यदि \(A={x:x\) (25) से छोटे पूर्ण वर्ग हैं और (x>0}) तो कौन सा विकल्प (A) के बराबर है?
If \(A={x:x\) is a positive perfect square less than (25)(}), which option is equal to (A)?
#sets
#equal_sets
#perfect_squares
A ({1,4,9,16})
B ({0,1,4,9,16})
C ({1,4,9,16,25})
D ({2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({1,4,9,16})
Step 1
Concept
The positive perfect squares are (1,4,9,16), and (25) is not included. Apply every condition together.
Step 2
Why this answer is correct
The correct answer is A. ({1,4,9,16}). The positive perfect squares are (1,4,9,16), and (25) is not included. Apply every condition together.
Step 3
Exam Tip
धनात्मक पूर्ण वर्ग (1,4,9,16) हैं और (25) सीमा में शामिल नहीं है। हर शर्त को साथ में लागू करें।
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यदि \(A={x:x\in\mathbb{Z}\) और \(-3\leq x<2}\) तो (A) के बराबर कौन सा समुच्चय है?
If \(A={x:x\in\mathbb{Z}\) and \(-3\leq x<2}\), which set is equal to (A)?
#sets
#equal_sets
#integer_interval
A ({-3,-2,-1,0,1})
B ({-2,-1,0,1,2})
C ({-3,-2,-1,0,1,2})
D ({-2,-1,0,1})
Explanation opens after your attempt
Correct Answer
A. ({-3,-2,-1,0,1})
Step 1
Concept
(-3) is included and (2) is not included. Read open and closed ends of inequalities carefully.
Step 2
Why this answer is correct
The correct answer is A. ({-3,-2,-1,0,1}). (-3) is included and (2) is not included. Read open and closed ends of inequalities carefully.
Step 3
Exam Tip
(-3) शामिल है और (2) शामिल नहीं है। असमानता में खुले और बंद सिरों को ध्यान से पढ़ें।
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यदि \(A={x:x\in\mathbb{N}\) और \(x\mid 18}\) तथा \(B=\{1,2,3,6,9,18\}\) हैं तो सही विकल्प चुनिए।
If \(A={x:x\in\mathbb{N}\) and \(x\mid 18}\) and \(B=\{1,2,3,6,9,18\}\), choose the correct option.
#sets
#equal_sets
#divisibility
A (A=B)
B (A) में केवल अभाज्य भाजक हैं / (A) contains only prime divisors
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(18\notin A\)
Explanation opens after your attempt
Step 1
Concept
\(x\mid 18\) means (x) divides (18). A number itself is also its positive divisor.
Step 2
Why this answer is correct
The correct answer is A. (A=B). \(x\mid 18\) means (x) divides (18). A number itself is also its positive divisor.
Step 3
Exam Tip
\(x\mid 18\) का अर्थ है (x) (18) का भाजक है। संख्या स्वयं भी उसका धनात्मक भाजक होती है।
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यदि \(A={x:x\) (42) का अभाज्य भाजक है(}) और \(B=\{2,3,7\}\) हैं तो कौन सा कथन सही है?
If \(A={x:x\) is a prime divisor of (42)(}) and \(B=\{2,3,7\}\), which statement is correct?
#sets
#equal_sets
#prime_divisors
A (A=B)
B \(A=\{1,2,3,6,7,14,21,42\}\)
C (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The prime divisors of (42) are (2,3,7). Understand the difference between all divisors and prime divisors.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The prime divisors of (42) are (2,3,7). Understand the difference between all divisors and prime divisors.
Step 3
Exam Tip
(42) के अभाज्य भाजक (2,3,7) हैं। सभी भाजकों और अभाज्य भाजकों में अंतर समझें।
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यदि \(A={x:x\in\mathbb{Z}\) और \(x^2-4x+3=0}\) तथा \(B=\{1,3\}\) हैं तो सही संबंध कौन सा है?
If \(A={x:x\in\mathbb{Z}\) and \(x^2-4x+3=0}\) and \(B=\{1,3\}\), which relation is correct?
#sets
#equal_sets
#quadratic_roots
A (A=B)
B (A) (B) का उचित उपसमुच्चय है / (A) is a proper subset of (B)
C (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The equation has roots (1) and (3), so both sets have the same elements. In equal sets order is not considered.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The equation has roots (1) and (3), so both sets have the same elements. In equal sets order is not considered.
