यदि \(A={x:x\in \mathbb{Z}, |x|<3}\) और \(B=\{-2,-1,0,1,2\}\) हैं तो कौन सा कथन सही है?
If \(A={x:x\in \mathbb{Z}, |x|<3}\) and \(B=\{-2,-1,0,1,2\}\) then which statement is correct?
#sets
#equal-sets
#absolute-value
A (A=B)
B \(A\subset B\) और \(A\neq B\) / \(A\subset B\) and \(A\neq B\)
C \(B\subset A\) और \(A\neq B\) / \(B\subset A\) and \(A\neq B\)
D \(3\in A\)
Explanation opens after your attempt
Step 1
Concept
The integers satisfying (|x|<3) are (-2,-1,0,1,2). Strict inequality excludes (-3) and (3).
Step 2
Why this answer is correct
The correct answer is A. (A=B). The integers satisfying (|x|<3) are (-2,-1,0,1,2). Strict inequality excludes (-3) and (3).
Step 3
Exam Tip
(|x|<3) के पूर्णांक (-2,-1,0,1,2) हैं। सख्त असमता में (-3) और (3) शामिल नहीं होते।
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यदि \(A={x:x\in \mathbb{N}, x\) (9) का भाजक है(}) और \(B=\{1,3,9\}\) हैं तो (A) और (B) कैसे हैं?
If \(A={x:x\in \mathbb{N}, x\) is a divisor of (9)(}) and \(B=\{1,3,9\}\) then how are (A) and (B) related?
#sets
#equal-sets
#divisors
A समान समुच्चय / Equal sets
B उचित उपसमुच्चय / Proper subsets only
C विसंयुक्त समुच्चय / Disjoint sets
D रिक्त समुच्चय / Empty sets
Explanation opens after your attempt
Correct Answer
A. समान समुच्चय / Equal sets
Step 1
Concept
The positive divisors of (9) are (1,3,9). While listing divisors, include (1) and the number itself.
Step 2
Why this answer is correct
The correct answer is A. समान समुच्चय / Equal sets. The positive divisors of (9) are (1,3,9). While listing divisors, include (1) and the number itself.
Step 3
Exam Tip
(9) के धनात्मक भाजक (1,3,9) हैं। भाजक सूची बनाते समय (1) और संख्या स्वयं को शामिल करें।
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यदि \(A=\{5,10,15\}\) और \(B={x:x\) (20) से कम (5) का धनात्मक गुणज है(}) हैं तो संबंध क्या है?
If \(A=\{5,10,15\}\) and \(B={x:x\) is a positive multiple of (5) less than (20)(}) then what is the relation?
#sets
#equal-sets
#multiples
A (A=B)
B \(A\subset B\) और \(A\neq B\) / \(A\subset B\) and \(A\neq B\)
C \(B\subset A\) और \(A\neq B\) / \(B\subset A\) and \(A\neq B\)
D \(20\in B\)
Explanation opens after your attempt
Step 1
Concept
The positive multiples of (5) less than (20) are (5,10,15). Check whether the boundary number is included or not.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive multiples of (5) less than (20) are (5,10,15). Check whether the boundary number is included or not.
Step 3
Exam Tip
(20) से कम (5) के धनात्मक गुणज (5,10,15) हैं। सीमा पर दी संख्या शामिल है या नहीं, यह जांचें।
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यदि \(A={x:x\) (30) से कम (6) का धनात्मक गुणज है(}) और \(B=\{6,12,18,24\}\) हैं तो सही कथन कौन सा है?
If \(A={x:x\) is a positive multiple of (6) less than (30)(}) and \(B=\{6,12,18,24\}\) then which statement is correct?
#sets
#equal-sets
#multiples
A (A=B)
B \(A\subset B\) और \(A\neq B\) / \(A\subset B\) and \(A\neq B\)
C \(B\subset A\) और \(A\neq B\) / \(B\subset A\) and \(A\neq B\)
D \(30\in A\)
Explanation opens after your attempt
Step 1
Concept
The positive multiples of (6) less than (30) are (6,12,18,24). Remember the difference between at most and less than.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive multiples of (6) less than (30) are (6,12,18,24). Remember the difference between at most and less than.
