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 \(B=\{-4,4\}\)?
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#quadratic
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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 \(A={X:X\) 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?
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#equal_sets
#singleton_subsets
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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 \(A=\{2,4,6,8\}\) 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?
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#roster_form
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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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यदि \(A={\varnothing,{\varnothing}}\) है तो निम्न में से कौन (A) का उपसमुच्चय नहीं है?
If \(A={\varnothing,{\varnothing}}\), which of the following is not a subset of (A)?
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#empty_set
#subset_test
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A \({\varnothing}\)
B \({{\varnothing}}\)
C \(\varnothing\)
D \({\varnothing,{{\varnothing}}}\)
Explanation opens after your attempt
Correct Answer
D. \({\varnothing,{{\varnothing}}}\)
Step 1
Concept
Option D contains \({{\varnothing}}\) as an element, which is not in (A). In empty set questions count the braces carefully.
Step 2
Why this answer is correct
The correct answer is D. \({\varnothing,{{\varnothing}}}\). Option D contains \({{\varnothing}}\) as an element, which is not in (A). In empty set questions count the braces carefully.
Step 3
Exam Tip
विकल्प D में \({{\varnothing}}\) अवयव है जो (A) में नहीं है। रिक्त समुच्चय वाले प्रश्नों में कोष्ठकों की संख्या गिनें।
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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)?
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#equal_sets
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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 \(A\subseteq B\), (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?
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#equal_sets
#cardinality_reasoning
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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 \(A=\{a,b,c\}\) है तो (A) के कुल उपसमुच्चयों की संख्या क्या होगी?
If \(A=\{a,b,c\}\), what is the total number of subsets of (A)?
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A (3)
B (6)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
A set with three elements has \(2^3=8\) subsets. Count the empty set and the set itself among all subsets.
Step 2
Why this answer is correct
The correct answer is C. (8). A set with three elements has \(2^3=8\) subsets. Count the empty set and the set itself among all subsets.
Step 3
Exam Tip
तीन अवयवों वाले समुच्चय के उपसमुच्चय \(2^3=8\) होते हैं। कुल उपसमुच्चय में रिक्त समुच्चय और वही समुच्चय भी गिनें।
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यदि \(A={x:x\in \mathbb{Z}\) और (|x-2|<2}) है तो निम्न में से कौन (A) का उचित उपसमुच्चय है?
If \(A={x:x\in \mathbb{Z}\) and (|x-2|<2}), which of the following is a proper subset of (A)?
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#integer_interval
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A ({1,2,3})
B ({1,3})
C ({0,1,2})
D ({2,4})
Explanation opens after your attempt
Correct Answer
B. ({1,3})
Step 1
Concept
The condition (|x-2|<2) gives integers (1,2,3), and ({1,3}) lies inside it but is not equal to it. A proper subset has all elements inside but is not the whole set.
Step 2
Why this answer is correct
The correct answer is B. ({1,3}). The condition (|x-2|<2) gives integers (1,2,3), and ({1,3}) lies inside it but is not equal to it. A proper subset has all elements inside but is not the whole set.
Step 3
Exam Tip
(|x-2|<2) से पूर्णांक (1,2,3) मिलते हैं और ({1,3}) इसके अंदर है पर बराबर नहीं है। उचित उपसमुच्चय में सभी अवयव अंदर होते हैं लेकिन पूरा समुच्चय नहीं होता।
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यदि किसी समुच्चय के उचित उपसमुच्चय (31) हैं तो उस समुच्चय में अवयवों की संख्या क्या है?
If a set has (31) proper subsets, how many elements does the set have?
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A (4)
B (5)
C (6)
D (31)
Explanation opens after your attempt
Step 1
Concept
The number of proper subsets is \(2^n-1\). From \(2^n-1=31\), we get (n=5).
Step 2
Why this answer is correct
The correct answer is B. (5). The number of proper subsets is \(2^n-1\). From \(2^n-1=31\), we get (n=5).
