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hole MCQ Questions for Class 11

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9 questions tagged with hole.

Question 1/9 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 36

फलन \(y=\frac{x^2-16}{x+4}\) के ग्राफ में (x=-4) पर क्या होता है?

What happens at (x=-4) in the graph of \(y=\frac{x^2-16}{x+4}\)?

Explanation opens after your attempt
Correct Answer

A. छिद्र बनता हैA hole occurs

Step 1

Concept

\(\frac{x^2-16}{x+4}=x-4\), but (x=-4) is not in the domain. Therefore the line-like graph has a hole at (x=-4).

Step 2

Why this answer is correct

The correct answer is A. छिद्र बनता है / A hole occurs. \(\frac{x^2-16}{x+4}=x-4\), but (x=-4) is not in the domain. Therefore the line-like graph has a hole at (x=-4).

Step 3

Exam Tip

\(\frac{x^2-16}{x+4}=x-4\) है लेकिन (x=-4) डोमेन में नहीं है। इसलिए रेखा जैसे ग्राफ में (x=-4) पर छिद्र बनता है।

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Question 2/9 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 36

फलन \(y=\frac{x^2-9}{x-3}\) में (x=3) पर ग्राफ में क्या दिखता है?

What appears in the graph of \(y=\frac{x^2-9}{x-3}\) at (x=3)?

Explanation opens after your attempt
Correct Answer

A. छिद्रA hole

Step 1

Concept

\(\frac{x^2-9}{x-3}=x+3\), but (x=3) remains excluded. Therefore the line-like graph has a hole.

Step 2

Why this answer is correct

The correct answer is A. छिद्र / A hole. \(\frac{x^2-9}{x-3}=x+3\), but (x=3) remains excluded. Therefore the line-like graph has a hole.

Step 3

Exam Tip

\(\frac{x^2-9}{x-3}=x+3\) है लेकिन (x=3) निषिद्ध रहता है। इसलिए रेखा जैसे ग्राफ में छिद्र होता है।

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Question 3/9 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

ग्राफ \(y=\frac{x^2-4}{x-2}\) में (x=2) पर क्या होता है?

What happens at (x=2) in the graph of \(y=\frac{x^2-4}{x-2}\)?

Explanation opens after your attempt
Correct Answer

A. छिद्र बनता हैA hole occurs

Step 1

Concept

(\frac{x-2-4}{x-2}=\frac{(x-2)(x+2)}{x-2}), but (x=2) remains excluded. So the graph is like (y=x+2) with a hole at (x=2).

Step 2

Why this answer is correct

The correct answer is A. छिद्र बनता है / A hole occurs. (\frac{x-2-4}{x-2}=\frac{(x-2)(x+2)}{x-2}), but (x=2) remains excluded. So the graph is like (y=x+2) with a hole at (x=2).

Step 3

Exam Tip

(\frac{x-2-4}{x-2}=\frac{(x-2)(x+2)}{x-2}) है पर (x=2) निषिद्ध रहता है। इसलिए ग्राफ (y=x+2) जैसा है लेकिन (x=2) पर छिद्र है।

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Question 4/9 Hard Mathematics Relations and Functions Graphs of standard functions Class 11 Level 36

फलन (f(x)=\frac{x-2-1}{x-1}) का ग्राफ \(x\ne1\) पर किस रेखा जैसा है?

For \(x\ne1\), the graph of (f(x)=\frac{x-2-1}{x-1}) is like which line?

Explanation opens after your attempt
Correct Answer

A. (y=x+1)

Step 1

Concept

(\frac{x-2-1}{x-1}=\frac{(x-1)(x+1)}{x-1}=x+1), but (x=1) is excluded. Do not forget the hole in such graphs.

Step 2

Why this answer is correct

The correct answer is A. (y=x+1). (\frac{x-2-1}{x-1}=\frac{(x-1)(x+1)}{x-1}=x+1), but (x=1) is excluded. Do not forget the hole in such graphs.

Step 3

Exam Tip

(\frac{x-2-1}{x-1}=\frac{(x-1)(x+1)}{x-1}=x+1), लेकिन (x=1) हटता है। ऐसे ग्राफ में छेद को न भूलें।

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Question 5/9 Expert Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 33

फलन (f(x)=\frac{x-2-16}{x-4}) का परिसर क्या है?

What is the range of (f(x)=\frac{x-2-16}{x-4})?