Step 3
Exam Tip
समीकरण के हल (1) और (3) हैं इसलिए दोनों समुच्चयों में वही अवयव हैं। बराबर समुच्चय में क्रम नहीं देखा जाता।
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यदि \(A\subseteq B\), (n(A)=8) और (B) में (A) से बाहर कोई अवयव नहीं है तो कौन सा निष्कर्ष निश्चित है?
If \(A\subseteq B\), (n(A)=8), and (B) has no element outside (A), which conclusion is certain?
#sets
#equal_sets
#cardinality_reasoning
A (A=B)
B \(A\subset B\) और \(A\ne B\) / \(A\subset B\) and \(A\ne B\)
C (B) रिक्त समुच्चय है / (B) is the empty set
D (n(B)=16)
Explanation opens after your attempt
Step 1
Concept
Since \(A\subseteq B\) and (B) has no new element outside (A), both have the same elements. Thinking about inclusion from both sides helps prove equality.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Since \(A\subseteq B\) and (B) has no new element outside (A), both have the same elements. Thinking about inclusion from both sides helps prove equality.
Step 3
Exam Tip
\(A\subseteq B\) है और (B) में (A) के अलावा कोई नया अवयव नहीं है इसलिए दोनों में वही अवयव हैं। बराबरी सिद्ध करने में दोनों ओर सम्मिलन की सोच उपयोगी है।
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यदि \(A={X:X\) समुच्चय ({a,b,c}) का एक-अवयवी उपसमुच्चय है(}) और \(B=\{{a},{b},{c}\}\) हैं तो सही संबंध क्या है?
If \(A={X:X\) is a singleton subset of the set ({a,b,c})(}) and \(B=\{{a},{b},{c}\}\), what is the correct relation?
#sets
#equal_sets
#singleton_subsets
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{a,b,c\}\)
Explanation opens after your attempt
Step 1
Concept
The singleton subsets are ({a},{b},{c}), so the two sets are equal. In exams carefully check the level of elements and subsets.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The singleton subsets are ({a},{b},{c}), so the two sets are equal. In exams carefully check the level of elements and subsets.
Step 3
Exam Tip
एक-अवयवी उपसमुच्चय ({a},{b},{c}) होते हैं इसलिए दोनों समुच्चय बराबर हैं। परीक्षा में अवयव और उपसमुच्चय के स्तर को ध्यान से देखें।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), और \(C={x:x\in A\) तथा (x) सम है(}) हैं तो कौन सा कथन सही है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), and \(C={x:x\in A\) and (x) is even(}), which statement is correct?
#sets
#equal_sets
#proper_subset
A (B=C) और \(B\subset A\) / (B=C) and \(B\subset A\)
B (B=C) और \(A\subset B\) / (B=C) and \(A\subset B\)
C \(B\ne C\)
D \(C=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. (B=C) और \(B\subset A\) / (B=C) and \(B\subset A\)
Step 1
Concept
The even elements of (A) are (2,4,6), so (C=B) and (B) is a proper subset of (A). Apply the condition inside the original set.
Step 2
Why this answer is correct
The correct answer is A. (B=C) और \(B\subset A\) / (B=C) and \(B\subset A\). The even elements of (A) are (2,4,6), so (C=B) and (B) is a proper subset of (A). Apply the condition inside the original set.
Step 3
Exam Tip
(A) के सम अवयव (2,4,6) हैं इसलिए (C=B) है और (B) (A) का उचित उपसमुच्चय है। शर्त को मूल समुच्चय के अंदर लागू करें।
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यदि \(A={x:x\) (30) का अभाज्य भाजक है(}) और \(B=\{2,3,5\}\) हैं तो संबंध क्या है?
If \(A={x:x\) is a prime divisor of (30)(}) and \(B=\{2,3,5\}\), what is the relation?
#sets
#equal_sets
#prime_divisors
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{1,2,3,5,30\}\)
Explanation opens after your attempt
Step 1
Concept
The prime divisors of (30) are (2,3,5). The numbers (1) and (30) are not prime divisors.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The prime divisors of (30) are (2,3,5). The numbers (1) and (30) are not prime divisors.
Step 3
Exam Tip
(30) के अभाज्य भाजक (2,3,5) हैं। (1) और (30) अभाज्य भाजक नहीं हैं।
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यदि \(A={x:x\) (9) से छोटे अऋण पूर्णांक हैं(}) और \(B=\{0,1,2,3,4,5,6,7,8\}\) हैं तो क्या सत्य है?
