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cross multiplication MCQ Questions for Class 12

cross multiplication se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

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2 questions tagged with cross multiplication.

Question 1/2 Expert Mathematics Relations and Functions One-one function Class 12 Level 24

यदि \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=\frac{3x-2}{x+5}) और \(x\ne-5\) है, तो (f) के एकैकीपन के बारे में सही कथन क्या है?

If \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=\frac{3x-2}{x+5}) and \(x\ne-5\), what is correct about the one-one nature of (f)?

Explanation opens after your attempt
Correct Answer

A. यह एकैकी हैIt is one-one

Step 1

Concept

Assume (f(a)=f(b)).

Step 2

Why this answer is correct

From \(\frac{3a-2}{a+5}=\frac{3b-2}{b+5}\), cross-multiplication gives (17a=17b), hence (a=b).

Step 3

Exam Tip

Cross-multiplication is very useful for fractional linear functions. चरण 1: मान लें (f(a)=f(b))। चरण 2: \(\frac{3a-2}{a+5}=\frac{3b-2}{b+5}\) से क्रॉस गुणा करने पर (17a=17b), अतः (a=b)। चरण 3: भिन्नात्मक रैखिक फलनों में क्रॉस गुणा बहुत उपयोगी होता है।

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Question 2/2 Expert Mathematics Relations and Functions One-one function Class 12 Level 23

फलन \(f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{1}\), (f(x)=\frac{x+1}{x-1}) के बारे में सही कथन क्या है?

What is correct about \(f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{1}\), (f(x)=\frac{x+1}{x-1})?

Explanation opens after your attempt
Correct Answer

A. यह एकैकी हैIt is one-one

Step 1

Concept

Assume (f(a)=f(b)).

Step 2

Why this answer is correct

\(\frac{a+1}{a-1}=\frac{b+1}{b-1}\) gives ((a+1)(b-1)=(b+1)(a-1)), leading to (a=b).

Step 3

Exam Tip

For fractional linear functions, cross-multiplication is a good way to test one-one nature. चरण 1: (f(a)=f(b)) मानें। चरण 2: \(\frac{a+1}{a-1}=\frac{b+1}{b-1}\) से ((a+1)(b-1)=(b+1)(a-1)), जिससे (a=b) मिलता है। चरण 3: भिन्नात्मक रैखिक फलनों में क्रॉस गुणा करके एकैकीपन जांचें।

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