यदि \(A=\{1,2,3\}\) है तो (\mathcal{P}(A)) में कितने तत्व होंगे?
If \(A=\{1,2,3\}\) then how many elements are in (\mathcal{P}(A))?
#sets
#power_set
#cardinality
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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. For exams remember \(2^n\) for number of elements in a power set.
Step 2
Why this answer is correct
The correct answer is C. (8). A set with three elements has \(2^3=8\) subsets. For exams remember \(2^n\) for number of elements in a power set.
Step 3
Exam Tip
तीन तत्वों वाले समुच्चय के उपसमुच्चय \(2^3=8\) होते हैं। परीक्षा में घात समुच्चय की संख्या के लिए \(2^n\) याद रखें।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,2\}\) है तो (\mathcal{P}(A')) में कितने तत्व होंगे?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,2\}\), how many elements will be in (\mathcal{P}(A'))?
#sets
#power_set
#universal_set
#complement
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
First (A'={3,4,5,6}), which has (4) elements. So (\mathcal{P}(A')) has \(2^4=16\) elements.
Step 2
Why this answer is correct
The correct answer is C. (16). First (A'={3,4,5,6}), which has (4) elements. So (\mathcal{P}(A')) has \(2^4=16\) elements.
Step 3
Exam Tip
पहले (A'={3,4,5,6}) मिलेगा जिसमें (4) तत्व हैं। इसलिए (\mathcal{P}(A')) में \(2^4=16\) तत्व होंगे।
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घात समुच्चय (\mathcal{P}(A)) किसका समुच्चय होता है?
The power set (\mathcal{P}(A)) is the set of what?
#sets
#power_set
#definition
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A (A) के सभी तत्व / all elements of (A)
B (A) के सभी उपसमुच्चय / all subsets of (A)
C केवल रिक्त समुच्चय / only empty set
D केवल सार्वत्रिक समुच्चय / only universal set
Explanation opens after your attempt
Correct Answer
B. (A) के सभी उपसमुच्चय / all subsets of (A)
Step 1
Concept
A power set is the set of all subsets of a given set. In exams keep the difference between element and subset clear.
Step 2
Why this answer is correct
The correct answer is B. (A) के सभी उपसमुच्चय / all subsets of (A). A power set is the set of all subsets of a given set. In exams keep the difference between element and subset clear.
Step 3
Exam Tip
घात समुच्चय किसी समुच्चय के सभी उपसमुच्चयों का समुच्चय होता है। परीक्षा में तत्व और उपसमुच्चय में अंतर रखें।
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यदि \(A=\{a,b\}\) है तो इनमें से कौन सा (\mathcal{P}(A)) का तत्व है?
If \(A=\{a,b\}\) then which of the following is an element of (\mathcal{P}(A))?
#sets
#power_set
#subset
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A (a)
B (b)
C ({a})
D (ab)
Explanation opens after your attempt
Step 1
Concept
({a}) is a subset of (A) so it is an element of (\mathcal{P}(A)). Elements of a power set are always subsets.
Step 2
Why this answer is correct
The correct answer is C. ({a}). ({a}) is a subset of (A) so it is an element of (\mathcal{P}(A)). Elements of a power set are always subsets.
Step 3
Exam Tip
({a}) समुच्चय (A) का उपसमुच्चय है इसलिए यह (\mathcal{P}(A)) का तत्व है। घात समुच्चय के तत्व हमेशा उपसमुच्चय होते हैं।
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यदि \(A=\emptyset\) है तो (\mathcal{P}(A)) क्या होगा?
If \(A=\emptyset\) then what is (\mathcal{P}(A))?
#sets
#power_set
#empty_set
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A \(\emptyset\)
B \({\emptyset}\)
C \({{\emptyset}}\)
D ({0})
Explanation opens after your attempt
Correct Answer
B. \({\emptyset}\)
Step 1
Concept
The empty set has only one subset which is \(\emptyset\). Hence (\mathcal{P}\(\emptyset\)={\emptyset}).
Step 2
Why this answer is correct
The correct answer is B. \({\emptyset}\). The empty set has only one subset which is \(\emptyset\). Hence (\mathcal{P}\(\emptyset\)={\emptyset}).
Step 3
Exam Tip
रिक्त समुच्चय का एक ही उपसमुच्चय \(\emptyset\) होता है। इसलिए (\mathcal{P}\(\emptyset\)={\emptyset}) है।
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सार्वत्रिक समुच्चय का सही अर्थ क्या है?
What is the correct meaning of universal set?
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#universal_set
#definition
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A चर्चा में सभी संबंधित तत्वों का समुच्चय / set of all relevant elements under discussion
B केवल एक तत्व वाला समुच्चय / set with only one element
C कोई तत्व न रखने वाला समुच्चय / set with no element
D केवल संख्याओं का समुच्चय / set of numbers only
Explanation opens after your attempt
Correct Answer
A. चर्चा में सभी संबंधित तत्वों का समुच्चय / set of all relevant elements under discussion
Step 1
Concept
The universal set contains all relevant elements in the given context. Decide (U) from the context of the question.
Step 2
Why this answer is correct
The correct answer is A. चर्चा में सभी संबंधित तत्वों का समुच्चय / set of all relevant elements under discussion. The universal set contains all relevant elements in the given context. Decide (U) from the context of the question.
