Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है • Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है • Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है
Mathematics Relations And Functions MCQ Questions for Class 11 Science
Related questions grouped automatically for chapter-wise practice. Topics include Algebra of real functions, Cartesian product of sets, Functions as a special kind of relation, Graphs of standard functions, Real valued functions, domain and range of these functions.
Class 11 Science Mathematics Relations And Functions Practice
Related questions grouped automatically for chapter-wise practice.
Practice Relations And Functions MCQs with instant answer feedback and easy explanations.
Use topic chips to revise important subtopics before starting the timed quiz.
Open individual question pages for shareable answers, explanations and related MCQs.
Relations And Functions - Topics Covered
Mathematics Relations And Functions ke topic-wise MCQs yahan grouped context me milenge. jo aap ko Exam ki preparation me madad milegi. Ye questions exam-oriented hai and students ko concept clarity, quick revision aur board exam preparation kaafi madad karenge. Sabhi se jude MCQs important topics ke anusar arranged hai, taaki aap Relations And Functions ko easy tarike se practice aur revise kar sake.
Algebra of real functions
600 MCQs
Cartesian product of sets
600 MCQs
Functions as a special kind of relation
600 MCQs
Graphs of standard functions
600 MCQs
Real valued functions, domain and range of these functions
600 MCQs
Relations
600 MCQs
Start Relations And Functions Quiz
Difficulty select karke Mathematics / Relations And Functions chapter-filtered timed practice karein. Har button me live question count show hoga.
A. (A) और (B) के सभी क्रमित युग्म/All ordered pairs of (A) and (B)
Step 1
Concept
In \(A\times B\), the first component comes from (A) and the second from (B). In exams, always check the order of the pair.
Step 2
Why this answer is correct
The correct answer is A. (A) और (B) के सभी क्रमित युग्म / All ordered pairs of (A) and (B). In \(A\times B\), the first component comes from (A) and the second from (B). In exams, always check the order of the pair.
Step 3
Exam Tip
\(A\times B\) में पहला घटक (A) से और दूसरा घटक (B) से आता है। परीक्षा में क्रमित युग्म का क्रम जरूर देखें।
There is no element in (A) for the first component, so no ordered pair is formed. Pay special attention to the empty set.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). There is no element in (A) for the first component, so no ordered pair is formed. Pay special attention to the empty set.
Step 3
Exam Tip
पहले घटक के लिए (A) में कोई तत्व नहीं है, इसलिए कोई क्रमित युग्म नहीं बनेगा। खाली समुच्चय पर विशेष ध्यान दें।
A. हां, क्योंकि \(2\in A\) और \(3\in B\)/Yes, because \(2\in A\) and \(3\in B\)
Step 1
Concept
In ((2,3)), the first component (2) is in (A) and the second (3) is in (B). Check both positions separately for membership.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि \(2\in A\) और \(3\in B\) / Yes, because \(2\in A\) and \(3\in B\). In ((2,3)), the first component (2) is in (A) and the second (3) is in (B). Check both positions separately for membership.
Step 3
Exam Tip
((2,3)) में पहला घटक (2) है जो (A) में है और दूसरा (3) है जो (B) में है। सदस्यता जांचते समय दोनों स्थान अलग-अलग जांचें।
A. \(p\in A\) और \(q\in B\)/\(p\in A\) and \(q\in B\)
Step 1
Concept
In \(A\times B\), the first component of an ordered pair is from (A) and the second is from (B). This rule solves most membership questions.
Step 2
Why this answer is correct
The correct answer is A. \(p\in A\) और \(q\in B\) / \(p\in A\) and \(q\in B\). In \(A\times B\), the first component of an ordered pair is from (A) and the second is from (B). This rule solves most membership questions.
Step 3
Exam Tip
\(A\times B\) में क्रमित युग्म का पहला घटक (A) से और दूसरा (B) से होता है। इसी नियम से अधिकतर सदस्यता प्रश्न हल होते हैं।
B. \(A\times B\) और \(B\times A\) सामान्यतः समान नहीं होते/\(A\times B\) and \(B\times A\) are generally not equal
Step 1
Concept
Order matters in Cartesian product, so \(A\times B\) is generally different from \(B\times A\). Reversed order is a common exam mistake.
Step 2
Why this answer is correct
The correct answer is B. \(A\times B\) और \(B\times A\) सामान्यतः समान नहीं होते / \(A\times B\) and \(B\times A\) are generally not equal. Order matters in Cartesian product, so \(A\times B\) is generally different from \(B\times A\). Reversed order is a common exam mistake.
