Class 11 Mathematics - Relations and Functions - Functions as a special kind of relation Hard Quiz

Mathematics Relations and Functions Functions as a special kind of relation Hard Class 11 Level 24

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Question 1/8 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 24

यदि \(A=\{2,3,4\}\) और \(B=\{6,8,9,12\}\) हैं, तो \(A\times B\) में कितने युग्म ((a,b)) ऐसे हैं जिनमें (a) (b) को विभाजित करता है?

If \(A=\{2,3,4\}\) and \(B=\{6,8,9,12\}\), how many pairs ((a,b)) in \(A\times B\) have (a) dividing (b)?

Explanation opens after your attempt

Correct Answer

B. (7)

Explanation

Simple Explanation

(a=2,3,4) के लिए (b) के क्रमशः (3,3,1) मान मिलते हैं, कुल (7)। विभाज्यता में प्रत्येक भाजक अलग जाँचें। / For (a=2,3,4), the counts of (b) are (3,3,1), totaling (7). Check each divisor separately.

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Question 2/8 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 24

यदि (|A|=4), (|B|=5) और \(R\subseteq A\times B\), तो (R) में ठीक (2) अवयव चुनने के कितने तरीके हैं?

If (|A|=4), (|B|=5), and \(R\subseteq A\times B\), in how many ways can (R) have exactly (2) elements?

Explanation opens after your attempt

Correct Answer

C. (190)

Explanation

Simple Explanation

\(|A\times B|=20\), इसलिए ठीक (2) युग्म चुनने के तरीके \(\binom{20}{2}=190\) हैं। ठीक संख्या पूछी हो तो संयोजन लगाएँ। / Since \(|A\times B|=20\), the number of ways to choose exactly (2) pairs is \(\binom{20}{2}=190\). Use combinations for exact-size subsets.

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Question 3/8 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 24

यदि (|A|=3) और (|B|=5) हैं, तो (A) से (B) तक संभव संबंधों की संख्या क्या है?

If (|A|=3) and (|B|=5), what is the number of possible relations from (A) to (B)?

Explanation opens after your attempt

Correct Answer

C. (32768)

Explanation

Simple Explanation

संबंध \(A\times B\) का उपसमुच्चय है और \(|A\times B|=15\), इसलिए संख्या \(2^{15}=32768\) है। संबंधों की संख्या के लिए (2) की घात लगती है। / A relation is a subset of \(A\times B\), and \(|A\times B|=15\), so the number is \(2^{15}=32768\). Number of relations uses a power of (2).

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Question 4/8 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 24

यदि \(A=\{1,2,3,4,5\}\) और \(B=\{3,6,9,12\}\) हैं, तो \(A\times B\) में कितने युग्म ((a,b)) ऐसे हैं जिनमें (b=3a) है?

If \(A=\{1,2,3,4,5\}\) and \(B=\{3,6,9,12\}\), how many pairs ((a,b)) in \(A\times B\) satisfy (b=3a)?

Explanation opens after your attempt

Correct Answer

C. (4)

Explanation

Simple Explanation

(a=1,2,3,4) पर (b=3,6,9,12) मिलता है, पर (a=5) पर \(15\notin B\)। इसलिए (4) युग्म हैं। / For (a=1,2,3,4), we get (b=3,6,9,12), but for (a=5), \(15\notin B\). Hence there are (4) pairs.

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Question 5/8 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 24

यदि \(A=\{1,2,3,4,5\}\) और \(B=\{1,2,3,4,5,6\}\) हैं, तो \(A\times B\) में कितने युग्म ((a,b)) ऐसे हैं जिनमें (b) (a) का गुणज है?

If \(A=\{1,2,3,4,5\}\) and \(B=\{1,2,3,4,5,6\}\), how many pairs ((a,b)) in \(A\times B\) have (b) as a multiple of (a)?

Explanation opens after your attempt

Correct Answer

C. (14)

Explanation

Simple Explanation

(a=1,2,3,4,5) के लिए (b) के (6,3,2,1,1) मान हैं, कुल (13)। हर (a) के गुणज (B) में गिनें। / For (a=1,2,3,4,5), the counts of (b) are (6,3,2,1,1), totaling (13). Count multiples of each (a) inside (B).