Step 3
Exam Tip
सार्वत्रिक समुच्चय उस संदर्भ के सभी संबंधित तत्व रखता है। प्रश्न में दिए गए संदर्भ को देखकर (U) तय करें।
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यदि \(U=\{1,2,3,4,5\}\) और \(A=\{2,4\}\) है तो (A') क्या होगा?
If \(U=\{1,2,3,4,5\}\) and \(A=\{2,4\}\) then what is (A')?
#sets
#universal_set
#complement
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A ({2,4})
B ({1,3,5})
C ({1,2,3,4,5})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({1,3,5})
Step 1
Concept
The complement contains elements of (U) that are not in (A). Here (1,3,5) are not in (A).
Step 2
Why this answer is correct
The correct answer is B. ({1,3,5}). The complement contains elements of (U) that are not in (A). Here (1,3,5) are not in (A).
Step 3
Exam Tip
पूरक में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। यहां (1,3,5) (A) में नहीं हैं।
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यदि किसी समुच्चय में (4) तत्व हैं तो उसके घात समुच्चय में कितने तत्व होंगे?
If a set has (4) elements then how many elements will its power set have?
#sets
#power_set
#formula
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
The number of elements in a power set is \(2^n\). Here \(2^4=16\).
Step 2
Why this answer is correct
The correct answer is C. (16). The number of elements in a power set is \(2^n\). Here \(2^4=16\).
Step 3
Exam Tip
घात समुच्चय में तत्वों की संख्या \(2^n\) होती है। यहां \(2^4=16\) है।
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यदि \(A=\{x\}\) है तो (\mathcal{P}(A)) कौन सा है?
If \(A=\{x\}\) then which is (\mathcal{P}(A))?
#sets
#power_set
#singleton
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A ({x})
B \({\emptyset,x}\)
C \({\emptyset,{x}}\)
D ({{x}})
Explanation opens after your attempt
Correct Answer
C. \({\emptyset,{x}}\)
Step 1
Concept
A one element set has subsets \(\emptyset\) and ({x}). So its power set is \({\emptyset,{x}}\).
Step 2
Why this answer is correct
The correct answer is C. \({\emptyset,{x}}\). A one element set has subsets \(\emptyset\) and ({x}). So its power set is \({\emptyset,{x}}\).
Step 3
Exam Tip
एक तत्व वाले समुच्चय के उपसमुच्चय \(\emptyset\) और ({x}) हैं। इसलिए घात समुच्चय \({\emptyset,{x}}\) है।
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यदि \(U=\{a,b,c,d\}\) और \(B=\{a,d\}\) है तो (B') कौन सा है?
If \(U=\{a,b,c,d\}\) and \(B=\{a,d\}\) then which is (B')?
#sets
#universal_set
#complement
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A ({a,d})
B ({b,c})
C ({a,b,c,d})
D ({c,d})
Explanation opens after your attempt
Correct Answer
B. ({b,c})
Step 1
Concept
The complement is (U-B). After removing (a,d) the remaining elements are (b,c).
Step 2
Why this answer is correct
The correct answer is B. ({b,c}). The complement is (U-B). After removing (a,d) the remaining elements are (b,c).
Step 3
Exam Tip
पूरक (U-B) होता है। (a,d) हटाने पर (b,c) बचते हैं।
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(\mathcal{P}({1,2})) में कौन सा तत्व नहीं है?
Which is not an element of (\mathcal{P}({1,2}))?
#sets
#power_set
#not_subset
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A \(\emptyset\)
B ({1})
C ({2})
D ({3})
Explanation opens after your attempt
Step 1
Concept
({3}) is not a subset of ({1,2}). So it cannot be an element of the power set.
Step 2
Why this answer is correct
The correct answer is D. ({3}). ({3}) is not a subset of ({1,2}). So it cannot be an element of the power set.
Step 3
Exam Tip
({3}) समुच्चय ({1,2}) का उपसमुच्चय नहीं है। इसलिए यह घात समुच्चय का तत्व नहीं हो सकता।
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हर समुच्चय के घात समुच्चय में कौन सा समुच्चय अवश्य होता है?
Which set is always present in the power set of every set?
#sets
#power_set
#empty_subset
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A केवल (U) / only (U)
B \(\emptyset\)
C केवल ({0}) / only ({0})
D केवल ({1}) / only ({1})
Explanation opens after your attempt
Correct Answer
B. \(\emptyset\)
Step 1
Concept
The empty set is a subset of every set. Therefore \(\emptyset\) is an element of every power set.
Step 2
Why this answer is correct
The correct answer is B. \(\emptyset\). The empty set is a subset of every set. Therefore \(\emptyset\) is an element of every power set.
Step 3
Exam Tip
रिक्त समुच्चय हर समुच्चय का उपसमुच्चय होता है। इसलिए \(\emptyset\) हर घात समुच्चय का तत्व है।
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यदि \(A\subseteq U\) है तो (A') किसका उपसमुच्चय होगा?
If \(A\subseteq U\) then (A') will be a subset of which set?
#sets
#universal_set
#complement
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A (A)
B (U)
C (\mathcal{P}(A))
D \(\emptyset\)
Explanation opens after your attempt
Step 1
Concept
All elements of a complement are taken from the universal set (U). Hence \(A'\subseteq U\).
Step 2
Why this answer is correct
The correct answer is B. (U). All elements of a complement are taken from the universal set (U). Hence \(A'\subseteq U\).