Step 3
Exam Tip
कार्तीय गुणन में क्रम महत्वपूर्ण है, इसलिए \(A\times B\) सामान्यतः \(B\times A\) से अलग होता है। परीक्षा में उल्टा क्रम गलती कराता है।
\(A\times B={(1,1),(1,2)}\) and \(B\times A={(1,1),(2,1)}\). Similar looking numbers do not remove the importance of order.
Step 2
Why this answer is correct
The correct answer is B. \(A\times B\ne B\times A\). \(A\times B={(1,1),(1,2)}\) and \(B\times A={(1,1),(2,1)}\). Similar looking numbers do not remove the importance of order.
Step 3
Exam Tip
\(A\times B={(1,1),(1,2)}\) और \(B\times A={(1,1),(2,1)}\) हैं। केवल दिखने में समान संख्याएं होने से क्रम नहीं बदलता।
In ((5,7)), the first component is (5) and the second component is (7). In Cartesian product, the first component comes from the first set.
Step 2
Why this answer is correct
The correct answer is A. (5). In ((5,7)), the first component is (5) and the second component is (7). In Cartesian product, the first component comes from the first set.
Step 3
Exam Tip
((5,7)) में पहला घटक (5) और दूसरा घटक (7) है। कार्तीय गुणन में पहला घटक पहले समुच्चय से आता है।
In ((3,5)), \(3\in A\) and \(5\in B\), so it belongs to \(A\times B\). Other options have wrong position or membership.
Step 2
Why this answer is correct
The correct answer is B. ((3,5)). In ((3,5)), \(3\in A\) and \(5\in B\), so it belongs to \(A\times B\). Other options have wrong position or membership.
Step 3
Exam Tip
((3,5)) में \(3\in A\) और \(5\in B\), इसलिए यह \(A\times B\) में है। बाकी विकल्पों में घटक का स्थान या सदस्यता गलत है।
The only element (0) of (A) stays in the first position and all elements of (B) come in the second position. Do not reverse order even for singleton sets.
Step 2
Why this answer is correct
The correct answer is A. ({(0,1),(0,2),(0,3)}). The only element (0) of (A) stays in the first position and all elements of (B) come in the second position. Do not reverse order even for singleton sets.
Step 3
Exam Tip
(A) का एकमात्र तत्व (0) पहले स्थान पर रहेगा और (B) के सभी तत्व दूसरे स्थान पर आएंगे। एकल तत्व वाले समुच्चय में भी क्रम न बदलें।
If (A) is not empty and still no pair is formed, then (B) must be empty. If a Cartesian product is empty, at least one set is empty.
Step 2
Why this answer is correct
The correct answer is A. \(B=\varnothing\). If (A) is not empty and still no pair is formed, then (B) must be empty. If a Cartesian product is empty, at least one set is empty.
Step 3
Exam Tip
यदि (A) खाली नहीं है फिर भी कोई युग्म नहीं बना, तो (B) खाली होना चाहिए। कार्तीय गुणन खाली होने पर कम से कम एक समुच्चय खाली होता है।
A. (A) से पहला घटक और (B) से दूसरा घटक वाले सभी युग्म/All pairs with first component from (A) and second component from (B)
Step 1
Concept
In \(A\times B\), the first position is filled from (A) and the second from (B). Confusing it with \(A\cup B\) is a common mistake.
Step 2
Why this answer is correct
The correct answer is A. (A) से पहला घटक और (B) से दूसरा घटक वाले सभी युग्म / All pairs with first component from (A) and second component from (B). In \(A\times B\), the first position is filled from (A) and the second from (B). Confusing it with \(A\cup B\) is a common mistake.
Step 3
Exam Tip
\(A\times B\) में पहला स्थान (A) और दूसरा स्थान (B) से भरा जाता है। इसे \(A\cup B\) समझना आम गलती है।
In \(A\times A\), every element of (A) pairs with every element of (A). Taking only equal component pairs is incomplete.
Step 2
Why this answer is correct
The correct answer is A. ({(1,1),(1,2),(2,1),(2,2)}). In \(A\times A\), every element of (A) pairs with every element of (A). Taking only equal component pairs is incomplete.
Step 3
Exam Tip
\(A\times A\) में (A) का हर तत्व (A) के हर तत्व के साथ युग्म बनाता है। केवल समान घटक वाले युग्म लेना अधूरा उत्तर है।
By definition, \(A\times B={(x,y):x\in A,\ y\in B}\). In set-builder form, keep the order of components unchanged.
