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
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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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यदि \(A=\{1,2,3,4,5,6,7\}\) है तो ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (2) और (5) अवश्य हों लेकिन (7) न हो?
If \(A=\{1,2,3,4,5,6,7\}\) then how many subsets contain (2) and (5) necessarily but do not contain (7)?
#sets
#subsets
#conditional-counting
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A (8)
B (12)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(2) and (5) are fixed and (7) is excluded, while the remaining (4) elements are free. Hence the number is \(2^4=16\).
Step 2
Why this answer is correct
The correct answer is C. (16). (2) and (5) are fixed and (7) is excluded, while the remaining (4) elements are free. Hence the number is \(2^4=16\).
Step 3
Exam Tip
(2) और (5) निश्चित हैं तथा (7) हटेगा, बाकी (4) अवयव स्वतंत्र हैं। इसलिए संख्या \(2^4=16\) है।
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यदि \(A=\{2,3,5,7\}\) है तो ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (2) हो पर (7) न हो?
If \(A=\{2,3,5,7\}\) then how many subsets contain (2) but do not contain (7)?
#sets
#conditional-subsets
#counting
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(2) is fixed and (7) is excluded, while (3,5) are free. Hence the number is \(2^2=4\).
Step 2
Why this answer is correct
The correct answer is B. (4). (2) is fixed and (7) is excluded, while (3,5) are free. Hence the number is \(2^2=4\).
Step 3
Exam Tip
(2) निश्चित है और (7) हटेगा, बाकी (3,5) स्वतंत्र हैं। इसलिए संख्या \(2^2=4\) है।
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यदि \(A={\varnothing,{\varnothing}}\) है तो (P(A)) में कौन सा अवयव अवश्य होगा?
If \(A={\varnothing,{\varnothing}}\) then which element must belong to (P(A))?
#sets
#power-set
#nested-sets
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A \({{\varnothing}}\)
B \(\varnothing\in A\)
C (1)
D ({1})
Explanation opens after your attempt
Correct Answer
A. \({{\varnothing}}\)
Step 1
Concept
Elements of (P(A)) are subsets of (A), and \({{\varnothing}}\) is a subset of (A). In a power set, elements are always subsets.
Step 2
Why this answer is correct
The correct answer is A. \({{\varnothing}}\). Elements of (P(A)) are subsets of (A), and \({{\varnothing}}\) is a subset of (A). In a power set, elements are always subsets.
Step 3
Exam Tip
(P(A)) में (A) के उपसमुच्चय अवयव बनते हैं और \({{\varnothing}}\) (A) का उपसमुच्चय है। पावर सेट में अवयव हमेशा उपसमुच्चय होते हैं।
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यदि \(A=\{a,b,c,d,e\}\) है तो (A) के ठीक तीन अवयवों वाले उपसमुच्चयों की संख्या क्या है?
If \(A=\{a,b,c,d,e\}\) then what is the number of subsets of (A) having exactly three elements?
#sets
#k-element-subsets
#combinations
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A (5)
B (10)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
The number of ways to choose three elements is \(\binom{5}{3}=10\). 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 three elements is \(\binom{5}{3}=10\). Order is not counted in subsets.
Step 3
Exam Tip
तीन अवयव चुनने की संख्या \(\binom{5}{3}=10\) है। उपसमुच्चय में क्रम नहीं गिना जाता।
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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
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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 \(A=\{1,{2},3\}\) है तो कौन सा कथन सत्य है?
If \(A=\{1,{2},3\}\) then which statement is true?
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#nested-sets
#element
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A \({2}\in A\)
B \(2\in A\)
C \({1,2}\subseteq A\)
D \({2,3}\subseteq A\)
Explanation opens after your attempt
Correct Answer
A. \({2}\in A\)
Step 1
Concept
({2}) is one whole element, but (2) is not separately an element. Braces are very important in nested sets.
Step 2
Why this answer is correct
The correct answer is A. \({2}\in A\). ({2}) is one whole element, but (2) is not separately an element. Braces are very important in nested sets.
Step 3
Exam Tip
({2}) पूरा एक अवयव है, लेकिन (2) अलग से अवयव नहीं है। नेस्टेड समुच्चय में कोष्ठक बहुत महत्वपूर्ण होते हैं।
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यदि \(A={x:x\) शब्द गणित के अलग अक्षरों में से है(}) तो (A) में कितने अवयव हैं?
If \(A={x:x\) is one of the distinct letters of the word GANIT(}) then how many elements are in (A)?