Step 3
Exam Tip
उचित उपसमुच्चय की संख्या \(2^n-1\) होती है। \(2^n-1=31\) से (n=5) मिलता है।
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यदि \(A=\varnothing\) और \(B=\{0\}\) हैं तो कौन सा विकल्प सही है?
If \(A=\varnothing\) and \(B=\{0\}\), which option is correct?
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A (A=B)
B \(A\subset B\) और \(A\ne B\) / \(A\subset B\) and \(A\ne B\)
C \(B\subset A\)
D \(0\in A\)
Explanation opens after your attempt
Correct Answer
B. \(A\subset B\) और \(A\ne B\) / \(A\subset B\) and \(A\ne B\)
Step 1
Concept
The empty set is a subset of every set and ({0}) is not empty. Keep \(\varnothing\) and (0) different.
Step 2
Why this answer is correct
The correct answer is B. \(A\subset B\) और \(A\ne B\) / \(A\subset B\) and \(A\ne B\). The empty set is a subset of every set and ({0}) is not empty. Keep \(\varnothing\) and (0) different.
Step 3
Exam Tip
रिक्त समुच्चय हर समुच्चय का उपसमुच्चय है और ({0}) रिक्त नहीं है। \(\varnothing\) और (0) को अलग रखें।
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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?
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#equal_sets
#letters
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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 \(A=\{1,3,5,7\}\) 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)?
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#equal_sets
#odd_numbers
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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 \(A=\{1,2,3,4\}\) और \(B=\{1,2\}\) है तो कौन सा कथन सही है?
If \(A=\{1,2,3,4\}\) and \(B=\{1,2\}\), which statement is correct?
#sets
#proper_subset
#basic_relation
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A \(A\subset B\)
B \(B\subset A\) और \(B\ne A\) / \(B\subset A\) and \(B\ne A\)
C (A=B)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(B\subset A\) और \(B\ne A\) / \(B\subset A\) and \(B\ne A\)
Step 1
Concept
All elements of (B) are in (A), but (A) has extra elements. This is a proper subset relation.
Step 2
Why this answer is correct
The correct answer is B. \(B\subset A\) और \(B\ne A\) / \(B\subset A\) and \(B\ne A\). All elements of (B) are in (A), but (A) has extra elements. This is a proper subset relation.
Step 3
Exam Tip
(B) के सभी अवयव (A) में हैं लेकिन (A) में अतिरिक्त अवयव भी हैं। इसे उचित उपसमुच्चय कहते हैं।
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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?
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#prime_factors
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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 \(A=\{1,2\}\) और \(B=\{{1,2}\}\) हैं तो कौन सा कथन सही है?
If \(A=\{1,2\}\) and \(B=\{{1,2}\}\), which statement is correct?
#sets
#element_vs_subset
#nested_sets
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A (A=B)
B \(A\in B\)
C \(B\subset A\)
D \(1\in B\)
Explanation opens after your attempt
Correct Answer
B. \(A\in B\)
Step 1
Concept
The only element of (B) is the whole set ({1,2}). Be careful with subset and element symbols.
Step 2
Why this answer is correct
The correct answer is B. \(A\in B\). The only element of (B) is the whole set ({1,2}). Be careful with subset and element symbols.
Step 3
Exam Tip
(B) का एकमात्र अवयव पूरा समुच्चय ({1,2}) है। उपसमुच्चय और अवयव के चिन्ह में सावधानी रखें।
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यदि \(A=\{p,q,r,s\}\) और \(B=\{p,r\}\) हैं तो (B) के कौन से उपसमुच्चय (A) के भी उपसमुच्चय हैं?
If \(A=\{p,q,r,s\}\) and \(B=\{p,r\}\), which subsets of (B) are also subsets of (A)?