Step 3
Exam Tip
(30) से कम (6) के धनात्मक गुणज (6,12,18,24) हैं। कम से कम और कम का अंतर याद रखें।
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यदि \(A={x:x\in \mathbb{N}, x^2-5x+6=0}\) है तो कौन सा समुच्चय (A) के बराबर है?
If \(A={x:x\in \mathbb{N}, x^2-5x+6=0}\) then which set is equal to (A)?
#sets
#equal-sets
#quadratic
A ({2,3})
B ({1,6})
C ({-2,-3})
D ({0,5})
Explanation opens after your attempt
Correct Answer
A. ({2,3})
Step 1
Concept
(x-2 -5x+6=(x-2)(x-3)), so the solutions are (2,3). First solve the equation and then write the set.
Step 2
Why this answer is correct
The correct answer is A. ({2,3}). (x-2 -5x+6=(x-2)(x-3)), so the solutions are (2,3). First solve the equation and then write the set.
Step 3
Exam Tip
(x-2 -5x+6=(x-2)(x-3)) है इसलिए हल (2,3) हैं। पहले समीकरण हल करें फिर समुच्चय लिखें।
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यदि \(A={x:x\in \mathbb{Z}, x^2=9}\) और \(B=\{-3,3\}\) हैं तो सही कथन कौन सा है?
If \(A={x:x\in \mathbb{Z}, x^2=9}\) and \(B=\{-3,3\}\) then which statement is correct?
#sets
#equal-sets
#equation
A (A=B)
B \(A=\{3\}\)
C \(B\subset A\) और \(A\neq B\) / \(B\subset A\) and \(A\neq B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The integer solutions of \(x^2=9\) are (-3) and (3). Check the negative solution in square equations too.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The integer solutions of \(x^2=9\) are (-3) and (3). Check the negative solution in square equations too.
Step 3
Exam Tip
\(x^2=9\) के पूर्णांक हल (-3) और (3) हैं। वर्ग वाले समीकरण में ऋणात्मक हल भी जांचें।
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यदि \(A={x:x\in \mathbb{N}, 10<x<16}\) और \(B=\{11,12,13,14,15\}\) हैं तो कौन सा सही है?
If \(A={x:x\in \mathbb{N}, 10<x<16}\) and \(B=\{11,12,13,14,15\}\) then which is correct?
#sets
#equal-sets
#inequality
A (A=B)
B \(A\subset B\) और \(A\neq B\) / \(A\subset B\) and \(A\neq B\)
C \(B\subset A\) और \(A\neq B\) / \(B\subset A\) and \(A\neq B\)
D \(16\in A\)
Explanation opens after your attempt
Step 1
Concept
For (10<x<16), the natural numbers are (11) to (15). Open boundaries do not include (10) and (16).
Step 2
Why this answer is correct
The correct answer is A. (A=B). For (10<x<16), the natural numbers are (11) to (15). Open boundaries do not include (10) and (16).
Step 3
Exam Tip
(10<x<16) में (11) से (15) तक प्राकृतिक संख्याएं आती हैं। खुली सीमा में (10) और (16) शामिल नहीं होते।
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यदि \(A\subseteq B\) और (n(A)=5), (n(B)=5) है तो कौन सा निष्कर्ष सही है?
If \(A\subseteq B\) and (n(A)=5), (n(B)=5), then which conclusion is correct?
#sets
#equal-sets
#cardinality
A (A=B)
B \(A\subset B\) और \(A\neq B\) / \(A\subset B\) and \(A\neq B\)
C \(B\subset A\) असंभव है / \(B\subset A\) is impossible
D दोनों रिक्त हैं / Both are empty
Explanation opens after your attempt
Step 1
Concept
If (A) is a subset of (B) and both have the same number of elements, they are equal. Equal cardinality is the key clue here.