If \(A={x:x\) is a non-negative integer less than (9)(}) and \(B=\{0,1,2,3,4,5,6,7,8\}\), what is true?
#sets
#equal_sets
#nonnegative_integers
A (A=B)
B \(A\ne B\) क्योंकि (0) प्राकृतिक नहीं है / \(A\ne B\) because (0) is not natural
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{1,2,3,4,5,6,7,8,9\}\)
Explanation opens after your attempt
Step 1
Concept
Non-negative integers start from (0) and those less than (9) go up to (8). Hence the two sets are equal.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Non-negative integers start from (0) and those less than (9) go up to (8). Hence the two sets are equal.
Step 3
Exam Tip
अऋण पूर्णांक (0) से शुरू होते हैं और (9) से छोटे होने पर (8) तक जाते हैं। इसलिए दोनों बराबर हैं।
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यदि \(A={x:x\) \(0\leq x<5\) और (x) पूर्णांक है(}) तथा \(B=\{0,1,2,3,4\}\) हैं तो क्या सत्य है?
If \(A={x:x\) is an integer with \(0\leq x<5\)(}) and \(B=\{0,1,2,3,4\}\), what is true?
#sets
#equal_sets
#inequality
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(5\in A\)
Explanation opens after your attempt
Step 1
Concept
The condition \(0\leq x<5\) includes (0) and excludes (5). Thus the elements are (0,1,2,3,4).
Step 2
Why this answer is correct
The correct answer is A. (A=B). The condition \(0\leq x<5\) includes (0) and excludes (5). Thus the elements are (0,1,2,3,4).
Step 3
Exam Tip
शर्त \(0\leq x<5\) में (0) शामिल और (5) बाहर है। इसलिए अवयव (0,1,2,3,4) हैं।
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यदि \(A={x:x\) \(x^2-4=0\) का प्राकृतिक हल है(}) और \(B=\{2\}\) हैं तो कौन सा विकल्प सही है?
If \(A={x:x\) is a natural solution of \(x^2-4=0\)(}) and \(B=\{2\}\), which option is correct?
#sets
#equal_sets
#natural_numbers
A (A=B)
B \(A=\{-2,2\}\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The equation has roots (-2,2), but the natural solution is only (2). Always check the given number set condition.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The equation has roots (-2,2), but the natural solution is only (2). Always check the given number set condition.
Step 3
Exam Tip
समीकरण के हल (-2,2) हैं पर प्राकृतिक हल केवल (2) है। दिए हुए संख्या समुच्चय की शर्त अवश्य देखें।
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यदि \(A={x:x\) (15) से छोटे (3) के धनात्मक गुणज हैं(}) और \(B=\{3,6,9,12\}\) हैं तो कौन सा निष्कर्ष सही है?
If \(A={x:x\) is a positive multiple of (3) less than (15)(}) and \(B=\{3,6,9,12\}\), which conclusion is correct?
#sets
#equal_sets
#multiples
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{3,6,9,12,15\}\)
Explanation opens after your attempt
Step 1
Concept
The positive multiples of (3) less than (15) are (3,6,9,12). The strict boundary excludes (15).
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive multiples of (3) less than (15) are (3,6,9,12). The strict boundary excludes (15).
Step 3
Exam Tip
(15) से छोटे (3) के धनात्मक गुणज (3,6,9,12) हैं। कठोर सीमा में (15) शामिल नहीं है।
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यदि \(A={x:x\in \mathbb{Z},x^2=1}\) और \(B=\{-1,1\}\) हैं तो क्या सत्य है?
If \(A={x:x\in \mathbb{Z},x^2=1}\) and \(B=\{-1,1\}\), what is true?
#sets
#equal_sets
#integer_solutions
A (A=B)
B \(A=\{1\}\)
C \(A=\{-1\}\)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
In integers, the solutions of \(x^2=1\) are (-1) and (1). Do not miss the negative solution.
Step 2
Why this answer is correct
The correct answer is A. (A=B). In integers, the solutions of \(x^2=1\) are (-1) and (1). Do not miss the negative solution.
Step 3
Exam Tip
पूर्णांकों में \(x^2=1\) के हल (-1) और (1) हैं। ऋणात्मक हल को न छोड़ें।
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यदि \(A\subseteq B\), (n(A)=6), और (n(B)=6) है तो (A) और (B) के बारे में क्या निश्चित है?
If \(A\subseteq B\), (n(A)=6), and (n(B)=6), what is certain about (A) and (B)?