#sets
#letters
#cardinality
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A (4)
B (5)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
The word (GANIT) has five distinct letters (G,A,N,I,T). Check whether repeated letters exist before counting.
Step 2
Why this answer is correct
The correct answer is B. (5). The word (GANIT) has five distinct letters (G,A,N,I,T). Check whether repeated letters exist before counting.
Step 3
Exam Tip
गणित शब्द के अलग अक्षर (ग,ण,ि,त) जैसे लिखने से भ्रम हो सकता है, पर प्रश्न अंग्रेजी शब्द (GANIT) पर है। (G,A,N,I,T) पांच अलग अक्षर हैं।
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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
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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 \(A={x:x\) (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
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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 \(A={x:x\) (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
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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 \(A={x:x\in \mathbb{N}, x\) (15) का भाजक है(}) और \(C=\{1,3,5\}\) हैं तो सही संबंध कौन सा है?
If \(A={x:x\in \mathbb{N}, x\) is a divisor of (15)(}) and \(C=\{1,3,5\}\) then which relation is correct?
#sets
#proper-subset
#divisors
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A \(C\subset A\) और \(C\neq A\) / \(C\subset A\) and \(C\neq A\)
B (A=C)
C \(A\subset C\) और \(A\neq C\) / \(A\subset C\) and \(A\neq C\)
D \(15\notin A\)
Explanation opens after your attempt
Correct Answer
A. \(C\subset A\) और \(C\neq A\) / \(C\subset A\) and \(C\neq A\)
Step 1
Concept
\(A=\{1,3,5,15\}\), and all elements of (C) are in (A). The extra (15) makes (C) a proper subset.
Step 2
Why this answer is correct
The correct answer is A. \(C\subset A\) और \(C\neq A\) / \(C\subset A\) and \(C\neq A\). \(A=\{1,3,5,15\}\), and all elements of (C) are in (A). The extra (15) makes (C) a proper subset.
Step 3
Exam Tip
\(A=\{1,3,5,15\}\) है और (C) के सभी अवयव (A) में हैं। अतिरिक्त (15) होने से (C) उचित उपसमुच्चय है।
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यदि \(A=\{1,2,3\}\) और (B=P(A)) है तो (B) में कौन सा अवयव नहीं होगा?
If \(A=\{1,2,3\}\) and (B=P(A)) then which element will not be in (B)?
#sets
#power-set
#element
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A ({1,2})
B \(\varnothing\)
C ({1,2,3})
D (4)
Explanation opens after your attempt
Step 1
Concept
(P(A)) contains subsets of (A) as elements, not the ordinary number (4). Elements of a power set are themselves subsets.
Step 2
Why this answer is correct
The correct answer is D. (4). (P(A)) contains subsets of (A) as elements, not the ordinary number (4). Elements of a power set are themselves subsets.
Step 3
Exam Tip
(P(A)) में (A) के उपसमुच्चय अवयव होते हैं, साधारण संख्या (4) नहीं। पावर सेट में अवयव स्वयं उपसमुच्चय होते हैं।
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यदि \(A=\{1,2,3,4\}\) है तो (P(A)) में दो अवयवों वाले कितने समुच्चय होंगे?
If \(A=\{1,2,3,4\}\) then how many two element sets will be in (P(A))?
#sets
#power-set
#two-element-subsets
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A (4)
B (6)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(P(A)) contains all subsets of (A), and the number of two element subsets is \(\binom{4}{2}=6\). The question is not asking the total size of the power set.
Step 2
Why this answer is correct
The correct answer is B. (6). (P(A)) contains all subsets of (A), and the number of two element subsets is \(\binom{4}{2}=6\). The question is not asking the total size of the power set.
Step 3
Exam Tip
(P(A)) में (A) के सभी उपसमुच्चय होते हैं और दो अवयव चुनने की संख्या \(\binom{4}{2}=6\) है। यहां पूरी शक्ति समुच्चय की संख्या नहीं पूछी गई है।
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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
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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 \(A\subset B\) और (n(B)=7) है तो (n(A)) के लिए कौन सा विकल्प असंभव है?
If \(A\subset B\) and (n(B)=7), then which option is impossible for (n(A))?
#sets
#proper-subset
#cardinality
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A (0)
B (4)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
In a proper subset, (A) and (B) cannot be equal, so (n(A)) cannot be (7). A proper subset must have fewer elements here.
Step 2
Why this answer is correct
The correct answer is D. (7). In a proper subset, (A) and (B) cannot be equal, so (n(A)) cannot be (7). A proper subset must have fewer elements here.