Step 2
Why this answer is correct
The correct answer is A. (A=B). If (A) is a subset of (B) and both have the same number of elements, they are equal. Equal cardinality is the key clue here.
Step 3
Exam Tip
यदि (A) (B) का उपसमुच्चय है और दोनों में समान संख्या में अवयव हैं, तो वे बराबर हैं। समान कार्डिनैलिटी यहां महत्वपूर्ण संकेत है।
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यदि \(A={x:x\) (16) का धनात्मक भाजक है और (x) सम है(}) तो कौन सा समुच्चय (A) के बराबर है?
If \(A={x:x\) is a positive divisor of (16) and (x) is even(}) then which set is equal to (A)?
#sets
#equal-sets
#divisors
A ({2,4,8,16})
B ({1,2,4,8,16})
C ({2,4,6,8})
D ({4,8,16})
Explanation opens after your attempt
Correct Answer
A. ({2,4,8,16})
Step 1
Concept
The even positive divisors of (16) are (2,4,8,16). First list all divisors and then apply the condition.
Step 2
Why this answer is correct
The correct answer is A. ({2,4,8,16}). The even positive divisors of (16) are (2,4,8,16). First list all divisors and then apply the condition.
Step 3
Exam Tip
(16) के सम धनात्मक भाजक (2,4,8,16) हैं। पहले सभी भाजक लिखें फिर शर्त लगाएं।
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यदि \(A={x:x\) (18) का अभाज्य गुणनखंड है(}) और \(B=\{2,3\}\) हैं तो कौन सा कथन सही है?
If \(A={x:x\) is a prime factor of (18)(}) and \(B=\{2,3\}\) then which statement is correct?
#sets
#equal-sets
#prime-factors
A (A=B)
B \(A=\{2,3,3\}\)
C \(A\subset B\) और \(A\neq B\) / \(A\subset B\) and \(A\neq B\)
D \(B\subset A\) और \(A\neq B\) / \(B\subset A\) and \(A\neq B\)
Explanation opens after your attempt
Step 1
Concept
\(18=2\times3^2\), but (3) is written once in a set. Keep factorization and set counting separate.
Step 2
Why this answer is correct
The correct answer is A. (A=B). \(18=2\times3^2\), but (3) is written once in a set. Keep factorization and set counting separate.
Step 3
Exam Tip
\(18=2\times3^2\) है, पर समुच्चय में (3) एक बार लिखा जाता है। गुणनखंड और समुच्चय की गिनती अलग रखें।
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यदि \(A={x:x\) अंग्रेजी शब्द (LEVEL) का अलग अक्षर है(}) और \(B=\{L,E,V\}\) हैं तो सही कथन क्या है?
If \(A={x:x\) is a distinct letter of the English word (LEVEL)(}) and \(B=\{L,E,V\}\) then what is correct?
#sets
#equal-sets
#letters
A (A=B)
B \(A\subset B\) और \(A\neq B\) / \(A\subset B\) and \(A\neq B\)
C \(B\subset A\) और \(A\neq B\) / \(B\subset A\) and \(A\neq B\)
D (A) में पांच अवयव हैं / (A) has five elements
Explanation opens after your attempt
Step 1
Concept
Repeated letters are counted once, so (LEVEL) gives (L,E,V). Repetition is not counted in sets.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Repeated letters are counted once, so (LEVEL) gives (L,E,V). Repetition is not counted in sets.
Step 3
Exam Tip
दोहराए गए अक्षर एक बार गिने जाते हैं, इसलिए (LEVEL) से (L,E,V) मिलते हैं। समुच्चय में पुनरावृत्ति नहीं गिनी जाती।
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यदि \(A={x:x\in \mathbb{Z}, -1\leq x\leq 2}\) और \(B=\{-1,0,1,2\}\) हैं तो सही कथन कौन सा है?
If \(A={x:x\in \mathbb{Z}, -1\leq x\leq 2}\) and \(B=\{-1,0,1,2\}\) then which statement is correct?
