Concept-wise Practice

domain-intersection MCQ Questions for Class 11

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

Practice Questions

2 questions tagged with domain-intersection.

यदि (f(x)=\sqrt{x}) और (g(x)=\frac{1}{x-4}) हैं, तो (f+g) का डोमेन क्या होगा?

If (f(x)=\sqrt{x}) and (g(x)=\frac{1}{x-4}), what is the domain of (f+g)?

Explanation opens after your attempt
Correct Answer

A. \( [0,\infty\)-{4} )

Step 1

Concept

For \(\sqrt{x}\), \(x\ge0\), and for \(\frac{1}{x-4}\), \(x\neq4\). Hence the domain is \( [0,\infty\)-{4} ).

Step 2

Why this answer is correct

The correct answer is A. \( [0,\infty\)-{4} ). For \(\sqrt{x}\), \(x\ge0\), and for \(\frac{1}{x-4}\), \(x\neq4\). Hence the domain is \( [0,\infty\)-{4} ).

Step 3

Exam Tip

\(\sqrt{x}\) के लिए \(x\ge0\) और \(\frac{1}{x-4}\) के लिए \(x\neq4\) चाहिए। इसलिए डोमेन \( [0,\infty\)-{4} ) है।

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यदि (f(x)=\sqrt{x+2}) और (g(x)=\frac{1}{x-1}) हों, तो ((f+g)(x)) का domain क्या है?

If (f(x)=\sqrt{x+2}) and (g(x)=\frac{1}{x-1}), what is the domain of ((f+g)(x))?

Explanation opens after your attempt
Correct Answer

A. \([-2,\infty\)-{1})

Step 1

Concept

For \(\sqrt{x+2}\), \(x\geq -2\), and for \(\frac{1}{x-1}\), \(x\neq 1\). Their intersection gives \([-2,\infty\)-{1}).

Step 2

Why this answer is correct

The correct answer is A. \([-2,\infty\)-{1}). For \(\sqrt{x+2}\), \(x\geq -2\), and for \(\frac{1}{x-1}\), \(x\neq 1\). Their intersection gives \([-2,\infty\)-{1}).

Step 3

Exam Tip

\(\sqrt{x+2}\) के लिए \(x\geq -2\) और \(\frac{1}{x-1}\) के लिए \(x\neq 1\)। intersection से domain \([-2,\infty\)-{1}) मिलता है।

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