Step 3
Exam Tip
पूरक के सभी तत्व सार्वत्रिक समुच्चय (U) से ही लिए जाते हैं। इसलिए \(A'\subseteq U\) होता है।
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यदि (n(A)=2) है तो (n(\mathcal{P}(A))) कितना होगा?
If (n(A)=2) then what is (n(\mathcal{P}(A)))?
#sets
#power_set
#cardinality
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The number of elements in the power set is \(2^{n(A)}\). Here \(2^2=4\).
Step 2
Why this answer is correct
The correct answer is C. (4). The number of elements in the power set is \(2^{n(A)}\). Here \(2^2=4\).
Step 3
Exam Tip
घात समुच्चय की संख्या \(2^{n(A)}\) होती है। यहां \(2^2=4\) है।
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यदि \(A=\{p,q,r\}\) है तो ({p,q}) का संबंध (\mathcal{P}(A)) से क्या है?
If \(A=\{p,q,r\}\) then what is the relation of ({p,q}) with (\mathcal{P}(A))?
#sets
#power_set
#element_relation
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A \({p,q}\in \mathcal{P}(A)\)
B \({p,q}\notin \mathcal{P}(A)\)
C ({p,q}=A)
D ({p,q}=U)
Explanation opens after your attempt
Correct Answer
A. \({p,q}\in \mathcal{P}(A)\)
Step 1
Concept
({p,q}) is a subset of (A). Therefore it is an element of (\mathcal{P}(A)).
Step 2
Why this answer is correct
The correct answer is A. \({p,q}\in \mathcal{P}(A)\). ({p,q}) is a subset of (A). Therefore it is an element of (\mathcal{P}(A)).
Step 3
Exam Tip
({p,q}) (A) का उपसमुच्चय है। इसलिए यह (\mathcal{P}(A)) का तत्व है।
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यदि \(U=\{1,2,3,4\}\) और (A=U) है तो (A') क्या होगा?
If \(U=\{1,2,3,4\}\) and (A=U) then what is (A')?
#sets
#universal_set
#complement
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A ({1,2,3,4})
B ({1})
C \(\emptyset\)
D ({0})
Explanation opens after your attempt
Correct Answer
C. \(\emptyset\)
Step 1
Concept
When (A=U), no element remains outside (A) in (U). Hence \(A'=\emptyset\).
Step 2
Why this answer is correct
The correct answer is C. \(\emptyset\). When (A=U), no element remains outside (A) in (U). Hence \(A'=\emptyset\).
Step 3
Exam Tip
जब (A=U) हो तो (U) में (A) के बाहर कोई तत्व नहीं बचता। इसलिए \(A'=\emptyset\) है।
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यदि \(U=\{1,2,3\}\) और \(A=\emptyset\) है तो (A') क्या होगा?
If \(U=\{1,2,3\}\) and \(A=\emptyset\) then what is (A')?
#sets
#universal_set
#empty_complement
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A \(\emptyset\)
B ({1})
C ({2,3})
D ({1,2,3})
Explanation opens after your attempt
Correct Answer
D. ({1,2,3})
Step 1
Concept
The empty set has no elements so its complement is the whole (U). Remember \(\emptyset'=U\) for exams.
Step 2
Why this answer is correct
The correct answer is D. ({1,2,3}). The empty set has no elements so its complement is the whole (U). Remember \(\emptyset'=U\) for exams.
Step 3
Exam Tip
रिक्त समुच्चय में कोई तत्व नहीं होता इसलिए उसका पूरक पूरा (U) होता है। परीक्षा में \(\emptyset'=U\) याद रखें।
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(\mathcal{P}({m,n})) में कुल कौन से उपसमुच्चय होंगे?
Which subsets will be in (\mathcal{P}({m,n}))?
#sets
#power_set
#list_subsets
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A \({\emptyset,{m},{n},{m,n}}\)
B ({m,n})
C ({{m},{n}})
D \({\emptyset,m,n}\)
Explanation opens after your attempt
Correct Answer
A. \({\emptyset,{m},{n},{m,n}}\)
Step 1
Concept
A two element set has four subsets. These include \(\emptyset\) and the whole set itself.
Step 2
Why this answer is correct
The correct answer is A. \({\emptyset,{m},{n},{m,n}}\). A two element set has four subsets. These include \(\emptyset\) and the whole set itself.
Step 3
Exam Tip
दो तत्वों वाले समुच्चय के चार उपसमुच्चय होते हैं। इनमें \(\emptyset\) और पूरा समुच्चय भी शामिल होते हैं।
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यदि \(A=\{1,2,3,4,5\}\) है तो (\mathcal{P}(A)) में कितने एक तत्व वाले समुच्चय होंगे?
If \(A=\{1,2,3,4,5\}\) then how many one element sets are in (\mathcal{P}(A))?
#sets
#power_set
#singleton_subsets
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A (1)
B (3)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
Each original element forms one singleton subset. So there will be five one element subsets.
Step 2
Why this answer is correct
The correct answer is C. (5). Each original element forms one singleton subset. So there will be five one element subsets.
Step 3
Exam Tip
हर मूल तत्व से एक एकल उपसमुच्चय बनता है। इसलिए पांच एक तत्व वाले उपसमुच्चय होंगे।
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यदि \(A=\{2,4,6\}\) है तो (A) स्वयं (\mathcal{P}(A)) का तत्व है या नहीं?
If \(A=\{2,4,6\}\), is (A) itself an element of (\mathcal{P}(A))?