#sets
#equal-sets
#integers
#roster-form
A (A=B)
B \(A\subset B\) और \(A\neq B\) / \(A\subset B\) and \(A\neq B\)
C \(B\subset A\) और \(A\neq B\) / \(B\subset A\) and \(A\neq B\)
D \(0\notin A\)
Explanation opens after your attempt
Step 1
Concept
The integers in the given range are exactly (-1,0,1,2) so both sets are equal. In exams first convert set-builder form to roster form.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The integers in the given range are exactly (-1,0,1,2) so both sets are equal. In exams first convert set-builder form to roster form.
Step 3
Exam Tip
दी गई सीमा में पूर्णांक (-1,0,1,2) ही हैं इसलिए दोनों समुच्चय समान हैं। परीक्षा में पहले वर्णन रूप को सूची रूप में बदलें।
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किस स्थिति में दो समुच्चय समान कहलाते हैं?
When are two sets called equal?
#sets
#equal-sets
#definition
A जब उनके सभी अवयव समान हों / When all their elements are the same
B जब उनके नाम समान हों / When their names are the same
C जब उनके अवयवों का क्रम समान हो / When the order of their elements is the same
D जब दोनों में कम से कम एक समान अवयव हो / When they have at least one common element
Explanation opens after your attempt
Correct Answer
A. जब उनके सभी अवयव समान हों / When all their elements are the same
Step 1
Concept
Equal sets must have every element in both sets. Names or order alone do not decide equality.
Step 2
Why this answer is correct
The correct answer is A. जब उनके सभी अवयव समान हों / When all their elements are the same. Equal sets must have every element in both sets. Names or order alone do not decide equality.
Step 3
Exam Tip
समान समुच्चय में प्रत्येक अवयव दोनों समुच्चयों में होना चाहिए। केवल नाम या क्रम से समानता तय नहीं होती।
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यदि \(A=\{2,4,6,8\}\) और \(B={x:x\) (10) से कम सम प्राकृतिक संख्या है(}) हैं तो कौन सा कथन सत्य है?
If \(A=\{2,4,6,8\}\) and \(B={x:x\) is an even natural number less than (10)(}) then which statement is true?
#sets
#equal-sets
#even-numbers
A (A=B)
B \(A\subset B\) पर \(A\neq B\) / \(A\subset B\) but \(A\neq B\)
C \(B\subset A\) पर \(A\neq B\) / \(B\subset A\) but \(A\neq B\)
D (A) में (10) है / (A) contains (10)
Explanation opens after your attempt
Step 1
Concept
Even natural numbers less than (10) are (2,4,6,8). Less than and at most mean different things.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Even natural numbers less than (10) are (2,4,6,8). Less than and at most mean different things.
Step 3
Exam Tip
(10) से कम सम प्राकृतिक संख्याएं (2,4,6,8) हैं। कम से कम और कम का अर्थ अलग होता है।
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यदि \(A={x:x\) (6) से छोटी विषम प्राकृतिक संख्या है(}) और \(B=\{1,3,5\}\) हैं तो सही कथन चुनिए।
If \(A={x:x\) is an odd natural number less than (6)(}) and \(B=\{1,3,5\}\) then choose the correct statement.
#sets
#equal-sets
#odd-numbers
A (A=B)
B \(A\subset B\)
C \(B\subset A\)
D (A) और (B) असंबंधित हैं / (A) and (B) are unrelated
Explanation opens after your attempt
Step 1
Concept
Odd natural numbers less than (6) are (1,3,5). Check the boundary in inequalities carefully.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Odd natural numbers less than (6) are (1,3,5). Check the boundary in inequalities carefully.
Step 3
Exam Tip
(6) से छोटी विषम प्राकृतिक संख्याएं (1,3,5) हैं। असमता में सीमा को ध्यान से देखें।
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यदि \(A={x:x\) (20) से कम अभाज्य संख्या है(}) और \(B=\{2,3,5,7,11,13,17,19\}\) हैं तो क्या (A=B) है?
If \(A={x:x\) is a prime number less than (20)(}) and \(B=\{2,3,5,7,11,13,17,19\}\) then is (A=B)?
