Class 11 Mathematics - Relations And Functions - Functions as a special kind of relation Medium Quiz

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यदि \(A=\{1,2,3\}\) और \(B=\{1,4,9\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि \(y=x^2\)?

If \(A=\{1,2,3\}\) and \(B=\{1,4,9\}\), how many pairs ((x,y)) in \(A\times B\) satisfy \(y=x^2\)?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

The valid pairs are ((1,1),(2,4),(3,9)). In a Cartesian product, applying a condition forms a subset relation.

Step 2

Why this answer is correct

The correct answer is A. (3). The valid pairs are ((1,1),(2,4),(3,9)). In a Cartesian product, applying a condition forms a subset relation.

Step 3

Exam Tip

सही युग्म ((1,1),(2,4),(3,9)) हैं। कार्तीय गुणन में दिए संबंध की शर्त लगाकर उपसमुच्चय बनाया जाता है।

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यदि \(A=\{1,2\}\) और \(B=\{3,4,5\}\) हैं, तो \(A\times B\) का कौन सा उपसमुच्चय एक संबंध हो सकता है?

If \(A=\{1,2\}\) and \(B=\{3,4,5\}\), which subset of \(A\times B\) can be a relation?

Explanation opens after your attempt
Correct Answer

A. ({(1,3),(2,5)})

Step 1

Concept

A relation from (A) to (B) is any subset of \(A\times B\). Only ({(1,3),(2,5)}) has both pairs in \(A\times B\).

Step 2

Why this answer is correct

The correct answer is A. ({(1,3),(2,5)}). A relation from (A) to (B) is any subset of \(A\times B\). Only ({(1,3),(2,5)}) has both pairs in \(A\times B\).

Step 3

Exam Tip

(A) से (B) में संबंध \(A\times B\) का कोई भी उपसमुच्चय होता है। केवल ({(1,3),(2,5)}) के दोनों युग्म \(A\times B\) में हैं।

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यदि (A) में (3) अवयव और (B) में (2) अवयव हैं, तो (A) से (B) तक कुल कितने संबंध संभव हैं?

If (A) has (3) elements and (B) has (2) elements, how many relations are possible from (A) to (B)?

Explanation opens after your attempt
Correct Answer

A. \(2^6\)

Step 1

Concept

(n\(A\times B\)=3\times2=6), and every relation is a subset of \(A\times B\). Therefore the number of relations is \(2^6\).

Step 2

Why this answer is correct

The correct answer is A. \(2^6\). (n\(A\times B\)=3\times2=6), and every relation is a subset of \(A\times B\). Therefore the number of relations is \(2^6\).

Step 3

Exam Tip

(n\(A\times B\)=3\times2=6), और हर संबंध \(A\times B\) का उपसमुच्चय है। इसलिए संबंधों की संख्या \(2^6\) होगी।

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यदि \(A=\{1,2,3\}\) और \(B=\{a\}\) हैं, तो (A) से (B) तक कुल संबंधों की संख्या कितनी है?

If \(A=\{1,2,3\}\) and \(B=\{a\}\), how many relations are possible from (A) to (B)?

Explanation opens after your attempt
Correct Answer

A. (8)

Step 1

Concept

(n\(A\times B\)=3\times1=3), so the number of subsets is \(2^3=8\). For counting relations, remember \(2^{n(A\times B)}\).

Step 2

Why this answer is correct

The correct answer is A. (8). (n\(A\times B\)=3\times1=3), so the number of subsets is \(2^3=8\). For counting relations, remember \(2^{n(A\times B)}\).

Step 3

Exam Tip

(n\(A\times B\)=3\times1=3), इसलिए उपसमुच्चयों की संख्या \(2^3=8\) है। संबंध गिनने में \(2^{n(A\times B)}\) याद रखें।

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