#sets
#subset_transitivity
#reasoning
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A केवल ({p,r}) / Only ({p,r})
B केवल \(\varnothing\) / Only \(\varnothing\)
C (B) के सभी उपसमुच्चय / All subsets of (B)
D केवल एकल अवयव वाले उपसमुच्चय / Only singleton subsets
Explanation opens after your attempt
Correct Answer
C. (B) के सभी उपसमुच्चय / All subsets of (B)
Step 1
Concept
Because \(B\subset A\), every subset of (B) is also a subset of (A). This uses transitive reasoning.
Step 2
Why this answer is correct
The correct answer is C. (B) के सभी उपसमुच्चय / All subsets of (B). Because \(B\subset A\), every subset of (B) is also a subset of (A). This uses transitive reasoning.
Step 3
Exam Tip
क्योंकि \(B\subset A\), इसलिए (B) का हर उपसमुच्चय (A) का भी उपसमुच्चय है। यह ट्रांजिटिव सोच का प्रयोग है।
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यदि \(A=\{0,1,2\}\) है तो निम्न में से कौन (A) का उपसमुच्चय नहीं है?
If \(A=\{0,1,2\}\), which of the following is not a subset of (A)?
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#subset_test
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A \(\varnothing\)
B ({0,2})
C ({1})
D \({\varnothing}\)
Explanation opens after your attempt
Correct Answer
D. \({\varnothing}\)
Step 1
Concept
\(\varnothing\) is a subset, but \({\varnothing}\) has \(\varnothing\) as an element, which is not in (A). This is a common mistake.
Step 2
Why this answer is correct
The correct answer is D. \({\varnothing}\). \(\varnothing\) is a subset, but \({\varnothing}\) has \(\varnothing\) as an element, which is not in (A). This is a common mistake.
Step 3
Exam Tip
\(\varnothing\) उपसमुच्चय है लेकिन \({\varnothing}\) में अवयव \(\varnothing\) है जो (A) में नहीं है। यह सामान्य गलती है।
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यदि (P(A)) में (16) अवयव हैं तो (A) में कितने अवयव होंगे?
If (P(A)) has (16) elements, how many elements does (A) have?
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A (2)
B (3)
C (4)
D (16)
Explanation opens after your attempt
Step 1
Concept
If (A) has (n) elements, then (P(A)) has \(2^n\) elements. From \(2^n=16\), (n=4).
Step 2
Why this answer is correct
The correct answer is C. (4). If (A) has (n) elements, then (P(A)) has \(2^n\) elements. From \(2^n=16\), (n=4).
Step 3
Exam Tip
यदि (A) में (n) अवयव हों तो (P(A)) में \(2^n\) अवयव होते हैं। \(2^n=16\) से (n=4) है।
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कौन सा विकल्प \(A=\{1,2,3\}\) के पावर समुच्चय का अवयव है?
Which option is an element of the power set of \(A=\{1,2,3\}\)?
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A (2)
B ({2,3})
C ({4})
D ({{1}})
Explanation opens after your attempt
Correct Answer
B. ({2,3})
Step 1
Concept
Elements of a power set are subsets of the original set. ({2,3}) is a subset of (A).
Step 2
Why this answer is correct
The correct answer is B. ({2,3}). Elements of a power set are subsets of the original set. ({2,3}) is a subset of (A).
Step 3
Exam Tip
पावर समुच्चय के अवयव मूल समुच्चय के उपसमुच्चय होते हैं। ({2,3}) (A) का उपसमुच्चय है।
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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
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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 \(A={x:x\) (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
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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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कौन सा विकल्प \(A=\{1,{2},3\}\) का उपसमुच्चय है?
Which option is a subset of \(A=\{1,{2},3\}\)?
#sets
#nested_sets
#subset_test
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A ({1,2})
B ({{2},3})
C ({{1,2}})
D ({2,3})
Explanation opens after your attempt
Correct Answer
B. ({{2},3})
Step 1
Concept
The set (A) has ({2}) as an element but not (2). Therefore ({{2},3}) is a subset.