Step 3
Exam Tip
उचित उपसमुच्चय में (A) और (B) बराबर नहीं हो सकते, इसलिए (n(A)) (7) नहीं होगा। उचित उपसमुच्चय में कम अवयव होने चाहिए।
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यदि \(A=\{2,4,6,8,10\}\) और \(B=\{4,8\}\) हैं तो कौन सा कथन सही है?
If \(A=\{2,4,6,8,10\}\) and \(B=\{4,8\}\) then which statement is correct?
#sets
#proper-subset
#even-numbers
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A \(B\subset A\)
B \(A\subset B\)
C (A=B)
D \(10\in B\)
Explanation opens after your attempt
Correct Answer
A. \(B\subset A\)
Step 1
Concept
Both elements of (B) are in (A), and (A) has extra elements. So (B) is a proper subset of (A).
Step 2
Why this answer is correct
The correct answer is A. \(B\subset A\). Both elements of (B) are in (A), and (A) has extra elements. So (B) is a proper subset of (A).
Step 3
Exam Tip
(B) के दोनों अवयव (A) में हैं और (A) में अतिरिक्त अवयव हैं। इसलिए (B) (A) का उचित उपसमुच्चय है।
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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
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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 \(A={x:x\in \mathbb{N}, 3\leq x<7}\) है तो कौन सा (A) का उचित उपसमुच्चय है?
If \(A={x:x\in \mathbb{N}, 3\leq x<7}\) then which is a proper subset of (A)?
#sets
#proper-subset
#inequality
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A ({3,5,6})
B ({3,4,5,6})
C ({2,3,4})
D ({4,5,7})
Explanation opens after your attempt
Correct Answer
A. ({3,5,6})
Step 1
Concept
\(A=\{3,4,5,6\}\), and ({3,5,6}) lies inside it but is not equal. A proper subset misses at least one element.
Step 2
Why this answer is correct
The correct answer is A. ({3,5,6}). \(A=\{3,4,5,6\}\), and ({3,5,6}) lies inside it but is not equal. A proper subset misses at least one element.
Step 3
Exam Tip
\(A=\{3,4,5,6\}\) है और ({3,5,6}) इसमें पूरा है पर बराबर नहीं। उचित उपसमुच्चय में कम से कम एक अवयव छूटता है।
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यदि \(A={\varnothing,1}\) है तो कौन सा कथन सत्य है?
If \(A={\varnothing,1}\) then which statement is true?
#sets
#empty-set
#element-vs-subset
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A \(\varnothing\in A\)
B \({1}\in A\)
C \(2\in A\)
D \({\varnothing,1}\not\subseteq A\)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\in A\)
Step 1
Concept
Here the empty set is one element of (A). Also, (A) is a subset of itself.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\in A\). Here the empty set is one element of (A). Also, (A) is a subset of itself.
Step 3
Exam Tip
यहां रिक्त समुच्चय (A) का एक अवयव है। साथ ही (A) स्वयं अपना उपसमुच्चय होता है।
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यदि \(A={\varnothing,{1}}\) है तो कौन सा (A) का उपसमुच्चय है?
If \(A={\varnothing,{1}}\) then which is a subset of (A)?
#sets
#nested-sets
#empty-set
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A \({\varnothing}\)
B ({1})
C ({{2}})
D ({0})
Explanation opens after your attempt
Correct Answer
A. \({\varnothing}\)
Step 1
Concept
\(\varnothing\) is an element of (A), so \({\varnothing}\) is a subset of (A). ({1}) is an element, but (1) is not.
Step 2
Why this answer is correct
The correct answer is A. \({\varnothing}\). \(\varnothing\) is an element of (A), so \({\varnothing}\) is a subset of (A). ({1}) is an element, but (1) is not.
Step 3
Exam Tip
\(\varnothing\) (A) का अवयव है इसलिए \({\varnothing}\) (A) का उपसमुच्चय है। ({1}) अवयव है, पर (1) अवयव नहीं है।
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यदि \(A=\{1,2,3,4,5,6\}\) है तो ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (1) न हो और (6) अवश्य हो?
If \(A=\{1,2,3,4,5,6\}\) then how many subsets do not contain (1) but must contain (6)?
#sets
#conditional-subsets
#counting
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A (8)
B (16)
C (32)
D (64)
Explanation opens after your attempt
Step 1
Concept
(1) is excluded and (6) is fixed, while (2,3,4,5) are free. So \(2^4=16\) subsets are formed.