#sets
#equal-sets
#prime-numbers
A हाँ क्योंकि दोनों में समान अभाज्य संख्याएं हैं / Yes because both have the same prime numbers
B नहीं क्योंकि (1) भी अभाज्य है / No because (1) is also prime
C नहीं क्योंकि (20) भी शामिल होगा / No because (20) will also be included
D नहीं क्योंकि (2) अभाज्य नहीं है / No because (2) is not prime
Explanation opens after your attempt
Correct Answer
A. हाँ क्योंकि दोनों में समान अभाज्य संख्याएं हैं / Yes because both have the same prime numbers
Step 1
Concept
The primes less than (20) are exactly the listed numbers. Remember that (1) is not a prime number.
Step 2
Why this answer is correct
The correct answer is A. हाँ क्योंकि दोनों में समान अभाज्य संख्याएं हैं / Yes because both have the same prime numbers. The primes less than (20) are exactly the listed numbers. Remember that (1) is not a prime number.
Step 3
Exam Tip
(20) से कम अभाज्य संख्याएं सूची में दी गई सभी संख्याएं हैं। याद रखें (1) अभाज्य संख्या नहीं है।
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यदि \(A={x:x\) (12) का धनात्मक भाजक है(}) और \(B=\{1,2,3,4,6,12\}\) हैं तो कौन सा कथन सही है?
If \(A={x:x\) is a positive divisor of (12)(}) and \(B=\{1,2,3,4,6,12\}\) then which statement is correct?
#sets
#equal-sets
#divisors
A (A=B)
B \(A\subset B\) पर \(A\neq B\) / \(A\subset B\) but \(A\neq B\)
C \(B\subset A\) पर \(A\neq B\) / \(B\subset A\) but \(A\neq B\)
D (A) रिक्त है / (A) is empty
Explanation opens after your attempt
Step 1
Concept
The positive divisors of (12) are (1,2,3,4,6,12). In divisor questions no divisor should be missed.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive divisors of (12) are (1,2,3,4,6,12). In divisor questions no divisor should be missed.
Step 3
Exam Tip
(12) के धनात्मक भाजक (1,2,3,4,6,12) हैं। भाजक वाले प्रश्नों में कोई भाजक छूटना नहीं चाहिए।
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यदि \(A={x:x\) अंग्रेजी शब्द (MATH) का अक्षर है(}) तो (A) किसके बराबर है?
If \(A={x:x\) is a letter of the English word (MATH)(}) then (A) is equal to which set?
#sets
#equal-sets
#letters
A ({M,A,T,H})
B ({M,A,T})
C ({A,T,H})
D ({MATH})
Explanation opens after your attempt
Correct Answer
A. ({M,A,T,H})
Step 1
Concept
The distinct letters of the word become elements of the set. The whole word and the set of letters are different.
Step 2
Why this answer is correct
The correct answer is A. ({M,A,T,H}). The distinct letters of the word become elements of the set. The whole word and the set of letters are different.
Step 3
Exam Tip
शब्द के अलग अलग अक्षर समुच्चय के अवयव बनते हैं। पूरा शब्द और अक्षरों का समुच्चय अलग होते हैं।
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यदि \(A={x:x^2=4}\) और \(B=\{-2,2\}\) हैं तो कौन सा कथन सही है?
If \(A={x:x^2=4}\) and \(B=\{-2,2\}\) then which statement is correct?
#sets
#equal-sets
#equation-set
A (A=B)
B \(A\subset B\) पर \(A\neq B\) / \(A\subset B\) but \(A\neq B\)
C \(B\subset A\) पर \(A\neq B\) / \(B\subset A\) but \(A\neq B\)
D \(A=\{2\}\)
Explanation opens after your attempt
Step 1
Concept
The solutions of \(x^2=4\) are (-2) and (2). Do not forget both signs in square equations.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The solutions of \(x^2=4\) are (-2) and (2). Do not forget both signs in square equations.