Step 2
Why this answer is correct
The correct answer is B. ({{2},3}). The set (A) has ({2}) as an element but not (2). Therefore ({{2},3}) is a subset.
Step 3
Exam Tip
(A) में ({2}) अवयव है पर (2) अवयव नहीं है। इसलिए ({{2},3}) उपसमुच्चय है।
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यदि \(A=\{1,2,3,4,5\}\) है तो (A) के दो अवयवों वाले उपसमुच्चयों की संख्या क्या है?
If \(A=\{1,2,3,4,5\}\), how many subsets of (A) have exactly two elements?
#sets
#subsets
#combinations
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A (5)
B (10)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
The number of ways to choose two elements is \(\binom{5}{2}=10\). Order is not counted in subsets.
Step 2
Why this answer is correct
The correct answer is B. (10). The number of ways to choose two elements is \(\binom{5}{2}=10\). Order is not counted in subsets.
Step 3
Exam Tip
दो अवयव चुनने की संख्या \(\binom{5}{2}=10\) है। उपसमुच्चय में क्रम नहीं गिना जाता।
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यदि \(A=\{a,b,c,d\}\) है तो (A) के कम से कम दो अवयवों वाले उपसमुच्चयों की संख्या क्या है?
If \(A=\{a,b,c,d\}\), how many subsets of (A) have at least two elements?
#sets
#subsets
#counting
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A (6)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
There are (16) total subsets and (1+4=5) subsets with zero or one element. So the answer is (16-5=11).
Step 2
Why this answer is correct
The correct answer is C. (11). There are (16) total subsets and (1+4=5) subsets with zero or one element. So the answer is (16-5=11).
Step 3
Exam Tip
कुल उपसमुच्चय (16) हैं और शून्य या एक अवयव वाले (1+4=5) हैं। इसलिए उत्तर (16-5=11) है।
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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
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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 \(A={x:x\) \(x^2-5x+6=0\) 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
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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 \(A=\{1,2,3\}\) और \(B=\{1,2,3,4\}\) हैं तो \(A\subset B\) के बारे में क्या सही है?
If \(A=\{1,2,3\}\) and \(B=\{1,2,3,4\}\), what is true about \(A\subset B\)?
#sets
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#definition
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A सत्य है और (A) उचित उपसमुच्चय है / It is true and (A) is a proper subset
B सत्य है पर (A=B) / It is true but (A=B)
C असत्य है क्योंकि \(4\notin A\) / It is false because \(4\notin A\)
D असत्य है क्योंकि (B) बड़ा है / It is false because (B) is larger
Explanation opens after your attempt
Correct Answer
A. सत्य है और (A) उचित उपसमुच्चय है / It is true and (A) is a proper subset
Step 1
Concept
All elements of (A) are in (B), and (B) has one extra element. Hence (A) is a proper subset.
Step 2
Why this answer is correct
The correct answer is A. सत्य है और (A) उचित उपसमुच्चय है / It is true and (A) is a proper subset. All elements of (A) are in (B), and (B) has one extra element. Hence (A) is a proper subset.
Step 3
Exam Tip
(A) के सभी अवयव (B) में हैं और (B) में एक अतिरिक्त अवयव है। इसलिए (A) उचित उपसमुच्चय है।
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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
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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 \(A={x:x\in \mathbb{N},x\leq 4}\) 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
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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 \(A=\{a,a,b,b,c\}\) 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
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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 \(A={1,2,\varnothing}\) है तो निम्न में से कौन (A) का उपसमुच्चय है?
If \(A={1,2,\varnothing}\), which of the following is a subset of (A)?
#sets
#empty_set
#subset_test
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A \({1,\varnothing}\)
B ({0})
C ({{1}})
D ({1,3})
Explanation opens after your attempt
Correct Answer
A. \({1,\varnothing}\)
Step 1
Concept
Both (1) and \(\varnothing\) are elements of (A). Every chosen element of a subset must belong to the original set.