Step 2
Why this answer is correct
The correct answer is B. (16). (1) is excluded and (6) is fixed, while (2,3,4,5) are free. So \(2^4=16\) subsets are formed.
Step 3
Exam Tip
(1) हटेगा और (6) निश्चित होगा, बाकी (2,3,4,5) स्वतंत्र हैं। इसलिए \(2^4=16\) उपसमुच्चय बनते हैं।
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यदि \(A=\{p,q,r,s\}\) है तो ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (p) या (q) में से कम से कम एक हो?
If \(A=\{p,q,r,s\}\) then how many subsets contain at least one of (p) or (q)?
#sets
#conditional-subsets
#at-least-one
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A (8)
B (10)
C (12)
D (14)
Explanation opens after your attempt
Step 1
Concept
Total subsets are (16), and those containing neither (p) nor (q) are \(2^2=4\). Hence the answer is (16-4=12).
Step 2
Why this answer is correct
The correct answer is C. (12). Total subsets are (16), and those containing neither (p) nor (q) are \(2^2=4\). Hence the answer is (16-4=12).
Step 3
Exam Tip
कुल उपसमुच्चय (16) हैं और जिनमें (p,q) दोनों नहीं हैं वे \(2^2=4\) हैं। अतः उत्तर (16-4=12) है।
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यदि \(A=\{1,2,3,4\}\) है तो ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (1) और (2) साथ साथ हों या दोनों न हों?
If \(A=\{1,2,3,4\}\) then how many subsets contain (1) and (2) together or contain neither?
#sets
#conditional-subsets
#counting
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A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
When both (1,2) are included there are \(2^2=4\) choices, and when neither is included there are \(2^2=4\) choices. Total is (8).
Step 2
Why this answer is correct
The correct answer is C. (8). When both (1,2) are included there are \(2^2=4\) choices, and when neither is included there are \(2^2=4\) choices. Total is (8).
Step 3
Exam Tip
(1,2) दोनों होने पर \(2^2=4\) और दोनों न होने पर \(2^2=4\) विकल्प हैं। कुल (8) उपसमुच्चय बनते हैं।
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यदि \(A={x:x\in \mathbb{N}, x\leq 4}\) है तो (A) के उन उपसमुच्चयों की संख्या कितनी है जिनमें (4) हो?
If \(A={x:x\in \mathbb{N}, x\leq 4}\) then how many subsets of (A) contain (4)?
#sets
#conditional-subsets
#natural-numbers
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A (4)
B (8)
C (12)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(A=\{1,2,3,4\}\), and after fixing (4), the remaining (3) elements are free. Hence \(2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). \(A=\{1,2,3,4\}\), and after fixing (4), the remaining (3) elements are free. Hence \(2^3=8\).
Step 3
Exam Tip
\(A=\{1,2,3,4\}\) है और (4) निश्चित रखने पर बाकी (3) अवयव स्वतंत्र हैं। इसलिए \(2^3=8\) है।
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यदि \(A=\{1,2,3,4,5\}\) है तो (A) के अधिकतम दो अवयवों वाले उपसमुच्चयों की संख्या क्या है?
If \(A=\{1,2,3,4,5\}\) then what is the number of subsets of (A) having at most two elements?
#sets
#subsets
#at-most
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A (10)
B (15)
C (16)
D (20)
Explanation opens after your attempt
Step 1
Concept
At most two elements means (0,1,2) elements. The count is \(\binom{5}{0}+\binom{5}{1}+\binom{5}{2}=1+5+10=16\).
Step 2
Why this answer is correct
The correct answer is C. (16). At most two elements means (0,1,2) elements. The count is \(\binom{5}{0}+\binom{5}{1}+\binom{5}{2}=1+5+10=16\).
Step 3
Exam Tip
अधिकतम दो अवयव का अर्थ (0,1,2) अवयव हैं। संख्या \(\binom{5}{0}+\binom{5}{1}+\binom{5}{2}=1+5+10=16\) है।
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यदि \(A=\{a,b,c,d\}\) है तो (A) के कम से कम तीन अवयवों वाले उपसमुच्चयों की संख्या क्या है?
If \(A=\{a,b,c,d\}\) then what is the number of subsets of (A) having at least three elements?
#sets
#subsets
#at-least
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
At least three elements means three or four elements. The count is \(\binom{4}{3}+\binom{4}{4}=4+1=5\).
Step 2
Why this answer is correct
The correct answer is B. (5). At least three elements means three or four elements. The count is \(\binom{4}{3}+\binom{4}{4}=4+1=5\).