#sets
#power_set
#self_subset
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A हां क्योंकि \(A\subseteq A\) / Yes because \(A\subseteq A\)
B नहीं क्योंकि (A) बड़ा है / No because (A) is large
C नहीं क्योंकि (A) में तीन तत्व हैं / No because (A) has three elements
D हां क्योंकि (A) सार्वत्रिक है / Yes because (A) is universal
Explanation opens after your attempt
Correct Answer
A. हां क्योंकि \(A\subseteq A\) / Yes because \(A\subseteq A\)
Step 1
Concept
Every set is a subset of itself. Therefore \(A\in \mathcal{P}(A)\) is correct.
Step 2
Why this answer is correct
The correct answer is A. हां क्योंकि \(A\subseteq A\) / Yes because \(A\subseteq A\). Every set is a subset of itself. Therefore \(A\in \mathcal{P}(A)\) is correct.
Step 3
Exam Tip
हर समुच्चय स्वयं का उपसमुच्चय होता है। इसलिए \(A\in \mathcal{P}(A)\) सही है।
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यदि (U) विद्यालय के सभी विद्यार्थियों का समुच्चय है और (A) कक्षा (11) के विद्यार्थियों का समुच्चय है तो (A') क्या दर्शाएगा?
If (U) is the set of all students in a school and (A) is the set of class (11) students, what does (A') represent?
#sets
#universal_set
#word_problem
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A कक्षा (11) के विद्यार्थी / class (11) students
B विद्यालय के वे विद्यार्थी जो कक्षा (11) में नहीं हैं / school students not in class (11)
C सभी शिक्षक / all teachers
D केवल कक्षा (12) के विद्यार्थी / only class (12) students
Explanation opens after your attempt
Correct Answer
B. विद्यालय के वे विद्यार्थी जो कक्षा (11) में नहीं हैं / school students not in class (11)
Step 1
Concept
The complement shows elements inside (U) but outside (A). Here it means school students who are not in class (11).
Step 2
Why this answer is correct
The correct answer is B. विद्यालय के वे विद्यार्थी जो कक्षा (11) में नहीं हैं / school students not in class (11). The complement shows elements inside (U) but outside (A). Here it means school students who are not in class (11).
Step 3
Exam Tip
पूरक (U) के अंदर (A) से बाहर के तत्वों को दिखाता है। यहां यह कक्षा (11) में न पढ़ने वाले विद्यालय के विद्यार्थी हैं।
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यदि (n(\mathcal{P}(A))=8) है तो (n(A)) कितना होगा?
If (n(\mathcal{P}(A))=8) then what is (n(A))?
#sets
#power_set
#reverse_formula
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Since \(8=2^3\), (n(A)=3). Match the power set size with \(2^n\) to find the original number.
Step 2
Why this answer is correct
The correct answer is B. (3). Since \(8=2^3\), (n(A)=3). Match the power set size with \(2^n\) to find the original number.
Step 3
Exam Tip
क्योंकि \(8=2^3\), इसलिए (n(A)=3) है। घात समुच्चय से मूल संख्या निकालते समय \(2^n\) मिलाएं।
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यदि \(A={\emptyset}\) है तो (n(\mathcal{P}(A))) कितना होगा?
If \(A={\emptyset}\) then what is (n(\mathcal{P}(A)))?
#sets
#power_set
#empty_element
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A (0)
B (1)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
(A) has one element and that element is \(\emptyset\). Therefore (n(\mathcal{P}(A))=21 =2).
Step 2
Why this answer is correct
The correct answer is C. (2). (A) has one element and that element is \(\emptyset\). Therefore (n(\mathcal{P}(A))=21 =2).
Step 3
Exam Tip
(A) में एक तत्व है और वह \(\emptyset\) है। इसलिए (n(\mathcal{P}(A))=21 =2) है।
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यदि \(A={\emptyset}\) है तो (\mathcal{P}(A)) कौन सा है?
If \(A={\emptyset}\) then which is (\mathcal{P}(A))?
#sets
#power_set
#empty_set_element
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A \(\emptyset\)
B \({\emptyset}\)
C \({\emptyset,{\emptyset}}\)
D \({{\emptyset}}\)
Explanation opens after your attempt
Correct Answer
C. \({\emptyset,{\emptyset}}\)
Step 1
Concept
The subsets of (A) are \(\emptyset\) and \({\emptyset}\). So its power set is \({\emptyset,{\emptyset}}\).
Step 2
Why this answer is correct
The correct answer is C. \({\emptyset,{\emptyset}}\). The subsets of (A) are \(\emptyset\) and \({\emptyset}\). So its power set is \({\emptyset,{\emptyset}}\).
Step 3
Exam Tip
(A) के उपसमुच्चय \(\emptyset\) और \({\emptyset}\) हैं। इसलिए उसका घात समुच्चय \({\emptyset,{\emptyset}}\) है।
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यदि \(U=\{0,1,2,3,4\}\) और \(A=\{0,2,4\}\) है तो (A') में कितने तत्व हैं?
If \(U=\{0,1,2,3,4\}\) and \(A=\{0,2,4\}\) then how many elements are in (A')?
#sets
#universal_set
#complement_count
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A (1)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
(A') contains (1) and (3). So it has (2) elements.
Step 2
Why this answer is correct
The correct answer is B. (2). (A') contains (1) and (3). So it has (2) elements.