Step 3
Exam Tip
समीकरण \(x^2=4\) के हल (-2) और (2) हैं। वर्ग समीकरण में दोनों चिह्नों को न भूलें।
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यदि \(A={x:x\) (10) से कम धनात्मक सम संख्या है(}) और \(B=\{2,4,6,8\}\) हैं तो कौन सा संबंध सही है?
If \(A={x:x\) is a positive even number less than (10)(}) and \(B=\{2,4,6,8\}\) then which relation is correct?
#sets
#equal-sets
#set-builder
A (A=B)
B \(A\subset B\)
C \(B\subset A\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The positive even numbers less than (10) are (2,4,6,8). Converting description to roster form is useful.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive even numbers less than (10) are (2,4,6,8). Converting description to roster form is useful.
Step 3
Exam Tip
(10) से कम धनात्मक सम संख्याएं (2,4,6,8) हैं। वर्णन को रोस्टर रूप में बदलना उपयोगी है।
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यदि \(A=\{2,4,6\}\) और \(B={x:x\) (2,4,6) में से कोई संख्या है(}) तो कौन सा कथन सत्य है?
If \(A=\{2,4,6\}\) and \(B={x:x\) is one of (2,4,6)(}) then which statement is true?
#sets
#equal-sets
#roster-form
A (A=B)
B \(A\subset B\) पर \(A\neq B\) / \(A\subset B\) but \(A\neq B\)
C \(B\subset A\) पर \(A\neq B\) / \(B\subset A\) but \(A\neq B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Both sets contain only (2,4,6). First convert roster and description forms to the same form.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Both sets contain only (2,4,6). First convert roster and description forms to the same form.
Step 3
Exam Tip
दोनों समुच्चयों में अवयव (2,4,6) ही हैं। रोस्टर और वर्णन रूप को पहले समान रूप में बदलें।
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यदि ({a,a,b}) और ({a,b}) दिए हैं तो वे किस प्रकार के समुच्चय हैं?
If ({a,a,b}) and ({a,b}) are given then what type of sets are they?
#sets
#equal-sets
#repetition
A समान समुच्चय / Equal sets
B विसंयुक्त समुच्चय / Disjoint sets
C अपरिमित समुच्चय / Infinite sets
D रिक्त समुच्चय / Empty sets
Explanation opens after your attempt
Correct Answer
A. समान समुच्चय / Equal sets
Step 1
Concept
Repeated elements in a set are counted only once. In exams ignore repetition in set notation.
Step 2
Why this answer is correct
The correct answer is A. समान समुच्चय / Equal sets. Repeated elements in a set are counted only once. In exams ignore repetition in set notation.
Step 3
Exam Tip
समुच्चय में दोहराए गए अवयव एक ही बार गिने जाते हैं। परीक्षा में पुनरावृत्ति को नजरअंदाज करें।
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यदि ({1,2,3}) और ({3,2,1}) दिए हैं तो सही कथन कौन सा है?
If ({1,2,3}) and ({3,2,1}) are given then which statement is correct?
#sets
#equal-sets
#order
A वे समान समुच्चय हैं / They are equal sets
B वे असमान समुच्चय हैं / They are unequal sets
C पहला दूसरे का उपसमुच्चय नहीं है / The first is not a subset of the second
D दूसरा रिक्त समुच्चय है / The second is an empty set
Explanation opens after your attempt
Correct Answer
A. वे समान समुच्चय हैं / They are equal sets
Step 1
Concept
Order does not matter in a set so both have the same elements. In exams always compare the elements.
Step 2
Why this answer is correct
The correct answer is A. वे समान समुच्चय हैं / They are equal sets. Order does not matter in a set so both have the same elements. In exams always compare the elements.
Step 3
Exam Tip
समुच्चय में क्रम का महत्व नहीं होता इसलिए दोनों में वही अवयव हैं। परीक्षा में हमेशा अवयवों को मिलाकर जांचें।
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यदि \(A\subseteq B\) और \(B\subseteq A\), तो कौन-सा निष्कर्ष सही है?