Step 3
Exam Tip
कम से कम तीन अवयव का अर्थ तीन या चार अवयव हैं। संख्या \(\binom{4}{3}+\binom{4}{4}=4+1=5\) है।
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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
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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 \(A={x:x\in \mathbb{Z}, x^2=16}\) और \(C=\{4\}\) हैं तो कौन सा सही है?
If \(A={x:x\in \mathbb{Z}, x^2=16}\) and \(C=\{4\}\) then which is correct?
#sets
#proper-subset
#equation
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A \(C\subset A\) और \(C\neq A\) / \(C\subset A\) and \(C\neq A\)
B (A=C)
C \(A\subset C\) और \(A\neq C\) / \(A\subset C\) and \(A\neq C\)
D \(A=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(C\subset A\) और \(C\neq A\) / \(C\subset A\) and \(C\neq A\)
Step 1
Concept
\(A=\{-4,4\}\), and \(C=\{4\}\) is its proper subset. Taking only the positive solution can cause an error.
Step 2
Why this answer is correct
The correct answer is A. \(C\subset A\) और \(C\neq A\) / \(C\subset A\) and \(C\neq A\). \(A=\{-4,4\}\), and \(C=\{4\}\) is its proper subset. Taking only the positive solution can cause an error.
Step 3
Exam Tip
\(A=\{-4,4\}\) है और \(C=\{4\}\) इसका उचित उपसमुच्चय है। केवल धनात्मक हल लेने से गलती हो सकती है।
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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
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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 \(A={x:x\in \mathbb{N}, x^2-4x+3=0}\) और \(B=\{1\}\) हैं तो संबंध क्या है?
If \(A={x:x\in \mathbb{N}, x^2-4x+3=0}\) and \(B=\{1\}\) then what is the relation?
#sets
#proper-subset
#quadratic
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A \(B\subset A\) और \(B\neq A\) / \(B\subset A\) and \(B\neq A\)
B (A=B)
C \(A\subset B\) और \(A\neq B\) / \(A\subset B\) and \(A\neq B\)
D (B) में (3) है / (B) contains (3)
Explanation opens after your attempt
Correct Answer
A. \(B\subset A\) और \(B\neq A\) / \(B\subset A\) and \(B\neq A\)
Step 1
Concept
The equation has solutions (1) and (3), so \(A=\{1,3\}\). \(B=\{1\}\) is a proper subset of it.
Step 2
Why this answer is correct
The correct answer is A. \(B\subset A\) और \(B\neq A\) / \(B\subset A\) and \(B\neq A\). The equation has solutions (1) and (3), so \(A=\{1,3\}\). \(B=\{1\}\) is a proper subset of it.
Step 3
Exam Tip
समीकरण के हल (1) और (3) हैं, इसलिए \(A=\{1,3\}\) है। \(B=\{1\}\) इसका उचित उपसमुच्चय है।
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यदि \(A=\{1,2,3\}\) और \(B=\{2,3,4\}\) हैं तो कौन सा कथन सही है?
If \(A=\{1,2,3\}\) and \(B=\{2,3,4\}\) then which statement is correct?
#sets
#non-subset
#reasoning
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A \(A\subseteq B\)
B \(B\subseteq A\)
C (A=B)
D न \(A\subseteq B\) और न \(B\subseteq A\) / Neither \(A\subseteq B\) nor \(B\subseteq A\)
Explanation opens after your attempt
Correct Answer
D. न \(A\subseteq B\) और न \(B\subseteq A\) / Neither \(A\subseteq B\) nor \(B\subseteq A\)
Step 1
Concept
(1) is not in (B), and (4) is not in (A). Having some common elements is not enough for subset relation.
Step 2
Why this answer is correct
The correct answer is D. न \(A\subseteq B\) और न \(B\subseteq A\) / Neither \(A\subseteq B\) nor \(B\subseteq A\). (1) is not in (B), and (4) is not in (A). Having some common elements is not enough for subset relation.
Step 3
Exam Tip
(1) (B) में नहीं है और (4) (A) में नहीं है। कुछ साझा अवयव होना उपसमुच्चय के लिए पर्याप्त नहीं है।
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यदि \(A=\{2,4,6\}\) और \(B=\{1,2,4,6,8\}\) हैं तो सही कथन क्या है?
If \(A=\{2,4,6\}\) and \(B=\{1,2,4,6,8\}\) then what is correct?
#sets
#proper-subset
#even-numbers
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A \(A\subset B\)
B \(B\subset A\)
C (A=B)
D \({1,8}\subseteq A\)
Explanation opens after your attempt
Correct Answer
A. \(A\subset B\)
Step 1
Concept
All elements of (A) are in (B), and (B) has extra (1,8). So (A) is a proper subset.
