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Mathematics Functions MCQ Questions for Class 12 General

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Question 171/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f(x)=\frac{x-2}{x+2}), तो कौन-सा मान (f) के परास में नहीं आएगा?

If (f(x)=\frac{x-2}{x+2}), which value will not be in the range of (f)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

\(y=\frac{x-2}{x+2}\) लिखें। / Write \(y=\frac{x-2}{x+2}\).

Step 2

Why this answer is correct

(y(x+2)=x-2) से (x(y-1)=-2-2y) मिलता है। / From (y(x+2)=x-2), we get (x(y-1)=-2-2y).

Step 3

Exam Tip

(y=1) रखने पर असंभव स्थिति बनती है, इसलिए (1) परास में नहीं है। / Putting (y=1) leads to an impossible statement, so (1) is not in the range.

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Question 172/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f(x)=\frac{x-2}{x+2}), तो वास्तविक परास क्या होगा?

If (f(x)=\frac{x-2}{x+2}), what is the real range?

Explanation opens after your attempt

Correct Answer

A. (R-{1})

Step 1

Concept

\(y=\frac{x-2}{x+2}\) मानें। / Let \(y=\frac{x-2}{x+2}\).

Step 2

Why this answer is correct

हल करने पर (x=\frac{-2(1+y)}{y-1}) मिलता है, जो \(y\ne1\) पर संभव है। / Solving gives (x=\frac{-2(1+y)}{y-1}), which is possible when \(y\ne1\).

Step 3

Exam Tip

इसलिए (1) को छोड़कर सभी वास्तविक मान परास में आते हैं। / Hence all real values except (1) are in the range.

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Question 173/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f(x)=x^-2) और प्रान्त ({-3,-2,-1,0,1,2,3}) है, तो परास में कितने अवयव होंगे?

If (f(x)=x^-2) and the domain is ({-3,-2,-1,0,1,2,3}), how many elements are in the range?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

दिए गए अवयवों के वर्ग (9,4,1,0,1,4,9) हैं। / The squares of the given elements are (9,4,1,0,1,4,9).

Step 2

Why this answer is correct

परास में दोहराए हुए मान एक बार लिखे जाते हैं। / Repeated values are written only once in the range.

Step 3

Exam Tip

परास ({0,1,4,9}) है, इसलिए (4) अवयव हैं। / The range is ({0,1,4,9}), so it has (4) elements.

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Question 174/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि \(f:A\to B\), \(A=\{1,2,3,4\}\), \(B=\{a,b\}\), और \(f=\{(1,a),(2,a),(3,b),(4,b)\}\), तो (f) कैसा है?

If \(f:A\to B\), \(A=\{1,2,3,4\}\), \(B=\{a,b\}\), and \(f=\{(1,a),(2,a),(3,b),(4,b)\}\), what type of function is (f)?

Explanation opens after your attempt

Correct Answer

A. आच्छादक पर एक-एकी नहींOnto but not one-one

Step 1

Concept

(a) और (b) दोनों छवि के रूप में मिलते हैं, इसलिए फलन आच्छादक है। / Both (a) and (b) appear as images, so the function is onto.

Step 2

Why this answer is correct

(1) और (2) दोनों (a) पर जाते हैं, इसलिए एक-एकी नहीं है। / Both (1) and (2) map to (a), so it is not one-one.

Step 3

Exam Tip

आच्छादक और एक-एकी को अलग-अलग जाँचना चाहिए। / Onto and one-one should be checked separately.

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Question 175/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f(x)=x^-2+1) और (g(x)=\sqrt{x-1}), तो (\(g\circ f\)(x)) क्या होगा?

If (f(x)=x^-2+1) and (g(x)=\sqrt{x-1}), what is (\(g\circ f\)(x))?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{x^2}\)

Step 1

Concept

(\(g\circ f\)(x)=g(f(x))) है। / (\(g\circ f\)(x)=g(f(x))).

Step 2

Why this answer is correct

(g) में (x) के स्थान पर \(x^2+1\) रखें। / Put \(x^2+1\) in place of (x) in (g).

Step 3

Exam Tip

(g(f(x))=\sqrt{\(x^2+1\)-1}=\sqrt{x^-2})। / (g(f(x))=\sqrt{\(x^2+1\)-1}=\sqrt{x^-2}).

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Question 176/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि \(f:R\to R\), (f(x)=x^-3), तो (f^{-1}(x)) क्या होगा?

If \(f:R\to R\), (f(x)=x^-3), what is (f^{-1}(x))?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt[3]{x}\)

Step 1

Concept

\(y=x^3\) लिखें। / Write \(y=x^3\).

Step 2

Why this answer is correct

\(x=\sqrt[3]{y}\) मिलेगा। / Then \(x=\sqrt[3]{y}\).

Step 3

Exam Tip

(y) को (x) से बदलने पर (f^{-1}(x)=\sqrt[3]{x})। / Replacing (y) by (x), (f^{-1}(x)=\sqrt[3]{x}).