#sets
#equal_sets
#cardinality
A (A=B)
B \(A\subset B\) और \(A\ne B\) / \(A\subset B\) and \(A\ne B\)
C \(A\cap B=\varnothing\)
D (B) में कम से कम सात अवयव हैं / (B) has at least seven elements
Explanation opens after your attempt
Step 1
Concept
When \(A\subseteq B\) and both have the same number of elements, no extra element remains. Hence (A=B).
Step 2
Why this answer is correct
The correct answer is A. (A=B). When \(A\subseteq B\) and both have the same number of elements, no extra element remains. Hence (A=B).
Step 3
Exam Tip
जब \(A\subseteq B\) और दोनों के अवयवों की संख्या समान हो तो कोई अतिरिक्त अवयव नहीं बचता। इसलिए (A=B)।
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यदि \(A=\{a,a,b,b,c\}\) और \(B=\{a,b,c\}\) हैं तो सही संबंध क्या है?
If \(A=\{a,a,b,b,c\}\) and \(B=\{a,b,c\}\), what is the correct relation?
#sets
#equal_sets
#repetition
A (A=B)
B \(A\ne B\) क्योंकि (A) में पाँच स्थान हैं / \(A\ne B\) because (A) has five positions
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Repeated elements are counted only once in a set. Therefore both have the same distinct elements.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Repeated elements are counted only once in a set. Therefore both have the same distinct elements.
Step 3
Exam Tip
दोहराए गए अवयव समुच्चय में एक बार ही माने जाते हैं। इसलिए दोनों में वही अलग अवयव हैं।
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यदि \(A={x:x\in \mathbb{N},x\leq 4}\) और \(B=\{4,3,2,1\}\) हैं तो कौन सा कथन सही है?
If \(A={x:x\in \mathbb{N},x\leq 4}\) and \(B=\{4,3,2,1\}\), which statement is correct?
#sets
#equal_sets
#order_irrelevant
A (A=B)
B \(A\ne B\) क्योंकि क्रम अलग है / \(A\ne B\) because the order is different
C \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
D \(B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Both sets contain only (1,2,3,4). Order has no importance in a set.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Both sets contain only (1,2,3,4). Order has no importance in a set.
Step 3
Exam Tip
दोनों समुच्चयों में (1,2,3,4) ही हैं। समुच्चय में क्रम का महत्व नहीं होता।
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यदि \(A={x:x\) (20) का धनात्मक भाजक है(}) और \(B=\{1,2,4,5,10,20\}\) हैं तो संबंध क्या है?
If \(A={x:x\) is a positive divisor of (20)(}) and \(B=\{1,2,4,5,10,20\}\), what is the relation?
#sets
#equal_sets
#divisors
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{2,4,5,10\}\)
Explanation opens after your attempt
Step 1
Concept
The positive divisors of (20) are (1,2,4,5,10,20). In divisor questions do not forget (1) and the number itself.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive divisors of (20) are (1,2,4,5,10,20). In divisor questions do not forget (1) and the number itself.
Step 3
Exam Tip
(20) के धनात्मक भाजक (1,2,4,5,10,20) हैं। भाजक वाले प्रश्न में (1) और संख्या स्वयं न भूलें।
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यदि \(A={x:x\) \(x^2-5x+6=0\) का हल है(}) और \(B=\{2,3\}\) हैं तो क्या सत्य है?
If \(A={x:x\) is a solution of \(x^2-5x+6=0\)(}) and \(B=\{2,3\}\), what is true?
#sets
#equal_sets
#quadratic_roots
A (A=B)
B \(A=\{6\}\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Since (x-2 -5x+6=(x-2)(x-3)), the solutions are (2,3). Make the roots the elements of the set.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Since (x-2 -5x+6=(x-2)(x-3)), the solutions are (2,3). Make the roots the elements of the set.
Step 3
Exam Tip
(x-2 -5x+6=(x-2)(x-3)) इसलिए हल (2,3) हैं। समीकरण के हलों को समुच्चय के अवयव बनाएं।
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यदि \(A=\{2,3,5,7\}\) और \(B={x:x\) दस से छोटे अभाज्य अंक हैं(}) हैं तो कौन सा विकल्प सही है?
If \(A=\{2,3,5,7\}\) and \(B={x:x\) is a prime digit less than ten(}), which option is correct?
#sets
#equal_sets
#prime_numbers
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\cap B={1}\)
Explanation opens after your attempt
Step 1
Concept
The prime digits less than ten are (2,3,5,7). The number (1) is not prime.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The prime digits less than ten are (2,3,5,7). The number (1) is not prime.