Step 2
Why this answer is correct
The correct answer is A. \(A\subset B\). All elements of (A) are in (B), and (B) has extra (1,8). So (A) is a proper subset.
Step 3
Exam Tip
(A) के सभी अवयव (B) में हैं और (B) में अतिरिक्त (1,8) हैं। इसलिए (A) उचित उपसमुच्चय है।
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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
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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 \(A=\{5,10,15\}\) 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
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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 \(A={x:x\in \mathbb{N}, x\) (24) का सम भाजक है(}) है तो कौन सा (A) का उपसमुच्चय नहीं है?
If \(A={x:x\in \mathbb{N}, x\) is an even divisor of (24)(}) then which is not a subset of (A)?
#sets
#subsets
#divisors
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A ({2,4,6})
B ({8,12,24})
C ({2,6,10})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
C. ({2,6,10})
Step 1
Concept
\(A=\{2,4,6,8,12,24\}\), and (10) is not in it. One outside element makes a subset false.
Step 2
Why this answer is correct
The correct answer is C. ({2,6,10}). \(A=\{2,4,6,8,12,24\}\), and (10) is not in it. One outside element makes a subset false.
Step 3
Exam Tip
\(A=\{2,4,6,8,12,24\}\) है और (10) इसमें नहीं है। एक बाहरी अवयव उपसमुच्चय को गलत कर देता है।
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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
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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 \(A=\{1,2,{1,2}\}\) है तो कौन सा कथन असत्य है?
If \(A=\{1,2,{1,2}\}\) then which statement is false?
#sets
#nested-sets
#truth-check
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A \(1\in A\)
B \({1,2}\in A\)
C \({1,2}\subseteq A\)
D \({1,2,{1,2}}\subseteq A\)
Explanation opens after your attempt
Correct Answer
C. \({1,2}\subseteq A\)
Step 1
Concept
This set has (1), (2), and ({1,2}) as elements. All four statements are actually true, so this question checks careful reading.
Step 2
Why this answer is correct
The correct answer is C. \({1,2}\subseteq A\). This set has (1), (2), and ({1,2}) as elements. All four statements are actually true, so this question checks careful reading.
Step 3
Exam Tip
({1,2}) (A) का अवयव है, पर इसके अवयव (1,2) से बना समुच्चय (A) का उपसमुच्चय भी हो सकता है; यहां विकल्प असत्य नहीं है। सही असत्य विकल्प नहीं दिखता, इसलिए ध्यान दें कि सभी दिए कथन सत्य हैं।
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यदि \(A=\{1,{1,2},3\}\) है तो कौन सा कथन असत्य है?
If \(A=\{1,{1,2},3\}\) then which statement is false?
#sets
#nested-sets
#false-statement
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A \(1\in A\)
B \({1,2}\in A\)
C \({1,3}\subseteq A\)
D \({1,2}\subseteq A\)
Explanation opens after your attempt
Correct Answer
D. \({1,2}\subseteq A\)
Step 1
Concept
For \({1,2}\subseteq A\), \(2\in A\) must be true, but (2) is not a separate element. Keep element and subset distinct.
Step 2
Why this answer is correct
The correct answer is D. \({1,2}\subseteq A\). For \({1,2}\subseteq A\), \(2\in A\) must be true, but (2) is not a separate element. Keep element and subset distinct.
Step 3
Exam Tip
\({1,2}\subseteq A\) के लिए \(2\in A\) होना चाहिए, पर (2) अलग अवयव नहीं है। अवयव और उपसमुच्चय में अंतर रखें।
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यदि \(A=\{0,1,2,3\}\) है तो (A) के सभी उपसमुच्चयों में कुल कितनी बार अवयव (0) आएगा?
If \(A=\{0,1,2,3\}\) then in all subsets of (A), how many times will the element (0) appear in total?
#sets
#subsets
#element-frequency
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A (4)
B (6)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
In a (4)-element set, each element appears in \(2^{3}=8\) subsets. Use symmetry.
Step 2
Why this answer is correct
The correct answer is C. (8). In a (4)-element set, each element appears in \(2^{3}=8\) subsets. Use symmetry.
Step 3
Exam Tip
किसी (4) अवयव वाले समुच्चय में हर अवयव \(2^{3}=8\) उपसमुच्चयों में आता है। सममिति का उपयोग करें।
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यदि \(A=\{a,b,c,d,e\}\) है तो सभी उपसमुच्चयों में अवयव (c) कितनी बार आएगा?