Step 2
Why this answer is correct
The correct answer is A. \({1,\varnothing}\). Both (1) and \(\varnothing\) are elements of (A). Every chosen element of a subset must belong to the original set.
Step 3
Exam Tip
(1) और \(\varnothing\) दोनों (A) के अवयव हैं। उपसमुच्चय में हर चुना अवयव मूल समुच्चय में होना चाहिए।
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यदि \(A=\{1,2,3\}\) है तो (A) के सभी उचित उपसमुच्चयों की संख्या क्या है?
If \(A=\{1,2,3\}\), what is the number of all proper subsets of (A)?
#sets
#proper_subsets
#counting
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
A three element set has \(2^3=8\) total subsets. Removing the whole set (A) gives (7) proper subsets.
Step 2
Why this answer is correct
The correct answer is B. (7). A three element set has \(2^3=8\) total subsets. Removing the whole set (A) gives (7) proper subsets.
Step 3
Exam Tip
तीन अवयवों के कुल उपसमुच्चय \(2^3=8\) हैं। उचित उपसमुच्चय में पूरा (A) हटाने पर (7) बचते हैं।
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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
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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 \(A={x:x\in \mathbb{Z},x^2=1}\) 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
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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 \(A={x:x\) (36) का धनात्मक पूर्ण वर्ग भाजक है(}) तो (A) कौन सा है?
If \(A={x:x\) is a positive square divisor of (36)(}), which set is (A)?
#sets
#set_builder
#divisors
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A ({1,4,9,36})
B ({4,9})
C ({1,6,36})
D ({2,3,6})
Explanation opens after your attempt
Correct Answer
A. ({1,4,9,36})
Step 1
Concept
The square divisors of (36) are (1,4,9,36). Check both conditions square and divisor.
Step 2
Why this answer is correct
The correct answer is A. ({1,4,9,36}). The square divisors of (36) are (1,4,9,36). Check both conditions square and divisor.
Step 3
Exam Tip
(36) के वर्ग भाजक (1,4,9,36) हैं। वर्ग होने और भाजक होने दोनों शर्तें जांचें।
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यदि \(A=\{1,2,3,4\}\) और \(C=\{2,4\}\) हैं तो \(C\subset A\) क्यों सत्य है?
If \(A=\{1,2,3,4\}\) and \(C=\{2,4\}\), why is \(C\subset A\) true?
#sets
#proper_subset
#reasoning
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A क्योंकि (C) का हर अवयव (A) में है और \(A\ne C\) / Because every element of (C) is in (A) and \(A\ne C\)
B क्योंकि (A) का हर अवयव (C) में है / Because every element of (A) is in (C)
C क्योंकि दोनों का पहला अवयव समान है / Because the first element of both is same
D क्योंकि (C) में कम अवयव हैं इसलिए हमेशा उपसमुच्चय है / Because (C) has fewer elements so it is always a subset
Explanation opens after your attempt
Correct Answer
A. क्योंकि (C) का हर अवयव (A) में है और \(A\ne C\) / Because every element of (C) is in (A) and \(A\ne C\)
Step 1
Concept
A proper subset needs inclusion of every element and inequality. Having fewer elements alone is not enough.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि (C) का हर अवयव (A) में है और \(A\ne C\) / Because every element of (C) is in (A) and \(A\ne C\). A proper subset needs inclusion of every element and inequality. Having fewer elements alone is not enough.
Step 3
Exam Tip
उचित उपसमुच्चय के लिए हर अवयव का सम्मिलन और असमानता दोनों चाहिए। केवल अवयवों की संख्या कम होना पर्याप्त नहीं है।
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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?
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#equal_sets
#multiples
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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 \(A=\{1,2\}\), \(B=\{1,2,3\}\), और \(C=\{1,2,3,4\}\) हैं तो कौन सा कथन सही है?
If \(A=\{1,2\}\), \(B=\{1,2,3\}\), and \(C=\{1,2,3,4\}\), which statement is correct?