Step 3
Exam Tip
दस से छोटे अभाज्य अंक (2,3,5,7) हैं। (1) अभाज्य नहीं होता।
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यदि \(A={x:x\) (18) का धनात्मक भाजक है और (x) विषम है(}) तो कौन सा समुच्चय (A) के बराबर है?
If \(A={x:x\) is a positive divisor of (18) and (x) is odd(}), which set is equal to (A)?
#sets
#equal_sets
#divisors
A ({1,3,9})
B ({2,6,18})
C ({1,2,3,6,9,18})
D ({3,6,9})
Explanation opens after your attempt
Correct Answer
A. ({1,3,9})
Step 1
Concept
The odd positive divisors of (18) are (1,3,9). Apply all conditions together.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,9}). The odd positive divisors of (18) are (1,3,9). Apply all conditions together.
Step 3
Exam Tip
(18) के विषम धनात्मक भाजक (1,3,9) हैं। सभी शर्तों को साथ में लागू करें।
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यदि \(A\subset B\) और \(B\subset A\) हैं तो सही निष्कर्ष क्या है?
If \(A\subset B\) and \(B\subset A\), what is the correct conclusion?
#sets
#equal_sets
#proof_method
A (A=B)
B \(A\cap B=\varnothing\)
C (A) और (B) अनंत हैं / (A) and (B) are infinite
D \(A\ne B\) हमेशा / \(A\ne B\) always
Explanation opens after your attempt
Step 1
Concept
Subset relation in both directions means both sets have exactly the same elements. This is a standard way to prove equality of sets.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Subset relation in both directions means both sets have exactly the same elements. This is a standard way to prove equality of sets.
Step 3
Exam Tip
दोनों दिशाओं में उपसमुच्चय होने का अर्थ है कि दोनों में ठीक वही अवयव हैं। बराबर समुच्चय सिद्ध करने की यह मानक विधि है।
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यदि \(A={x:x\) (12) का अभाज्य गुणनखंड है(}) और \(B=\{2,3\}\) हैं तो क्या सत्य है?
If \(A={x:x\) is a prime factor of (12)(}) and \(B=\{2,3\}\), what is true?
#sets
#equal_sets
#prime_factors
A (A=B)
B \(A=\{2,2,3\}\) इसलिए \(A\ne B\) / \(A=\{2,2,3\}\) so \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\cap B={12}\)
Explanation opens after your attempt
Step 1
Concept
The distinct prime factors of (12) are (2) and (3). Repeated factors are not repeated in a set.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The distinct prime factors of (12) are (2) and (3). Repeated factors are not repeated in a set.
Step 3
Exam Tip
(12) के अलग अभाज्य गुणनखंड (2) और (3) हैं। समुच्चय में दोहराव नहीं लिखा जाता।
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यदि \(A=\{1,3,5,7\}\) और \(B={x:x\) आठ से छोटे धनात्मक विषम पूर्णांक हैं(}) तो (A) और (B) का संबंध क्या है?
If \(A=\{1,3,5,7\}\) and \(B={x:x\) is a positive odd integer less than eight(}), what is the relation between (A) and (B)?
#sets
#equal_sets
#odd_numbers
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\not\subset B\)
Explanation opens after your attempt
Step 1
Concept
The positive odd integers less than eight are (1,3,5,7). Write the described set in elements before comparing.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive odd integers less than eight are (1,3,5,7). Write the described set in elements before comparing.
Step 3
Exam Tip
आठ से छोटे धनात्मक विषम पूर्णांक (1,3,5,7) हैं। शब्दों में दिए समुच्चय को अवयवों में लिखें।
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यदि \(A={x:x\) अंग्रेजी शब्द गणित के अक्षर हैं(}) और \(B=\{m,a,t,h\}\) हैं तो सही कथन क्या है?
If \(A={x:x\) is a letter of the English word math(}) and \(B=\{m,a,t,h\}\), what is the correct statement?
#sets
#equal_sets
#letters
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Both sets contain the same four distinct letters. Repetition and order do not affect a set.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Both sets contain the same four distinct letters. Repetition and order do not affect a set.
Step 3
Exam Tip
दोनों में वही चार अलग अक्षर हैं। समुच्चय में दोहराव और क्रम का प्रभाव नहीं होता।
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यदि \(A=\{1,2,{3}\}\) है तो कौन सा समुच्चय (A) के बराबर है?