Step 2
Why this answer is correct
The correct answer is A. \({(x,y):x\in A,\ y\in B}\). By definition, \(A\times B={(x,y):x\in A,\ y\in B}\). In set-builder form, keep the order of components unchanged.
Step 3
Exam Tip
परिभाषा के अनुसार \(A\times B={(x,y):x\in A,\ y\in B}\)। सेट-बिल्डर रूप में घटकों का क्रम वही रखें।
In \(B\times A\), the first component is (2) from (B) and the second is (1) or (2) from (A). Reversing the order changes the answer.
Step 2
Why this answer is correct
The correct answer is B. ({(2,1),(2,2)}). In \(B\times A\), the first component is (2) from (B) and the second is (1) or (2) from (A). Reversing the order changes the answer.
Step 3
Exam Tip
\(B\times A\) में पहला घटक (B) से (2) होगा और दूसरा घटक (A) से (1) या (2) होगा। क्रम बदलने से उत्तर बदलता है।
Both counts are (n(A)n(B)), so the numbers are equal. Remember that counts may be equal even when the sets are different.
Step 2
Why this answer is correct
The correct answer is A. (n\(A\times B\)=n\(B\times A\)). Both counts are (n(A)n(B)), so the numbers are equal. Remember that counts may be equal even when the sets are different.
Step 3
Exam Tip
दोनों की संख्या (n(A)n(B)) होती है, इसलिए संख्याएं बराबर होती हैं। ध्यान रखें कि संख्या बराबर हो सकती है पर समुच्चय अलग हो सकते हैं।
Both elements of (A) come in the first position and (0) from (B) comes in the second position. A negative number is used like any other element.
Step 2
Why this answer is correct
The correct answer is A. ({(-1,0),(1,0)}). Both elements of (A) come in the first position and (0) from (B) comes in the second position. A negative number is used like any other element.
Step 3
Exam Tip
(A) के दोनों तत्व पहले स्थान पर और (B) का (0) दूसरे स्थान पर आता है। ऋणात्मक संख्या भी सामान्य तत्व की तरह ही प्रयोग होती है।
In ((6,2)), \(6\in A\) and \(2\in B\), so it is correct. Having both numbers present is not enough; their positions must also be correct.
Step 2
Why this answer is correct
The correct answer is C. ((6,2)). In ((6,2)), \(6\in A\) and \(2\in B\), so it is correct. Having both numbers present is not enough; their positions must also be correct.
Step 3
Exam Tip
((6,2)) में \(6\in A\) और \(2\in B\), इसलिए यह सही है। केवल दोनों संख्याएं मौजूद होना काफी नहीं, स्थान भी सही होना चाहिए।
In ((1,0)), both components are from (A), so it belongs to \(A\times A\). In \(A\times A\), elements of (A) fill both positions.
Step 2
Why this answer is correct
The correct answer is B. ((1,0)). In ((1,0)), both components are from (A), so it belongs to \(A\times A\). In \(A\times A\), elements of (A) fill both positions.
Step 3
Exam Tip
((1,0)) में दोनों घटक (A) से हैं, इसलिए यह \(A\times A\) में होगा। \(A\times A\) में दोनों स्थानों पर (A) के तत्व आते हैं।
If every element of (A) is in (B), then every pair of \(A\times C\) is also in \(B\times C\). In subset questions, focus on the first component.
Step 2
Why this answer is correct
The correct answer is A. \(A\times C\subset B\times C\). If every element of (A) is in (B), then every pair of \(A\times C\) is also in \(B\times C\). In subset questions, focus on the first component.
Step 3
Exam Tip
यदि (A) का हर तत्व (B) में है, तो \(A\times C\) का हर युग्म \(B\times C\) में भी होगा। उपसमुच्चय वाले प्रश्न में पहले घटक पर ध्यान दें।
There is no element in (C) for the second component, so no ordered pair is formed. Cartesian product with an empty set is empty.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). There is no element in (C) for the second component, so no ordered pair is formed. Cartesian product with an empty set is empty.
Step 3
Exam Tip
दूसरे घटक के लिए (C) में कोई तत्व नहीं है, इसलिए कोई क्रमित युग्म नहीं बनेगा। खाली समुच्चय के साथ कार्तीय गुणन खाली होता है।
An ordered pair is written as ((a,b)), while ({a,b}) is a set. In exams, notice the difference between parentheses and braces.
Step 2
Why this answer is correct
The correct answer is A. ((a,b)). An ordered pair is written as ((a,b)), while ({a,b}) is a set. In exams, notice the difference between parentheses and braces.