#sets
#subset_chain
#transitivity
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A \(A\subset B\subset C\)
B \(C\subset B\subset A\)
C (A=B=C)
D \(A\not\subset C\)
Explanation opens after your attempt
Correct Answer
A. \(A\subset B\subset C\)
Step 1
Concept
Each next set contains all elements of the previous one and one extra element. Hence it forms a chain of proper subsets.
Step 2
Why this answer is correct
The correct answer is A. \(A\subset B\subset C\). Each next set contains all elements of the previous one and one extra element. Hence it forms a chain of proper subsets.
Step 3
Exam Tip
हर अगले समुच्चय में पिछले के सभी अवयव और एक अतिरिक्त अवयव है। इसलिए उचित उपसमुच्चय की शृंखला बनती है।
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यदि \(A={x:x\in \mathbb{N},2<x\leq 6}\) तो निम्न में से कौन (A) का उचित उपसमुच्चय है?
If \(A={x:x\in \mathbb{N},2<x\leq 6}\), which of the following is a proper subset of (A)?
#sets
#proper_subset
#set_builder
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A ({3,4,5,6})
B ({3,5})
C ({2,3})
D ({6,7})
Explanation opens after your attempt
Correct Answer
B. ({3,5})
Step 1
Concept
Here \(A=\{3,4,5,6\}\), and ({3,5}) lies inside it but is not equal to it. So it is a proper subset.
Step 2
Why this answer is correct
The correct answer is B. ({3,5}). Here \(A=\{3,4,5,6\}\), and ({3,5}) lies inside it but is not equal to it. So it is a proper subset.
Step 3
Exam Tip
\(A=\{3,4,5,6\}\) है और ({3,5}) इसके अंदर है पर बराबर नहीं है। इसलिए यह उचित उपसमुच्चय है।
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यदि \(A=\{1,2,3\}\) और \(B=\{1,2,3,{1}\}\) हैं तो (A) और (B) का संबंध क्या है?
If \(A=\{1,2,3\}\) and \(B=\{1,2,3,{1}\}\), what is the relation between (A) and (B)?
#sets
#nested_sets
#proper_subset
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A (A=B)
B \(A\subset B\) और \(A\ne B\) / \(A\subset B\) and \(A\ne B\)
C \(B\subset A\) और \(A\ne B\) / \(B\subset A\) and \(A\ne B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(A\subset B\) और \(A\ne B\) / \(A\subset B\) and \(A\ne B\)
Step 1
Concept
All elements of (A) are in (B), and (B) has the extra element ({1}). Treat ({1}) as different from (1).
Step 2
Why this answer is correct
The correct answer is B. \(A\subset B\) और \(A\ne B\) / \(A\subset B\) and \(A\ne B\). All elements of (A) are in (B), and (B) has the extra element ({1}). Treat ({1}) as different from (1).
Step 3
Exam Tip
(A) के सभी अवयव (B) में हैं और (B) में अतिरिक्त अवयव ({1}) है। ({1}) को (1) से अलग मानें।
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यदि \(A={x:x\) (50) से छोटे (10) के धनात्मक गुणज हैं(}) तो (A) के उचित उपसमुच्चयों की संख्या क्या है?
If \(A={x:x\) is a positive multiple of (10) less than (50)(}), how many proper subsets does (A) have?
#sets
#proper_subsets
#multiples
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A (7)
B (15)
C (16)
D (31)
Explanation opens after your attempt
Step 1
Concept
\(A=\{10,20,30,40\}\) has (4) elements. Proper subsets are \(2^4-1=15\).
Step 2
Why this answer is correct
The correct answer is B. (15). \(A=\{10,20,30,40\}\) has (4) elements. Proper subsets are \(2^4-1=15\).