If \(A=\{1,2,{3}\}\), which set is equal to (A)?
#sets
#equal_sets
#nested_sets
A ({2,{3},1})
B ({1,2,3})
C ({1,{2,3}})
D ({{1},2,{3}})
Explanation opens after your attempt
Correct Answer
A. ({2,{3},1})
Step 1
Concept
Changing order does not change a set but ({3}) and (3) are different. Identify nested elements carefully.
Step 2
Why this answer is correct
The correct answer is A. ({2,{3},1}). Changing order does not change a set but ({3}) and (3) are different. Identify nested elements carefully.
Step 3
Exam Tip
समुच्चय में क्रम बदलने से समुच्चय नहीं बदलता पर ({3}) और (3) अलग हैं। नेस्टेड अवयव को अलग पहचानें।
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यदि \(A=\{2,4,6,8\}\) और \(B={x:x\) दस से छोटे धनात्मक सम पूर्णांक हैं(}) तो कौन सा विकल्प सही है?
If \(A=\{2,4,6,8\}\) and \(B={x:x\) is a positive even integer less than ten(}), which option is correct?
#sets
#equal_sets
#roster_form
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(B\ne A\)
D \(A\not\subset B\)
Explanation opens after your attempt
Step 1
Concept
The positive even integers less than ten are (2,4,6,8). Convert set builder form to roster form before comparing.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive even integers less than ten are (2,4,6,8). Convert set builder form to roster form before comparing.
Step 3
Exam Tip
दस से छोटे धनात्मक सम पूर्णांक (2,4,6,8) हैं। वर्णनात्मक रूप को रोस्टर रूप में बदलकर मिलान करें।
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समुच्चय \(A={x:x^2=16}\) और \(B=\{-4,4\}\) के बारे में सही कथन कौन सा है?
Which statement is correct about the sets \(A={x:x^2=16}\) and \(B=\{-4,4\}\)?
#sets
#equal_sets
#quadratic
A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The solutions of \(x^2=16\) are (-4) and (4) so both sets have the same elements. In exams compare elements not order.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The solutions of \(x^2=16\) are (-4) and (4) so both sets have the same elements. In exams compare elements not order.
Step 3
Exam Tip
\(x^2=16\) के हल (-4) और (4) हैं इसलिए दोनों में वही अवयव हैं। परीक्षा में क्रम नहीं अवयव देखें।
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यदि \(A\subseteq B\), \(B\subseteq C\) और (A=C) हैं तो (A,B,C) के बारे में कौन सा निष्कर्ष सही है?
If \(A\subseteq B\), \(B\subseteq C\), and (A=C), then which conclusion about (A,B,C) is correct?
#sets
#subset-chain
#equal-sets
#reasoning
A (A=B=C)
B केवल \(A\subset B\) / Only \(A\subset B\)
C केवल \(B\subset C\) / Only \(B\subset C\)
D तीनों समुच्चय असमान हैं / All three sets are unequal
Explanation opens after your attempt
Correct Answer
A. (A=B=C)
Step 1
Concept
(B) lies between (A) and (C), and (A=C), so (B) must also be equal to them. In subset chains, check equality conditions carefully.
Step 2
Why this answer is correct
The correct answer is A. (A=B=C). (B) lies between (A) and (C), and (A=C), so (B) must also be equal to them. In subset chains, check equality conditions carefully.
Step 3
Exam Tip
(B) (A) और (C) के बीच है और (A=C) है, इसलिए (B) भी उसी के बराबर होगा। उपसमुच्चय शृंखला में बराबरी की स्थिति ध्यान से देखें।
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यदि \(A={x:x\in \mathbb{N}, x^2-7x+12=0}\) और \(B=\{3,4\}\) हैं तो सही कथन कौन सा है?
If \(A={x:x\in \mathbb{N}, x^2-7x+12=0}\) and \(B=\{3,4\}\) then which statement is correct?
#sets
#equal-sets
#quadratic
#pyq
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 \(2\in A\)
Explanation opens after your attempt
Step 1
Concept
The solutions of the equation are (3) and (4), so the two sets are equal. First solve the equation and then match the elements.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The solutions of the equation are (3) and (4), so the two sets are equal. First solve the equation and then match the elements.
Step 3
Exam Tip
समीकरण के हल (3) और (4) हैं इसलिए दोनों समुच्चय समान हैं। पहले समीकरण हल करें फिर अवयव मिलाएं।
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