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

Mathematics Relations And Functions Functions as a special kind of relation Expert Class 11 Level 22

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Question 1/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि (|A|=2) और (|B|=5) हैं, तो \(A\times B\) के ठीक (5) अवयवों वाले उपसमुच्चयों की संख्या क्या है?

If (|A|=2) and (|B|=5), what is the number of subsets of \(A\times B\) having exactly (5) elements?

Explanation opens after your attempt
Correct Answer

C. (252)

Step 1

Concept

\(|A\times B|=10\), so choosing exactly (5) pairs gives \(\binom{10}{5}=252\). Use combinations for exact-size subsets.

Step 2

Why this answer is correct

The correct answer is C. (252). \(|A\times B|=10\), so choosing exactly (5) pairs gives \(\binom{10}{5}=252\). Use combinations for exact-size subsets.

Step 3

Exam Tip

\(|A\times B|=10\), इसलिए ठीक (5) युग्म चुनने के तरीके \(\binom{10}{5}=252\) हैं। ठीक संख्या के लिए संयोजन लगाएँ।

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Question 2/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{2,3,4,5,6,7,8\}\), \(B=\{1,2,3,4,5\}\) और \(R=\{(a,b):a+3b=17\}\) है, तो (|R|) क्या है?

If \(A=\{2,3,4,5,6,7,8\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):a+3b=17\}\), what is (|R|)?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

The condition gives ((8,3)) and ((5,4)), so (|R|=2). Check possible (b)-values systematically.

Step 2

Why this answer is correct

The correct answer is B. (2). The condition gives ((8,3)) and ((5,4)), so (|R|=2). Check possible (b)-values systematically.

Step 3

Exam Tip

शर्त से ((8,3)) और ((5,4)) मिलते हैं, इसलिए (|R|=2)। समीकरण में (b) के संभावित मान व्यवस्थित रूप से जाँचें।

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Question 3/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{0,1,2,3\}\), \(B=\{0,1,2,3,4\}\) और \(R=\{(a,b):b\ge a^2-1\}\) है, तो (|R|) क्या है?

If \(A=\{0,1,2,3\}\), \(B=\{0,1,2,3,4\}\), and \(R=\{(a,b):b\ge a^2-1\}\), what is (|R|)?

Explanation opens after your attempt
Correct Answer

B. (12)

Step 1

Concept

For (a=0,1,2,3), the counts of (b) are (5,5,2,0), totaling (12). Check the boundary separately for each (a).

Step 2

Why this answer is correct

The correct answer is B. (12). For (a=0,1,2,3), the counts of (b) are (5,5,2,0), totaling (12). Check the boundary separately for each (a).

Step 3

Exam Tip

(a=0,1,2,3) के लिए (b) के क्रमशः (5,5,2,0) मान मिलते हैं, कुल (12)। हर (a) पर सीमा अलग जाँचें।

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Question 4/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4,5\}\) और \(R=\{(a,b):a^2<b\}\) है, तो (|R|) क्या है?

If \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):a^2<b\}\), what is (|R|)?

Explanation opens after your attempt
Correct Answer

A. (5)

Step 1

Concept

For (a=1), there are (4) values, and for (a=2), there is (1); none for the rest. Total is (5).

Step 2

Why this answer is correct

The correct answer is A. (5). For (a=1), there are (4) values, and for (a=2), there is (1); none for the rest. Total is (5).

Step 3

Exam Tip

(a=1) पर (4) और (a=2) पर (1) मान मिलते हैं, बाकी पर कोई नहीं। कुल (5) युग्म हैं।

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Question 5/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\) और \(R=\{(a,b):a+b=7\}\) है, तो \(R^{-1}\) में कौन सा युग्म अवश्य होगा?

If \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):a+b=7\}\), which pair must be in \(R^{-1}\)?

Explanation opens after your attempt
Correct Answer

C. ((5,2))

Step 1

Concept

Since \((2,5)\in R\), we have \((5,2)\in R^{-1}\). In an inverse relation, the order reverses.

Step 2

Why this answer is correct

The correct answer is C. ((5,2)). Since \((2,5)\in R\), we have \((5,2)\in R^{-1}\). In an inverse relation, the order reverses.

Step 3

Exam Tip

क्योंकि \((2,5)\in R\), इसलिए \((5,2)\in R^{-1}\)। प्रतिलोम संबंध में क्रम उलटता है।

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Question 6/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\) और \(R=\{(a,b):a+b\le6\}\) है, तो (R) में ऐसे कितने युग्म हैं जिनमें (a) सम है?

If \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):a+b\le6\}\), how many pairs in (R) have (a) even?

Explanation opens after your attempt
Correct Answer

B. (6)

Step 1

Concept

For even (a), (a=2) gives (4) values and (a=4) gives (2). Total is (6) pairs.

Step 2

Why this answer is correct

The correct answer is B. (6). For even (a), (a=2) gives (4) values and (a=4) gives (2). Total is (6) pairs.

Step 3

Exam Tip

सम (a) के लिए (a=2) पर (4) और (a=4) पर (2) मान मिलते हैं। कुल (6) युग्म हैं।

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Question 7/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

\(यदि (A={1,2,3,4}), (B={1,2,3,4}) और (R={(a,b):a+b\) is odd}) है, तो (R) के उपसमुच्चयों की संख्या क्या है?

\(If (A={1,2,3,4}), (B={1,2,3,4}), and (R={(a,b):a+b\) is odd}), what is the number of subsets of (R)?

Explanation opens after your attempt
Correct Answer

B. (256)

Step 1

Concept

There are (8) pairs with odd sum, so subsets of (R) are \(2^8=256\). First find the cardinality of the relation.