Step 3
Exam Tip
(A') में (1) और (3) आएंगे। इसलिए इसमें (2) तत्व हैं।
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यदि \(A=\{1,2\}\) है तो (1) और ({1}) में कौन सा (\mathcal{P}(A)) का तत्व है?
If \(A=\{1,2\}\) then between (1) and ({1}), which is an element of (\mathcal{P}(A))?
#sets
#power_set
#common_mistake
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A केवल (1) / only (1)
B केवल ({1}) / only ({1})
C दोनों / both
D कोई नहीं / none
Explanation opens after your attempt
Correct Answer
B. केवल ({1}) / only ({1})
Step 1
Concept
(\mathcal{P}(A)) contains subsets, not direct elements. ({1}) is a subset, so it is correct.
Step 2
Why this answer is correct
The correct answer is B. केवल ({1}) / only ({1}). (\mathcal{P}(A)) contains subsets, not direct elements. ({1}) is a subset, so it is correct.
Step 3
Exam Tip
(\mathcal{P}(A)) में उपसमुच्चय होते हैं, सीधे तत्व नहीं। ({1}) उपसमुच्चय है इसलिए सही है।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(E=\{2,4,6\}\) है तो (E') क्या है?
If \(U=\{1,2,3,4,5,6\}\) and \(E=\{2,4,6\}\) then what is (E')?
#sets
#universal_set
#even_odd
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A ({1,3,5})
B ({2,4,6})
C ({1,2,3})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5})
Step 1
Concept
(E) contains even numbers and the remaining numbers in (U) are (1,3,5). Hence (E'={1,3,5}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5}). (E) contains even numbers and the remaining numbers in (U) are (1,3,5). Hence (E'={1,3,5}).
Step 3
Exam Tip
(E) में सम संख्याएं हैं और (U) में बची संख्याएं (1,3,5) हैं। इसलिए (E'={1,3,5}) है।
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यदि \(A=\{1,3,5\}\) है तो ({1,5}) किसका तत्व है?
If \(A=\{1,3,5\}\) then ({1,5}) is an element of which set?
#sets
#power_set
#element_vs_subset
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A (A)
B (\mathcal{P}(A))
C दोनों (A) और (\mathcal{P}(A)) / both (A) and (\mathcal{P}(A))
D न तो (A) न (\mathcal{P}(A)) / neither (A) nor (\mathcal{P}(A))
Explanation opens after your attempt
Correct Answer
B. (\mathcal{P}(A))
Step 1
Concept
({1,5}) is a subset of (A) but not a direct element of (A). So it is an element of (\mathcal{P}(A)).
Step 2
Why this answer is correct
The correct answer is B. (\mathcal{P}(A)). ({1,5}) is a subset of (A) but not a direct element of (A). So it is an element of (\mathcal{P}(A)).
Step 3
Exam Tip
({1,5}) (A) का उपसमुच्चय है लेकिन (A) का सीधा तत्व नहीं है। इसलिए यह (\mathcal{P}(A)) का तत्व है।
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यदि किसी समुच्चय का घात समुच्चय (32) तत्वों वाला है तो मूल समुच्चय में कितने तत्व हैं?
If the power set of a set has (32) elements then how many elements are in the original set?
#sets
#power_set
#reverse_count
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A (4)
B (5)
C (6)
D (16)
Explanation opens after your attempt
Step 1
Concept
Since \(32=2^5\), the original set has (5) elements. The size of a power set is always a power of (2).
Step 2
Why this answer is correct
The correct answer is B. (5). Since \(32=2^5\), the original set has (5) elements. The size of a power set is always a power of (2).
Step 3
Exam Tip
क्योंकि \(32=2^5\), मूल समुच्चय में (5) तत्व होंगे। घात समुच्चय की संख्या हमेशा (2) की घात होती है।
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यदि (A) में (0) तत्व हैं तो (\mathcal{P}(A)) में कितने तत्व होंगे?
If (A) has (0) elements then how many elements will (\mathcal{P}(A)) have?
#sets
#power_set
#zero_elements
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A (0)
B (1)
C (2)
D (10)
Explanation opens after your attempt
Step 1
Concept
For a set with (0) elements, \(2^0=1\). So the power set of the empty set has one element.
Step 2
Why this answer is correct
The correct answer is B. (1). For a set with (0) elements, \(2^0=1\). So the power set of the empty set has one element.
Step 3
Exam Tip
(0) तत्वों वाले समुच्चय के लिए \(2^0=1\) होता है। इसलिए रिक्त समुच्चय का घात समुच्चय एक तत्व वाला है।
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यदि \(U=\{क,ख,ग,घ\}\) और \(A=\{क,ग\}\) है तो (A') क्या होगा?
If \(U=\{a,b,c,d\}\) and \(A=\{a,c\}\) then what is (A')?
#sets
#universal_set
#letters
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A ({क,ग}) / ({a,c})
B ({ख,घ}) / ({b,d})
C ({क,ख}) / ({a,b})
D ({ग,घ}) / ({c,d})
Explanation opens after your attempt
Correct Answer
B. ({ख,घ}) / ({b,d})
Step 1
Concept
The complement contains elements of (U) not in (A). Here (b) and (d) remain.
Step 2
Why this answer is correct
The correct answer is B. ({ख,घ}) / ({b,d}). The complement contains elements of (U) not in (A). Here (b) and (d) remain.
Step 3
Exam Tip
पूरक में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। यहां (ख) और (घ) बचते हैं।
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यदि \(A=\{1,2,3\}\) है तो (\mathcal{P}(A)) में कितने दो तत्व वाले उपसमुच्चय होंगे?