If \(A\subseteq B\) and \(B\subseteq A\), which conclusion is correct?
#equal-sets
#subset-theorem
#reasoning
A \(A\neq B\) / (A) is not equal to (B)
B (A=B) / (A) equals (B)
C \(A=\varnothing\) ही होगा / (A) must be empty
D (B) में कोई सदस्य नहीं होगा / (B) has no element
Explanation opens after your attempt
Correct Answer
B. (A=B) / (A) equals (B)
Step 1
Concept
\(A\subseteq B\) means all elements of (A) are in (B).
Step 2
Why this answer is correct
\(B\subseteq A\) means all elements of (B) are in (A).
Step 3
Exam Tip
Subset relation both ways implies the sets are equal. चरण 1: \(A\subseteq B\) से (A) के सभी सदस्य (B) में हैं। चरण 2: \(B\subseteq A\) से (B) के सभी सदस्य (A) में हैं। चरण 3: दोनों दिशाओं में उपसमुच्चय संबंध होने पर समुच्चय बराबर होते हैं।
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यदि \(A=\{1,2,3\}\) और \(B=\{1,2,3\}\), तो कौन-सा कथन सही है?
If \(A=\{1,2,3\}\) and \(B=\{1,2,3\}\), which statement is correct?
#equal-sets
#subsets
#sets
A \(A \subseteq B\) और \(B \subseteq A\) / \(A \subseteq B\) and \(B \subseteq A\)
B केवल \(A \subseteq B\) / only \(A \subseteq B\)
C केवल \(B \subseteq A\) / only \(B \subseteq A\)
D कोई भी उपसमुच्चय नहीं / no subset relation
Explanation opens after your attempt
Correct Answer
A. \(A \subseteq B\) और \(B \subseteq A\) / \(A \subseteq B\) and \(B \subseteq A\)
Step 1
Concept
Both sets have exactly the same elements.
Step 2
Why this answer is correct
Every element of (A) is in (B), and every element of (B) is in (A).
Step 3
Exam Tip
Equal sets have subset relation in both directions. चरण 1: दोनों समुच्चयों में बिल्कुल वही सदस्य हैं। चरण 2: इसलिए (A) का हर सदस्य (B) में और (B) का हर सदस्य (A) में है। चरण 3: बराबर समुच्चयों में उपसमुच्चय संबंध दोनों दिशाओं में होता है।
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यदि \(A={x \in \mathbb{Z}:x^3=x}\) और \(B=\{-1,0,1\}\), तो सही निष्कर्ष चुनिए।
If \(A={x \in \mathbb{Z}:x^3=x}\) and \(B=\{-1,0,1\}\), choose the correct conclusion.
#sets
#equal sets
#finite set
#integer solutions
A (A=B)
B (A) रिक्त है / (A) is empty
C (A) में केवल (0) है / (A) contains only (0)
D (A) अनंत है / (A) is infinite
Explanation opens after your attempt
Step 1
Concept
From \(x^3=x\), we get \(x^3-x=0\).
Step 2
Why this answer is correct
Writing it as (x(x-1)(x+1)=0) gives the integer solutions (-1,0,1).
Step 3
Exam Tip
Since (A) and (B) have exactly the same three elements, the sets are equal. चरण 1: \(x^3=x\) से \(x^3-x=0\) मिलता है। चरण 2: इसे (x(x-1)(x+1)=0) लिखने पर पूर्णांक हल (-1,0,1) मिलते हैं। चरण 3: (A) और (B) में वही तीन तत्व हैं, इसलिए दोनों समान समुच्चय हैं।
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यदि \(A={x \in \mathbb{N}:x\) (12) का गुणनखंड है(}) और \(B=\{1,2,3,4,6,12\}\), तो सही निष्कर्ष क्या है?
If \(A={x \in \mathbb{N}:x\) is a factor of (12)(}) and \(B=\{1,2,3,4,6,12\}\), what is the correct conclusion?