Step 2

Why this answer is correct

The correct answer is B. (256). There are (8) pairs with odd sum, so subsets of (R) are \(2^8=256\). First find the cardinality of the relation.

Step 3

Exam Tip

विषम योग वाले युग्म (8) हैं, इसलिए (R) के उपसमुच्चय \(2^8=256\) हैं। पहले संबंध की कार्डिनलिटी निकालें।

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Question 8/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{0,1,2,3,4\}\), \(B=\{0,1,2,3,4\}\) और (R={(a,b):\(a^2\equiv b \pmod{5}\)}) है, तो (|R|) क्या है?

If \(A=\{0,1,2,3,4\}\), \(B=\{0,1,2,3,4\}\), and (R={(a,b):\(a^2\equiv b \pmod{5}\)}), what is (|R|)?

Explanation opens after your attempt
Correct Answer

C. (5)

Step 1

Concept

For each (a), exactly one residue for (b) appears in (B). Therefore there are (5) pairs.

Step 2

Why this answer is correct

The correct answer is C. (5). For each (a), exactly one residue for (b) appears in (B). Therefore there are (5) pairs.

Step 3

Exam Tip

प्रत्येक (a) के लिए (b) का ठीक एक अवशेष (B) में मिलता है। इसलिए कुल (5) युग्म हैं।

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Question 9/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\) और \(R=\{(a,b):a+b=6\}\) है, तो \(R\circ R\) में कितने युग्म होंगे?

If \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):a+b=6\}\), how many pairs are in \(R\circ R\)?

Explanation opens after your attempt
Correct Answer

B. (5)

Step 1

Concept

For each (x), (R) maps it to (6-x) and then back to (x). Thus \(R\circ R={(x,x):x\in A}\) has (5) pairs.

Step 2

Why this answer is correct

The correct answer is B. (5). For each (x), (R) maps it to (6-x) and then back to (x). Thus \(R\circ R={(x,x):x\in A}\) has (5) pairs.

Step 3

Exam Tip

हर (x) के लिए (R) उसे (6-x) से और फिर वापस (x) से जोड़ता है। इसलिए \(R\circ R={(x,x):x\in A}\) में (5) युग्म हैं।

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Question 10/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\) और \(R=\{(a,b):a<b\}\) है, तो \(R^{-1}\cap R\) में कितने युग्म होंगे?

If \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):a<b\}\), how many pairs are in \(R^{-1}\cap R\)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

\(R^{-1}\) has the condition (a>b), which cannot hold together with (a<b). Therefore the intersection is empty.

Step 2

Why this answer is correct

The correct answer is A. (0). \(R^{-1}\) has the condition (a>b), which cannot hold together with (a<b). Therefore the intersection is empty.

Step 3

Exam Tip

\(R^{-1}\) में (a>b) वाली शर्त होगी, जो (a<b) के साथ एक साथ संभव नहीं है। इसलिए प्रतिच्छेद रिक्त है।

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Question 11/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4,5\}\) और \(R=\{(a,b):b-a\in{0,2}\}\) है, तो (|R|) क्या है?

If \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):b-a\in{0,2}\}\), what is (|R|)?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

The condition (b-a=0) gives (4) pairs and (b-a=2) gives (3). The total is (7) pairs.

Step 2

Why this answer is correct

The correct answer is B. (7). The condition (b-a=0) gives (4) pairs and (b-a=2) gives (3). The total is (7) pairs.

Step 3

Exam Tip

(b-a=0) से (4) और (b-a=2) से (3) युग्म मिलते हैं। कुल (7) युग्म हैं।

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Question 12/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4\}\) और \(R=\{(a,b):a+b\le5\}\) है, तो (R) में कितने युग्म ऐसे हैं जिनका प्रतिलोम युग्म भी (R) में है?

If \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4\}\), and \(R=\{(a,b):a+b\le5\}\), how many pairs in (R) have their inverse pair also in (R)?

Explanation opens after your attempt
Correct Answer

C. (10)

Step 1

Concept

The condition \(a+b\le5\) remains the same after reversal, so all (10) pairs of (R) qualify. Recognize symmetric conditions.

Step 2

Why this answer is correct

The correct answer is C. (10). The condition \(a+b\le5\) remains the same after reversal, so all (10) pairs of (R) qualify. Recognize symmetric conditions.

Step 3

Exam Tip

शर्त \(a+b\le5\) उलटने पर भी वही रहती है, इसलिए (R) के सभी (10) युग्म योग्य हैं। सममित शर्त को पहचानें।

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Question 13/13 Expert Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{1,2,3,4,5,6\}\) और \(R=\{(a,b):a+b=7\}\) है, तो (R) के कितने उपसमुच्चय कम से कम एक युग्म रखते हैं जिसका पहला अवयव (1) है?

If \(A=\{1,2,3,4,5,6\}\), \(B=\{1,2,3,4,5,6\}\), and \(R=\{(a,b):a+b=7\}\), how many subsets of (R) contain at least one pair whose first component is (1)?

Explanation opens after your attempt
Correct Answer

B. (32)

Step 1

Concept

There are (6) pairs in (R), and only ((1,6)) has first component (1). It must be included, so the other (5) pairs are free, giving \(2^5=32\).

Step 2

Why this answer is correct

The correct answer is B. (32). There are (6) pairs in (R), and only ((1,6)) has first component (1). It must be included, so the other (5) pairs are free, giving \(2^5=32\).

Step 3

Exam Tip

(R) में (6) युग्म हैं और पहला अवयव (1) वाला केवल ((1,6)) है। उसे रखना होगा, इसलिए बाकी (5) युग्म स्वतंत्र हैं और संख्या \(2^5=32\) है।

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