If \(A=\{1,2,3\}\) then how many two element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#two_element_subsets
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A (1)
B (2)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
The two element subsets are ({1,2},{1,3},{2,3}). So the number is (3).
Step 2
Why this answer is correct
The correct answer is C. (3). The two element subsets are ({1,2},{1,3},{2,3}). So the number is (3).
Step 3
Exam Tip
दो तत्व वाले उपसमुच्चय ({1,2},{1,3},{2,3}) हैं। इसलिए संख्या (3) है।
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यदि \(U=\{1,2,3,4,5\}\) और (A'={4,5}) है तो (A) क्या हो सकता है?
If \(U=\{1,2,3,4,5\}\) and (A'={4,5}), what can (A) be?
#sets
#universal_set
#find_set
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A ({1,2,3})
B ({4,5})
C ({1,4,5})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. ({1,2,3})
Step 1
Concept
If the complement is (4,5), then (A) contains the remaining elements of (U). So \(A=\{1,2,3\}\).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3}). If the complement is (4,5), then (A) contains the remaining elements of (U). So \(A=\{1,2,3\}\).
Step 3
Exam Tip
यदि पूरक (4,5) है तो (A) में (U) के बाकी तत्व होंगे। इसलिए \(A=\{1,2,3\}\) है।
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यदि \(A=\{2,3\}\) है तो \(\emptyset\) का (\mathcal{P}(A)) से संबंध क्या है?
If \(A=\{2,3\}\) then what is the relation of \(\emptyset\) with (\mathcal{P}(A))?
#sets
#power_set
#empty_subset
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A \(\emptyset\in \mathcal{P}(A)\)
B \(\emptyset\notin \mathcal{P}(A)\)
C \(\emptyset=A\)
D \(\emptyset=U\)
Explanation opens after your attempt
Correct Answer
A. \(\emptyset\in \mathcal{P}(A)\)
Step 1
Concept
\(\emptyset\) is a subset of every set. So it is an element of (\mathcal{P}(A)).
Step 2
Why this answer is correct
The correct answer is A. \(\emptyset\in \mathcal{P}(A)\). \(\emptyset\) is a subset of every set. So it is an element of (\mathcal{P}(A)).
Step 3
Exam Tip
\(\emptyset\) हर समुच्चय का उपसमुच्चय है। इसलिए यह (\mathcal{P}(A)) का तत्व है।
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यदि \(A=\{7,8\}\) है तो ({7,8}) (\mathcal{P}(A)) में क्यों है?
If \(A=\{7,8\}\), why is ({7,8}) in (\mathcal{P}(A))?
#sets
#power_set
#self_subset
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A क्योंकि हर समुच्चय स्वयं का उपसमुच्चय है / because every set is a subset of itself
B क्योंकि यह रिक्त है / because it is empty
C क्योंकि यह सार्वत्रिक है / because it is universal
D क्योंकि इसमें तीन तत्व हैं / because it has three elements
Explanation opens after your attempt
Correct Answer
A. क्योंकि हर समुच्चय स्वयं का उपसमुच्चय है / because every set is a subset of itself
Step 1
Concept
({7,8}=A) and every set is a subset of itself. Hence it is included in the power set.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि हर समुच्चय स्वयं का उपसमुच्चय है / because every set is a subset of itself. ({7,8}=A) and every set is a subset of itself. Hence it is included in the power set.
Step 3
Exam Tip
({7,8}=A) और हर समुच्चय स्वयं का उपसमुच्चय होता है। इसलिए यह घात समुच्चय में शामिल है।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और \(A=\{1,3,5,7\}\) है तो (A') क्या है?
If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{1,3,5,7\}\), what is (A')?
#sets
#universal_set
#complement
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A ({2,4,6})
B ({1,3,5,7})
C ({1,2,3})
D ({7})
Explanation opens after your attempt
Correct Answer
A. ({2,4,6})
Step 1
Concept
(A) contains odd numbers and the remaining numbers in (U) are (2,4,6). Therefore (A'={2,4,6}).
Step 2
Why this answer is correct
The correct answer is A. ({2,4,6}). (A) contains odd numbers and the remaining numbers in (U) are (2,4,6). Therefore (A'={2,4,6}).
Step 3
Exam Tip
(A) में विषम संख्याएं हैं और (U) में बची संख्याएं (2,4,6) हैं। इसलिए (A'={2,4,6}) है।
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किस स्थिति में \(A'=\emptyset\) होगा?
In which case will \(A'=\emptyset\)?
#sets
#universal_set
#empty_complement
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A जब (A=U) / when (A=U)
B जब \(A=\emptyset\) / when \(A=\emptyset\)
C जब (A) में एक तत्व हो / when (A) has one element
D जब \(U=\emptyset\) हमेशा / when \(U=\emptyset\) always
Explanation opens after your attempt
Correct Answer
A. जब (A=U) / when (A=U)
Step 1
Concept
The complement is empty when (A) takes the whole universal set. Therefore (A=U) is the correct case.
Step 2
Why this answer is correct
The correct answer is A. जब (A=U) / when (A=U). The complement is empty when (A) takes the whole universal set. Therefore (A=U) is the correct case.
Step 3
Exam Tip
पूरक तब रिक्त होगा जब (A) ने पूरे सार्वत्रिक समुच्चय को ले लिया हो। इसलिए (A=U) सही स्थिति है।
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किस स्थिति में (A'=U) होगा?