#sets
#equal sets
#factors
#roster form
A (A=B)
B \(A\neq B\)
C (A) रिक्त है / (A) is empty
D (B) अनंत है / (B) is infinite
Explanation opens after your attempt
Step 1
Concept
The n
tural factors of (12) are (1,2,3,4,6,12).
Step 2
Why this answer is correct
(B) lists exactly these elements.
Step 3
Exam Tip
Therefore, (A) and (B) are equal sets. चरण 1: (12) के प्राकृतिक गुणनखंड (1,2,3,4,6,12) हैं। चरण 2: (B) में यही सभी तत्व दिए गए हैं। चरण 3: इसलिए (A) और (B) समान समुच्चय हैं।
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यदि \(A={x \in \mathbb{N}:x^2-5x+6=0}\), तो (A) किसके समान है?
If \(A={x \in \mathbb{N}:x^2-5x+6=0}\), which set is equal to (A)?
#sets
#equal sets
#quadratic
#natural numbers
A ({1,6})
B ({2,3})
C ({-2,-3})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
B. ({2,3})
Step 1
Concept
(x-2 -5x+6=(x-2)(x-3)).
Step 2
Why this answer is correct
The solutions are (x=2) and (x=3).
Step 3
Exam Tip
Both are natural numbers, so \(A=\{2,3\}\). चरण 1: (x-2 -5x+6=(x-2)(x-3)) है। चरण 2: हल (x=2) और (x=3) हैं। चरण 3: दोनों प्राकृतिक संख्याएँ हैं, इसलिए \(A=\{2,3\}\)।
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\(\varnothing\) और \({\varnothing}\) के बारे में कौन सा कथन सही है?
Which statement about \(\varnothing\) and \({\varnothing}\) is correct?
#sets
#empty set
#singleton
#equal sets
A दोनों समान हैं / Both are equal
B दोनों रिक्त हैं / Both are empty
C \(\varnothing\) रिक्त है पर \({\varnothing}\) एकांक है / \(\varnothing\) is empty but \({\varnothing}\) is singleton
D \(\varnothing\) अनंत है / \(\varnothing\) is infinite
Explanation opens after your attempt
Correct Answer
C. \(\varnothing\) रिक्त है पर \({\varnothing}\) एकांक है / \(\varnothing\) is empty but \({\varnothing}\) is singleton
Step 1
Concept
\(\varnothing\) has no element.
Step 2
Why this answer is correct
\({\varnothing}\) has one element, namely \(\varnothing\).
Step 3
Exam Tip
Therefore, they are not equal. चरण 1: \(\varnothing\) में कोई तत्व नहीं होता। चरण 2: \({\varnothing}\) में एक तत्व है और वह \(\varnothing\) है। चरण 3: इसलिए दोनों समान नहीं हैं।
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क्या ({1,{2,3}}) और ({1,2,3}) समान समुच्चय हैं?
Are ({1,{2,3}}) and ({1,2,3}) equal sets?
#sets
#equal sets
#nested set
#advanced
A हाँ, क्योंकि दोनों में (1,2,3) दिखते हैं / Yes, because (1,2,3) appear in both
B नहीं, क्योंकि ({2,3}) एक अलग तत्व है / No, because ({2,3}) is a single different element
C हाँ, क्योंकि क्रम अलग हो सकता है / Yes, because order can differ
D नहीं, क्योंकि दोनों रिक्त हैं / No, because both are empty
Explanation opens after your attempt
Correct Answer
B. नहीं, क्योंकि ({2,3}) एक अलग तत्व है / No, because ({2,3}) is a single different element
Step 1
Concept
({1,{2,3}}) has two elements: (1) and ({2,3}).
Step 2
Why this answer is correct
({1,2,3}) has three elements: (1,2,3).
Step 3
Exam Tip
The elements are not the same, so the sets are not equal. चरण 1: ({1,{2,3}}) में दो तत्व हैं, (1) और ({2,3})। चरण 2: ({1,2,3}) में तीन तत्व (1,2,3) हैं। चरण 3: तत्व समान नहीं हैं, इसलिए समुच्चय समान नहीं हैं।
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