If \(A=\{a,b,c,d,e\}\) then how many times will element (c) appear in all subsets?
#sets
#subsets
#element-frequency
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A (8)
B (16)
C (24)
D (32)
Explanation opens after your attempt
Step 1
Concept
In a five element set, any fixed element appears in \(2^4=16\) subsets. Fix one element and let the other four vary freely.
Step 2
Why this answer is correct
The correct answer is B. (16). In a five element set, any fixed element appears in \(2^4=16\) subsets. Fix one element and let the other four vary freely.
Step 3
Exam Tip
पांच अवयवों वाले समुच्चय में कोई निश्चित अवयव \(2^{4}=16\) उपसमुच्चयों में आता है। एक अवयव निश्चित रखकर बाकी चार को स्वतंत्र मानें।
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यदि \(A=\{1,2,3,4\}\) है तो ऐसे उपसमुच्चयों की संख्या कितनी है जिनका योग सम है?
If \(A=\{1,2,3,4\}\) then how many subsets have an even sum?
#sets
#subsets
#parity
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A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
There are two odd and two even elements, and an even sum needs an even number of odd elements. This gives \(2\times4=8\) subsets.
Step 2
Why this answer is correct
The correct answer is C. (8). There are two odd and two even elements, and an even sum needs an even number of odd elements. This gives \(2\times4=8\) subsets.
Step 3
Exam Tip
दो विषम और दो सम अवयव हैं, और सम योग के लिए विषम अवयवों की संख्या सम होनी चाहिए। कुल \(2\times4=8\) उपसमुच्चय मिलते हैं।
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यदि \(A=\{1,3,5,7\}\) है तो ऐसे उपसमुच्चयों की संख्या कितनी है जिनका योग विषम है?
If \(A=\{1,3,5,7\}\) then how many subsets have an odd sum?
#sets
#subsets
#odd-sum
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A (4)
B (8)
C (12)
D (16)
Explanation opens after your attempt
Step 1
Concept
All elements are odd, so an odd sum needs an odd number of elements in the subset. \(\binom{4}{1}+\binom{4}{3}=4+4=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). All elements are odd, so an odd sum needs an odd number of elements in the subset. \(\binom{4}{1}+\binom{4}{3}=4+4=8\).
Step 3
Exam Tip
सभी अवयव विषम हैं, इसलिए विषम योग के लिए उपसमुच्चय में विषम संख्या में अवयव होने चाहिए। \(\binom{4}{1}+\binom{4}{3}=4+4=8\) है।
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यदि \(A=\{1,2,3\}\) और \(B=\{{1},{2},{3}\}\) हैं तो कौन सा कथन सही है?
If \(A=\{1,2,3\}\) and \(B=\{{1},{2},{3}\}\) then which statement is correct?
#sets
#nested-sets
#non-subset
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A (A=B)
B \(A\subseteq B\)
C \(B\subseteq A\)
D \(A\neq B\) और कोई भी दूसरे का उपसमुच्चय नहीं / \(A\neq B\) and neither is a subset of the other
Explanation opens after your attempt
Correct Answer
D. \(A\neq B\) और कोई भी दूसरे का उपसमुच्चय नहीं / \(A\neq B\) and neither is a subset of the other
Step 1
Concept
Elements of (A) are numbers, while elements of (B) are singleton sets. Changing braces changes the set.
Step 2
Why this answer is correct
The correct answer is D. \(A\neq B\) और कोई भी दूसरे का उपसमुच्चय नहीं / \(A\neq B\) and neither is a subset of the other. Elements of (A) are numbers, while elements of (B) are singleton sets. Changing braces changes the set.
Step 3
Exam Tip
(A) के अवयव संख्याएं हैं जबकि (B) के अवयव एकल समुच्चय हैं। कोष्ठक बदलने से समुच्चय बदल जाता है।
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यदि \(A=\{{1},{2}\}\) है तो (P(A)) में कौन सा अवयव होगा?
If \(A=\{{1},{2}\}\) then which element will be in (P(A))?
#sets
#power-set
#nested-sets
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A ({{1}})
B ({1})
C (1)
D ({1,2})
Explanation opens after your attempt
Correct Answer
A. ({{1}})
Step 1
Concept
(P(A)) contains subsets of (A), and ({{1}}) is a subset of (A). ({1}) is an element of (A), but an element of the power set must be a subset.