Step 3
Exam Tip
क्रमित युग्म को ((a,b)) के रूप में लिखा जाता है, जबकि ({a,b}) समुच्चय है। परीक्षा में कोष्ठक और मध्यम कोष्ठक का अंतर पहचानें।
A. ((a,b)) और ((b,a)) सामान्यतः अलग होते हैं/((a,b)) and ((b,a)) are generally different
Step 1
Concept
The first and second positions in an ordered pair have different meanings. Therefore, do not generally treat ((a,b)) and ((b,a)) as equal.
Step 2
Why this answer is correct
The correct answer is A. ((a,b)) और ((b,a)) सामान्यतः अलग होते हैं / ((a,b)) and ((b,a)) are generally different. The first and second positions in an ordered pair have different meanings. Therefore, do not generally treat ((a,b)) and ((b,a)) as equal.
Step 3
Exam Tip
क्रमित युग्म में पहला और दूसरा स्थान अलग अर्थ रखते हैं। इसलिए ((a,b)) और ((b,a)) को सामान्यतः समान न मानें।
In Cartesian product, each element of (A) pairs with every element of (B), so the total count is (mn). For counting questions, multiply, do not add.
Step 2
Why this answer is correct
The correct answer is B. (mn). In Cartesian product, each element of (A) pairs with every element of (B), so the total count is (mn). For counting questions, multiply, do not add.
Step 3
Exam Tip
कार्तीय गुणन में प्रत्येक (A) तत्व (B) के हर तत्व से जुड़ता है, इसलिए कुल संख्या (mn) होती है। गिनती वाले प्रश्न में जोड़ नहीं, गुणा करें।
In \(A\times B\), (1,2) from (A) come first and (3,4) from (B) come second. The full list should have \(2\times 2=4\) pairs.
Step 2
Why this answer is correct
The correct answer is A. ({(1,3),(1,4),(2,3),(2,4)}). In \(A\times B\), (1,2) from (A) come first and (3,4) from (B) come second. The full list should have \(2\times 2=4\) pairs.
Step 3
Exam Tip
\(A\times B\) में (A) के (1,2) पहले स्थान पर और (B) के (3,4) दूसरे स्थान पर आते हैं। पूरी सूची में \(2\times 2=4\) युग्म होने चाहिए।
The first component comes from the first set ({4,5}), so (x) can be (4) or (5). Do not mix the first and second components.
Step 2
Why this answer is correct
The correct answer is A. (4) या (5) / (4) or (5). The first component comes from the first set ({4,5}), so (x) can be (4) or (5). Do not mix the first and second components.
Step 3
Exam Tip
पहला घटक पहले समुच्चय ({4,5}) से आता है, इसलिए (x) (4) या (5) हो सकता है। पहले और दूसरे घटक को न मिलाएं।
When the first component (1) is fixed, the second component can be any of the (3) elements of (B). With a fixed first component, the number of pairs is (n(B)).
Step 2
Why this answer is correct
The correct answer is C. (3). When the first component (1) is fixed, the second component can be any of the (3) elements of (B). With a fixed first component, the number of pairs is (n(B)).
Step 3
Exam Tip
पहला घटक (1) तय होने पर दूसरा घटक (B) के (3) तत्वों में से कोई भी हो सकता है। निश्चित पहले घटक के साथ युग्मों की संख्या (n(B)) होती है।
The element (a) of (A) stays in the first position and both elements of (B) come in the second position. The same rule works for letter elements too.
Step 2
Why this answer is correct
The correct answer is A. ({\(a,b_1\),\(a,b_2\)}). The element (a) of (A) stays in the first position and both elements of (B) come in the second position. The same rule works for letter elements too.
Step 3
Exam Tip
(A) का (a) पहले स्थान पर रहेगा और (B) के दोनों तत्व दूसरे स्थान पर आएंगे। अक्षरों वाले प्रश्नों में भी नियम वही रहता है।
A. \((a,b)\in A\times B\Rightarrow a\in A,\ b\in B\)
Step 1
Concept
The basic condition of Cartesian product is that the first component is from (A) and the second from (B). Remember this statement like a definition.
Step 2
Why this answer is correct
The correct answer is A. \((a,b)\in A\times B\Rightarrow a\in A,\ b\in B\). The basic condition of Cartesian product is that the first component is from (A) and the second from (B). Remember this statement like a definition.
Step 3
Exam Tip
कार्तीय गुणन की मूल शर्त है कि पहला घटक (A) से और दूसरा (B) से हो। इस कथन को परिभाषा की तरह याद रखें।
When the second component (4) is fixed, the first component can be any of the (3) elements of (A). With a fixed second component, the count is (n(A)).