In which case will (A'=U)?
#sets
#universal_set
#full_complement
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A जब (A=U) / when (A=U)
B जब \(A=\emptyset\) / when \(A=\emptyset\)
C जब (A) में दो तत्व हों / when (A) has two elements
D जब (A) सार्वत्रिक हो / when (A) is universal
Explanation opens after your attempt
Correct Answer
B. जब \(A=\emptyset\) / when \(A=\emptyset\)
Step 1
Concept
The empty set has no element, so its complement is the whole (U). This basic rule is very useful in exams.
Step 2
Why this answer is correct
The correct answer is B. जब \(A=\emptyset\) / when \(A=\emptyset\). The empty set has no element, so its complement is the whole (U). This basic rule is very useful in exams.
Step 3
Exam Tip
रिक्त समुच्चय में कोई तत्व नहीं होता इसलिए उसका पूरक पूरा (U) है। परीक्षा में यह मूल नियम बहुत उपयोगी है।
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यदि \(A=\{1,2,3,4\}\) है तो (\mathcal{P}(A)) में कितने तीन तत्व वाले उपसमुच्चय होंगे?
If \(A=\{1,2,3,4\}\), how many three element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#subset_count
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
There are (4) ways to choose three elements from four. So there are (4) three element subsets.
Step 2
Why this answer is correct
The correct answer is C. (4). There are (4) ways to choose three elements from four. So there are (4) three element subsets.
Step 3
Exam Tip
चार तत्वों में से तीन चुनने के (4) तरीके हैं। इसलिए तीन तत्व वाले उपसमुच्चय (4) होंगे।
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यदि \(A=\{a,b,c\}\) है तो (\mathcal{P}(A)) में कितने शून्य तत्व वाले उपसमुच्चय होंगे?
If \(A=\{a,b,c\}\), how many zero element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#empty_subset_count
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A (0)
B (1)
C (3)
D (8)
Explanation opens after your attempt
Step 1
Concept
The only zero element subset is \(\emptyset\). Therefore the number is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). The only zero element subset is \(\emptyset\). Therefore the number is (1).
Step 3
Exam Tip
शून्य तत्व वाला उपसमुच्चय केवल \(\emptyset\) होता है। इसलिए संख्या (1) है।
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यदि \(U=\{लाल,नीला,हरा\}\) और \(A=\{लाल\}\) है तो (A') कौन सा है?
If \(U=\{red,blue,green\}\) and \(A=\{red\}\), which is (A')?
#sets
#universal_set
#real_context
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A ({लाल}) / ({red})
B ({नीला,हरा}) / ({blue,green})
C ({हरा}) / ({green})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({नीला,हरा}) / ({blue,green})
Step 1
Concept
(A') contains the colors in (U) that are not in (A). So blue and green are correct.
Step 2
Why this answer is correct
The correct answer is B. ({नीला,हरा}) / ({blue,green}). (A') contains the colors in (U) that are not in (A). So blue and green are correct.
Step 3
Exam Tip
(A') में (U) के वे रंग होंगे जो (A) में नहीं हैं। इसलिए नीला और हरा सही हैं।
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यदि (\mathcal{P}(A)={\emptyset,{5}}) है तो (A) क्या है?
If (\mathcal{P}(A)={\emptyset,{5}}), what is (A)?
#sets
#power_set
#identify_set
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A \(\emptyset\)
B ({5})
C ({0,5})
D \({\emptyset}\)
Explanation opens after your attempt
Step 1
Concept
A power set contains both \(\emptyset\) and the whole original set. Here the whole original set is ({5}).
Step 2
Why this answer is correct
The correct answer is B. ({5}). A power set contains both \(\emptyset\) and the whole original set. Here the whole original set is ({5}).
Step 3
Exam Tip
घात समुच्चय में \(\emptyset\) और पूरा मूल समुच्चय दोनों होते हैं। यहां पूरा मूल समुच्चय ({5}) है।
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यदि \(A=\{1,2\}\) है तो (\mathcal{P}(A)) में ({1,2,3}) क्यों नहीं होगा?
If \(A=\{1,2\}\), why will ({1,2,3}) not be in (\mathcal{P}(A))?
#sets
#power_set
#extra_element
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A क्योंकि (3) (A) में नहीं है / because (3) is not in (A)
B क्योंकि (1) (A) में है / because (1) is in (A)
C क्योंकि (2) (A) में है / because (2) is in (A)
D क्योंकि \(\emptyset\) नहीं लिखा है / because \(\emptyset\) is not written
Explanation opens after your attempt
Correct Answer
A. क्योंकि (3) (A) में नहीं है / because (3) is not in (A)
Step 1
Concept
({1,2,3}) is not a subset of (A) because it has the extra element (3). A power set contains only subsets.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि (3) (A) में नहीं है / because (3) is not in (A). ({1,2,3}) is not a subset of (A) because it has the extra element (3). A power set contains only subsets.
Step 3
Exam Tip
({1,2,3}) (A) का उपसमुच्चय नहीं है क्योंकि इसमें अतिरिक्त तत्व (3) है। घात समुच्चय में केवल उपसमुच्चय आते हैं।
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यदि \(U=\{1,2,3,4\}\), \(A=\{1,4\}\) और (B=A') है तो (B) क्या है?
If \(U=\{1,2,3,4\}\), \(A=\{1,4\}\) and (B=A'), what is (B)?
