों भाग साथ बढ़ते हैं। चरण 3: बढ़ता हुआ फलन एकैकी होता है, इसलिए अलग आगत समान मान नहीं दे सकते।

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Question 3/3 Medium Mathematics Relations and Functions One-one function Class 12 Level 23

फलन \(f:\mathbb{Z}\to\mathbb{Z}\), (f(n)=n-3+n) के लिए सही विकल्प चुनिए।

Choose the correct option for \(f:\mathbb{Z}\to\mathbb{Z}\), (f(n)=n-3+n).

Explanation opens after your attempt
Correct Answer

A. एकैकी हैIt is one-one

Step 1

Concept

Let (a>b), where (a,b) are integers.

Step 2

Why this answer is correct

Then \(a^3>b^3\) and (a>b), so \(a^3+a>b^3+b\).

Step 3

Exam Tip

The function increases, so different integers give different images. चरण 1: मान लें (a>b) जहाँ (a,b) पूर्णांक हैं। चरण 2: \(a^3>b^3\) और (a>b), इसलिए \(a^3+a>b^3+b\)। चरण 3: फलन बढ़ता है इसलिए अलग पूर्णांक अलग छवि देंगे।

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