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Question 177/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि \(f:[0,\infty\)\to[0,\infty)), (f(x)=x^-2), तो (f^{-1}(9)) क्या होगा?

If \(f:[0,\infty\)\to[0,\infty)), (f(x)=x^-2), what is (f^{-1}(9))?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

(f^{-1}(9)) के लिए \(x^2=9\) हल करें। / To find (f^{-1}(9)), solve \(x^2=9\).

Step 2

Why this answer is correct

वास्तविक हल (x=3) और (x=-3) होते हैं। / The real solutions are (x=3) and (x=-3).

Step 3

Exam Tip

प्रान्त \([0,\infty\)) है, इसलिए केवल (3) मान्य है। / Since the domain is \([0,\infty\)), only (3) is valid.

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Question 178/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि \(f:R\to R\), (f(x)=x^-2), तो (f^{-1}({4})) क्या होगा?

If \(f:R\to R\), (f(x)=x^-2), what is (f^{-1}({4}))?

Explanation opens after your attempt

Correct Answer

A. ({-2,2})

Step 1

Concept

पूर्वछवि के लिए \(x^2=4\) हल करें। / For the preimage, solve \(x^2=4\).

Step 2

Why this answer is correct

इससे (x=2) या (x=-2) मिलता है। / This gives (x=2) or (x=-2).

Step 3

Exam Tip

इसलिए (f^{-1}({4})={-2,2}) है। / Therefore (f^{-1}({4})={-2,2}).

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Question 179/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f(x)=x^-2-3x+2), तो (f(0), f(1), f(2)) में से कौन-से मान शून्य हैं?

If (f(x)=x^-2-3x+2), which of (f(0), f(1), f(2)) are zero?

Explanation opens after your attempt

Correct Answer

A. (f(1)) और (f(2))(f(1)) and (f(2))

Step 1

Concept

(f(x)=x^-2-3x+2=(x-1)(x-2))। / (f(x)=x^-2-3x+2=(x-1)(x-2)).

Step 2

Why this answer is correct

(x=1) और (x=2) पर गुणनफल शून्य होगा। / At (x=1) and (x=2), the product becomes zero.

Step 3

Exam Tip

(x=0) पर (f(0)=2), इसलिए वह शून्य नहीं है। / At (x=0), (f(0)=2), so it is not zero.

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Question 180/574 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि \(f:R\to R\), (f(x)=|x|+2), तो परास क्या होगा?

If \(f:R\to R\), (f(x)=|x|+2), what is the range?

Explanation opens after your attempt

Correct Answer

A. \([2,\infty\))

Step 1

Concept

\(|x|\ge0\) हर वास्तविक (x) के लिए। / \(|x|\ge0\) for every real (x).

Step 2

Why this answer is correct

इसलिए \(|x|+2\ge2\)। / Therefore \(|x|+2\ge2\).

Step 3

Exam Tip

(x=0) पर न्यूनतम मान (2) मिलता है, अतः परास \([2,\infty\)) है। / At (x=0), the minimum value (2) is obtained, so the range is \([2,\infty\)).

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Mathematics Functions MCQ Questions for Class 12 General

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यदि (f(x)=\frac{x-2}{x+2}), तो कौन-सा मान (f) के परास में नहीं आएगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=\frac{x-2}{x+2}), तो वास्तविक परास क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2) और प्रान्त ({-3,-2,-1,0,1,2,3}) है, तो परास में कितने अवयव होंगे?

Concept

Why this answer is correct

Exam Tip

यदि \(f:A\to B\), \(A=\{1,2,3,4\}\), \(B=\{a,b\}\), और \(f=\{(1,a),(2,a),(3,b),(4,b)\}\), तो (f) कैसा है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2+1) और (g(x)=\sqrt{x-1}), तो (\(g\circ f\)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(f:R\to R\), (f(x)=x-3), तो (f^{-1}(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(f:[0,\infty\)\to[0,\infty)), (f(x)=x-2), तो (f^{-1}(9)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(f:R\to R\), (f(x)=x-2), तो (f^{-1}({4})) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2-3x+2), तो (f(0), f(1), f(2)) में से कौन-से मान शून्य हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(f:R\to R\), (f(x)=|x|+2), तो परास क्या होगा?

Concept

Why this answer is correct

Exam Tip

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यदि (f(x)=x^-2) और प्रान्त ({-3,-2,-1,0,1,2,3}) है, तो परास में कितने अवयव होंगे?

यदि (f(x)=x^-2+1) और (g(x)=\sqrt{x-1}), तो (\(g\circ f\)(x)) क्या होगा?

यदि \(f:R\to R\), (f(x)=x^-3), तो (f^{-1}(x)) क्या होगा?

यदि \(f:[0,\infty\)\to[0,\infty)), (f(x)=x^-2), तो (f^{-1}(9)) क्या होगा?

यदि \(f:R\to R\), (f(x)=x^-2), तो (f^{-1}({4})) क्या होगा?

यदि (f(x)=x^-2-3x+2), तो (f(0), f(1), f(2)) में से कौन-से मान शून्य हैं?