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Question 6/8 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 24

यदि \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4\}\) और \(R=\{(a,b):a+b=5\}\), तो (R) में कितने अवयव हैं?

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

Explanation opens after your attempt

Correct Answer

C. (4)

Explanation

Simple Explanation

शर्त से ((1,4),(2,3),(3,2),(4,1)) मिलते हैं, इसलिए (4) अवयव हैं। संबंध \(A\times B\) का उपसमुच्चय होता है। / The condition gives ((1,4),(2,3),(3,2),(4,1)), so there are (4) elements. A relation is a subset of \(A\times B\).

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Question 7/8 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 24

यदि \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4\}\) और \(R=\{(a,b):a\le b\}\), तो (R) में कितने अवयव हैं?

If \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4\}\), and \(R=\{(a,b):a\le b\}\), how many elements are in (R)?

Explanation opens after your attempt

Correct Answer

C. (10)

Explanation

Simple Explanation

(a=1,2,3,4) के लिए (b) के (4,3,2,1) मान मिलते हैं, कुल (10)। \(\le\) में बराबरी शामिल होती है। / For (a=1,2,3,4), the counts of (b) are (4,3,2,1), totaling (10). The symbol \(\le\) includes equality.

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Question 8/8 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 24

यदि \(A=\{1,2,3,4\}\), \(B=\{2,3,4,5,6\}\) और \(S=\{(a,b):b>a+2\}\) है, तो \(S\subseteq A\times B\) में कितने अवयव हैं?

If \(A=\{1,2,3,4\}\), \(B=\{2,3,4,5,6\}\), and \(S=\{(a,b):b>a+2\}\), how many elements are in \(S\subseteq A\times B\)?

Explanation opens after your attempt

Correct Answer

B. (6)

Explanation

Simple Explanation

(a=1,2,3,4) के लिए (b) के क्रमशः (3,2,1,0) मान मिलते हैं, कुल (6)। शर्त को हर पहले अवयव पर लगाएँ। / For (a=1,2,3,4), the counts of (b) are (3,2,1,0), totaling (6). Apply the condition to each first component.

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Class 11 Mathematics - Relations and Functions - Functions as a special kind of relation Hard Quiz

यदि \(A=\{2,3,4\}\) और \(B=\{6,8,9,12\}\) हैं, तो \(A\times B\) में कितने युग्म ((a,b)) ऐसे हैं जिनमें (a) (b) को विभाजित करता है?

Simple Explanation

यदि (|A|=4), (|B|=5) और \(R\subseteq A\times B\), तो (R) में ठीक (2) अवयव चुनने के कितने तरीके हैं?

Simple Explanation

यदि (|A|=3) और (|B|=5) हैं, तो (A) से (B) तक संभव संबंधों की संख्या क्या है?

Simple Explanation

यदि \(A=\{1,2,3,4,5\}\) और \(B=\{3,6,9,12\}\) हैं, तो \(A\times B\) में कितने युग्म ((a,b)) ऐसे हैं जिनमें (b=3a) है?

Simple Explanation

यदि \(A=\{1,2,3,4,5\}\) और \(B=\{1,2,3,4,5,6\}\) हैं, तो \(A\times B\) में कितने युग्म ((a,b)) ऐसे हैं जिनमें (b) (a) का गुणज है?

Simple Explanation

यदि \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4\}\) और \(R=\{(a,b):a+b=5\}\), तो (R) में कितने अवयव हैं?

Simple Explanation

यदि \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4\}\) और \(R=\{(a,b):a\le b\}\), तो (R) में कितने अवयव हैं?

Simple Explanation

यदि \(A=\{1,2,3,4\}\), \(B=\{2,3,4,5,6\}\) और \(S=\{(a,b):b>a+2\}\) है, तो \(S\subseteq A\times B\) में कितने अवयव हैं?

Simple Explanation

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