Explanation opens after your attempt
Correct Answer

A. \( \mathbb{R}\setminus{8} \)

Step 1

Concept

For \(x\ne 4\), the function equals (x+4). The value (8), which would come from (x=4), will not be in the range.

Step 2

Why this answer is correct

The correct answer is A. \( \mathbb{R}\setminus{8} \). For \(x\ne 4\), the function equals (x+4). The value (8), which would come from (x=4), will not be in the range.

Step 3

Exam Tip

\(x\ne 4\) पर फलन (x+4) के बराबर है। (x=4) से आने वाला मान (8) परिसर में नहीं आएगा।

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Question 6/9 Expert Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 32

फलन (f(x)=\frac{x-2-9}{x-3}) का परिसर क्या है?

What is the range of (f(x)=\frac{x-2-9}{x-3})?

Explanation opens after your attempt
Correct Answer

A. \( \mathbb{R}\setminus{6} \)

Step 1

Concept

The original domain has \(x\ne 3\), and simplification gives (f(x)=x+3). Hence the value (6), which would occur at (x=3), is excluded from the range.

Step 2

Why this answer is correct

The correct answer is A. \( \mathbb{R}\setminus{6} \). The original domain has \(x\ne 3\), and simplification gives (f(x)=x+3). Hence the value (6), which would occur at (x=3), is excluded from the range.

Step 3

Exam Tip

मूल प्रांत में \(x\ne 3\) है और सरलीकरण से (f(x)=x+3)। इसलिए (x=3) पर आने वाला मान (6) परिसर से हटेगा।

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Question 7/9 Expert Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 31

फलन (f(x)=\frac{x-2-4}{x-2}) का परिसर क्या है?

What is the range of (f(x)=\frac{x-2-4}{x-2})?

Explanation opens after your attempt
Correct Answer

A. \( \mathbb{R}\setminus{4} \)

Step 1

Concept

For \(x\ne 2\), the function equals (x+2). Thus the value (4), which would occur at (x=2), is not in the range.

Step 2

Why this answer is correct

The correct answer is A. \( \mathbb{R}\setminus{4} \). For \(x\ne 2\), the function equals (x+2). Thus the value (4), which would occur at (x=2), is not in the range.

Step 3

Exam Tip

\(x\ne 2\) पर फलन (x+2) के बराबर है। इसलिए (x=2) से मिलने वाला मान (4) परिसर में नहीं आता।

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Question 8/9 Hard Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 31

यदि (f(x)=\frac{x-2-4}{x-2}) और \(x\ne 2\) है तो परिसर क्या है?

If (f(x)=\frac{x-2-4}{x-2}) and \(x\ne 2\), what is the range?

Explanation opens after your attempt
Correct Answer

A. \(\mathbb{R}\setminus{4}\)

Step 1

Concept

Simplification gives (f(x)=x+2), but (x=2) is excluded. Therefore (y=4) is removed from the range.

Step 2

Why this answer is correct

The correct answer is A. \(\mathbb{R}\setminus{4}\). Simplification gives (f(x)=x+2), but (x=2) is excluded. Therefore (y=4) is removed from the range.

Step 3

Exam Tip

सरलीकरण से (f(x)=x+2) मिलता है पर (x=2) हटाया गया है। इसलिए (y=4) परिसर से हटेगा।

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Question 9/9 Hard Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 31

यदि (f(x)=\frac{x-2-1}{x-1}) और \(x\ne 1\) है तो (f) का परिसर क्या है?

If (f(x)=\frac{x-2-1}{x-1}) and \(x\ne 1\), what is the range of (f)?

Explanation opens after your attempt
Correct Answer

A. \(\mathbb{R}\setminus{2}\)

Step 1

Concept

Here (f(x)=x+1), but (x=1) is not allowed, so (y=2) is not obtained. After simplification, always track excluded domain values.

Step 2

Why this answer is correct

The correct answer is A. \(\mathbb{R}\setminus{2}\). Here (f(x)=x+1), but (x=1) is not allowed, so (y=2) is not obtained. After simplification, always track excluded domain values.

Step 3

Exam Tip

(f(x)=x+1) है पर (x=1) अनुमत नहीं है इसलिए (y=2) नहीं मिलेगा। सरलीकरण के बाद हटाए गए प्रांत मान का प्रभाव जरूर देखें।

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