Step 2
Why this answer is correct
The correct answer is C. (3). When the second component (4) is fixed, the first component can be any of the (3) elements of (A). With a fixed second component, the count is (n(A)).
Step 3
Exam Tip
दूसरा घटक (4) तय होने पर पहला घटक (A) के (3) तत्वों में से कोई भी हो सकता है। निश्चित दूसरे घटक के साथ संख्या (n(A)) होती है।
The first component (2) is fixed and the second component is chosen from the (2) elements of (B). Therefore, there are (2) such pairs.
Step 2
Why this answer is correct
The correct answer is B. (2). The first component (2) is fixed and the second component is chosen from the (2) elements of (B). Therefore, there are (2) such pairs.
Step 3
Exam Tip
पहला घटक (2) तय है और दूसरा घटक (B) के (2) तत्वों में से चुना जाएगा। इसलिए ऐसे (2) युग्म होंगे।
B. नहीं, क्योंकि \(3\notin A\)/No, because \(3\notin A\)
Step 1
Concept
The first component of ((3,1)) is (3), but \(3\notin A\). A correct second component alone does not make the whole pair correct.
Step 2
Why this answer is correct
The correct answer is B. नहीं, क्योंकि \(3\notin A\) / No, because \(3\notin A\). The first component of ((3,1)) is (3), but \(3\notin A\). A correct second component alone does not make the whole pair correct.
Step 3
Exam Tip
((3,1)) का पहला घटक (3) है, लेकिन \(3\notin A\)। दूसरे घटक के सही होने से पूरा युग्म सही नहीं हो जाता।
A. \(A\times B={(0,1)}\) और \(B\times A={(1,0)}\)/\(A\times B={(0,1)}\) and \(B\times A={(1,0)}\)
Step 1
Concept
In \(A\times B\), (0) is first and (1) is second, while in \(B\times A\) the order is reversed. Order remains important even with one element in each set.
Step 2
Why this answer is correct
The correct answer is A. \(A\times B={(0,1)}\) और \(B\times A={(1,0)}\) / \(A\times B={(0,1)}\) and \(B\times A={(1,0)}\). In \(A\times B\), (0) is first and (1) is second, while in \(B\times A\) the order is reversed. Order remains important even with one element in each set.
Step 3
Exam Tip
\(A\times B\) में (0) पहले और (1) दूसरे स्थान पर है, जबकि \(B\times A\) में क्रम उल्टा है। एक-एक तत्व होने पर भी क्रम महत्वपूर्ण रहता है।
(A) has (2) elements and (B) has (2) elements, so \(2\times 2=4\) options are formed. Real-life choices can also be counted by Cartesian product.
Step 2
Why this answer is correct
The correct answer is C. (4) विकल्प / (4) options. (A) has (2) elements and (B) has (2) elements, so \(2\times 2=4\) options are formed. Real-life choices can also be counted by Cartesian product.
Step 3
Exam Tip
(A) में (2) और (B) में (2) तत्व हैं, इसलिए \(2\times 2=4\) विकल्प बनते हैं। वास्तविक जीवन के चुनाव भी कार्तीय गुणन से गिने जा सकते हैं।
(n\(A\times B\)=n(A)n(B)=3\times 2=6), so there are (6) points. Cartesian product can also be understood as coordinate points.
Step 2
Why this answer is correct
The correct answer is C. (6) बिंदु / (6) points. (n\(A\times B\)=n(A)n(B)=3\times 2=6), so there are (6) points. Cartesian product can also be understood as coordinate points.
Step 3
Exam Tip
(n\(A\times B\)=n(A)n(B)=3\times 2=6), इसलिए कुल (6) बिंदु मिलेंगे। कार्तीय गुणन को निर्देशांक बिंदुओं की तरह भी समझ सकते हैं।
Related questions grouped automatically for chapter-wise practice. Topics include Algebra of real functions, Cartesian product of sets, Functions as a special kind of relation, Graphs of standard functions, Real valued functions, domain and range of these functions.
How should I practice this Mathematics chapter?
Start with Easy MCQs, review explanations after every answer, then move to Medium, Hard and Expert timed quizzes for stronger exam preparation.
Are topic-wise questions available?
Yes, this page includes topic-wise practice such as Algebra of real functions, Cartesian product of sets, Functions as a special kind of relation, Graphs of standard functions, Real valued functions, domain and range of these functions, Relations.
Login to view answers
Use Google login or mobile OTP. Admin can block users and control login providers.