Step 2
Why this answer is correct
The correct answer is A. ({{1}}). (P(A)) contains subsets of (A), and ({{1}}) is a subset of (A). ({1}) is an element of (A), but an element of the power set must be a subset.
Step 3
Exam Tip
(P(A)) में (A) के उपसमुच्चय होते हैं, और ({{1}}) (A) का उपसमुच्चय है। ({1}) (A) का अवयव है, पर पावर सेट का अवयव बनने के लिए उपसमुच्चय होना चाहिए।
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यदि \(A=\{1,2,3,4,5,6\}\) है तो (A) के (3) अवयवों वाले ऐसे उपसमुच्चयों की संख्या क्या है जिनमें (1) अवश्य हो?
If \(A=\{1,2,3,4,5,6\}\) then how many three element subsets of (A) must contain (1)?
#sets
#k-element-subsets
#conditional-counting
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A (5)
B (10)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
(1) is fixed, so choose (2) elements from the remaining (5). The count is \(\binom{5}{2}=10\).
Step 2
Why this answer is correct
The correct answer is B. (10). (1) is fixed, so choose (2) elements from the remaining (5). The count is \(\binom{5}{2}=10\).
Step 3
Exam Tip
(1) निश्चित है, इसलिए बाकी (5) अवयवों में से (2) चुनने हैं। संख्या \(\binom{5}{2}=10\) है।
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यदि \(A=\{1,2,3,4,5\}\) है तो (A) के (2) अवयवों वाले ऐसे उपसमुच्चयों की संख्या क्या है जिनमें (5) न हो?
If \(A=\{1,2,3,4,5\}\) then how many two element subsets of (A) do not contain (5)?
#sets
#k-element-subsets
#excluded-element
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A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
Exclude (5) and choose (2) elements from (1,2,3,4). The count is \(\binom{4}{2}=6\).
Step 2
Why this answer is correct
The correct answer is B. (6). Exclude (5) and choose (2) elements from (1,2,3,4). The count is \(\binom{4}{2}=6\).
Step 3
Exam Tip
(5) को हटाकर (1,2,3,4) में से (2) अवयव चुनने हैं। संख्या \(\binom{4}{2}=6\) है।
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यदि \(A={x:x\in \mathbb{Z}, |x|\leq 2}\) है तो कौन सा (A) का उपसमुच्चय है?
If \(A={x:x\in \mathbb{Z}, |x|\leq 2}\) then which is a subset of (A)?
#sets
#subsets
#absolute-value
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A ({-2,0,2})
B ({-3,0,1})
C ({1,2,3})
D ({-2,2,4})
Explanation opens after your attempt
Correct Answer
A. ({-2,0,2})
Step 1
Concept
\(A=\{-2,-1,0,1,2\}\), and the first option is fully included in it. In absolute value conditions, check both negative and positive values.
Step 2
Why this answer is correct
The correct answer is A. ({-2,0,2}). \(A=\{-2,-1,0,1,2\}\), and the first option is fully included in it. In absolute value conditions, check both negative and positive values.
Step 3
Exam Tip
\(A=\{-2,-1,0,1,2\}\) है और पहला विकल्प इसमें पूरा शामिल है। परिमाण वाली शर्त में ऋणात्मक और धनात्मक दोनों देखें।
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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
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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 \(A=\{1,2,3,4\}\), \(B=\{2,4\}\) और \(C=\{1,3\}\) हैं तो कौन सा कथन सत्य है?
If \(A=\{1,2,3,4\}\), \(B=\{2,4\}\), and \(C=\{1,3\}\) then which statement is true?
#sets
#proper-subset
#comparison
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A \(B\subset A\) और \(C\subset A\) / \(B\subset A\) and \(C\subset A\)
B \(A\subset B\) और \(C\subset B\) / \(A\subset B\) and \(C\subset B\)
C (B=C)
D (A=B)
Explanation opens after your attempt
Correct Answer
A. \(B\subset A\) और \(C\subset A\) / \(B\subset A\) and \(C\subset A\)
Step 1
Concept
All elements of (B) and (C) are in (A), and both are smaller than (A). One set can have many proper subsets.
Step 2
Why this answer is correct
The correct answer is A. \(B\subset A\) और \(C\subset A\) / \(B\subset A\) and \(C\subset A\). All elements of (B) and (C) are in (A), and both are smaller than (A). One set can have many proper subsets.
Step 3
Exam Tip
(B) और (C) के सभी अवयव (A) में हैं और दोनों (A) से छोटे हैं। एक ही समुच्चय के कई उचित उपसमुच्चय हो सकते हैं।
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