Step 3
Exam Tip
\(A=\{10,20,30,40\}\) में (4) अवयव हैं। उचित उपसमुच्चय \(2^4-1=15\) होते 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
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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 \(A={x:x\) (24) का सम धनात्मक भाजक है(}) तो कौन सा विकल्प (A) का उपसमुच्चय है?
If \(A={x:x\) is an even positive divisor of (24)(}), which option is a subset of (A)?
#sets
#subset_test
#divisors
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A ({2,6,8})
B ({1,2,3})
C ({2,5,12})
D ({4,9})
Explanation opens after your attempt
Correct Answer
A. ({2,6,8})
Step 1
Concept
Here \(A=\{2,4,6,8,12,24\}\), and (2,6,8) all belong to (A). An option with an outside element is not a subset.
Step 2
Why this answer is correct
The correct answer is A. ({2,6,8}). Here \(A=\{2,4,6,8,12,24\}\), and (2,6,8) all belong to (A). An option with an outside element is not a subset.
Step 3
Exam Tip
\(A=\{2,4,6,8,12,24\}\) है और विकल्प में (2,6,8) सभी (A) में हैं। बाहरी अवयव वाला विकल्प उपसमुच्चय नहीं होता।
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यदि \(A=\{1,2,3,4\}\) है तो (A) के तीन अवयवों वाले उचित उपसमुच्चयों की संख्या क्या है?
If \(A=\{1,2,3,4\}\), how many proper subsets of (A) have exactly three elements?
#sets
#proper_subsets
#combinations
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A (3)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The number of ways to choose three elements is \(\binom{4}{3}=4\). All are proper because the whole set has four elements.
Step 2
Why this answer is correct
The correct answer is B. (4). The number of ways to choose three elements is \(\binom{4}{3}=4\). All are proper because the whole set has four elements.
Step 3
Exam Tip
तीन अवयव चुनने की संख्या \(\binom{4}{3}=4\) है। ये सभी उचित हैं क्योंकि पूरा समुच्चय चार अवयवों का है।
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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
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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 \(A=\{1,2,3\}\) है तो (P(A)) में ({1,3}) के बारे में कौन सा कथन सही है?
If \(A=\{1,2,3\}\), which statement about ({1,3}) in (P(A)) is correct?
#sets
#power_set
#subset_element
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A \({1,3}\in P(A)\)
B \({1,3}\notin P(A)\)
C \(1,3\notin A\)
D (P(A)=A)
Explanation opens after your attempt
Correct Answer
A. \({1,3}\in P(A)\)
Step 1
Concept
Since \({1,3}\subseteq A\), ({1,3}) is an element of the power set. In a power set, subsets become elements.
Step 2
Why this answer is correct
The correct answer is A. \({1,3}\in P(A)\). Since \({1,3}\subseteq A\), ({1,3}) is an element of the power set. In a power set, subsets become elements.
Step 3
Exam Tip
क्योंकि \({1,3}\subseteq A\), इसलिए ({1,3}) पावर समुच्चय का अवयव है। पावर समुच्चय में उपसमुच्चय अवयव बनते 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
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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 \(A=\{2,4,6\}\) है तो कौन सा विकल्प (A) का उपसमुच्चय है पर उचित उपसमुच्चय नहीं है?
If \(A=\{2,4,6\}\), which option is a subset of (A) but not a proper subset?
#sets
#proper_subset
#self_subset
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A ({2,4})
B ({2,4,6})
C \(\varnothing\)
D ({6})
Explanation opens after your attempt
Correct Answer
B. ({2,4,6})
Step 1
Concept
A set is a subset of itself but not a proper subset of itself. Proper relation excludes equality.
Step 2
Why this answer is correct
The correct answer is B. ({2,4,6}). A set is a subset of itself but not a proper subset of itself. Proper relation excludes equality.
Step 3
Exam Tip
समुच्चय अपने आप का उपसमुच्चय है पर अपने आप का उचित उपसमुच्चय नहीं है। उचित संबंध में बराबरी हटती है।
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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
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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 \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), 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
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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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