#sets
#universal_set
#notation
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A ({1,4})
B ({2,3})
C ({1,2})
D ({3,4})
Explanation opens after your attempt
Correct Answer
B. ({2,3})
Step 1
Concept
(A') contains the elements left after removing (1) and (4) from (U). Hence \(B=\{2,3\}\).
Step 2
Why this answer is correct
The correct answer is B. ({2,3}). (A') contains the elements left after removing (1) and (4) from (U). Hence \(B=\{2,3\}\).
Step 3
Exam Tip
(A') में (U) से (1) और (4) हटाने पर बचे तत्व आते हैं। इसलिए \(B=\{2,3\}\) है।
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यदि \(A=\{किताब,कलम\}\) है तो (\mathcal{P}(A)) में कितने तत्व होंगे?
If \(A=\{book,pen\}\), how many elements are in (\mathcal{P}(A))?
#sets
#power_set
#daily_life
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
A set with two objects has \(2^2=4\) subsets. The rule stays the same whatever the names are.
Step 2
Why this answer is correct
The correct answer is C. (4). A set with two objects has \(2^2=4\) subsets. The rule stays the same whatever the names are.
Step 3
Exam Tip
दो वस्तुओं वाले समुच्चय के उपसमुच्चय \(2^2=4\) होते हैं। नाम कुछ भी हो नियम वही रहता है।
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यदि \(A=\{2,4,8\}\) है तो ({4,8}) के बारे में सही कथन कौन सा है?
If \(A=\{2,4,8\}\), which statement about ({4,8}) is correct?
#sets
#power_set
#subset_relation
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A \({4,8}\subseteq A\) और \({4,8}\in \mathcal{P}(A)\) / \({4,8}\subseteq A\) and \({4,8}\in \mathcal{P}(A)\)
B \({4,8}\in A\) केवल / \({4,8}\in A\) only
C \({4,8}\not\subseteq A\)
D ({4,8}=U)
Explanation opens after your attempt
Correct Answer
A. \({4,8}\subseteq A\) और \({4,8}\in \mathcal{P}(A)\) / \({4,8}\subseteq A\) and \({4,8}\in \mathcal{P}(A)\)
Step 1
Concept
Both (4) and (8) are in (A), so \({4,8}\subseteq A\). Therefore it is an element of (\mathcal{P}(A)).
Step 2
Why this answer is correct
The correct answer is A. \({4,8}\subseteq A\) और \({4,8}\in \mathcal{P}(A)\) / \({4,8}\subseteq A\) and \({4,8}\in \mathcal{P}(A)\). Both (4) and (8) are in (A), so \({4,8}\subseteq A\). Therefore it is an element of (\mathcal{P}(A)).
Step 3
Exam Tip
(4) और (8) दोनों (A) में हैं इसलिए \({4,8}\subseteq A\) है। इसी कारण यह (\mathcal{P}(A)) का तत्व है।
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सार्वत्रिक समुच्चय \(U=\{1,2,3,4,5,6,7,8,9\}\) और \(A=\{3,6,9\}\) है। (A') में कौन सा तत्व होगा?
Universal set \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{3,6,9\}\). Which element will be in (A')?
#sets
#universal_set
#element_check
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A (3)
B (6)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(8) is in (U) but not in (A). Therefore (8) will be in (A').
Step 2
Why this answer is correct
The correct answer is C. (8). (8) is in (U) but not in (A). Therefore (8) will be in (A').
Step 3
Exam Tip
(8) (U) में है लेकिन (A) में नहीं है। इसलिए (8) (A') में होगा।
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यदि \(A=\{1,2,3,4\}\) है तो (\mathcal{P}(A)) में पूरा (A) कितनी बार आता है?
If \(A=\{1,2,3,4\}\), how many times does the whole (A) appear in (\mathcal{P}(A))?
#sets
#power_set
#whole_set
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A (0)
B (1)
C (4)
D (16)
Explanation opens after your attempt
Step 1
Concept
The whole set itself appears once as a subset. So the answer is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). The whole set itself appears once as a subset. So the answer is (1).
Step 3
Exam Tip
पूरा समुच्चय स्वयं एक उपसमुच्चय के रूप में एक बार आता है। इसलिए उत्तर (1) है।
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यदि \(U=\{a,e,i,o,u\}\) और \(A=\{a,i,u\}\) है तो (A') कौन सा है?
If \(U=\{a,e,i,o,u\}\) and \(A=\{a,i,u\}\), which is (A')?
#sets
#universal_set
#vowels
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A ({a,i,u})
B ({e,o})
C ({a,e})
D ({i,o,u})
Explanation opens after your attempt
Correct Answer
B. ({e,o})
Step 1
Concept
After removing (a,i,u) from (U), (e,o) remain. Hence (A'={e,o}).
Step 2
Why this answer is correct
The correct answer is B. ({e,o}). After removing (a,i,u) from (U), (e,o) remain. Hence (A'={e,o}).
Step 3
Exam Tip
(U) से (a,i,u) हटाने पर (e,o) बचते हैं। इसलिए (A'={e,o}) है।
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यदि \(A=\{10,20,30\}\) है तो (\mathcal{P}(A)) में कौन सा अवश्य होगा?
If \(A=\{10,20,30\}\), which one must be in (\mathcal{P}(A))?
#sets
#power_set
#singleton
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A (10)
B ({20})
C (40)
D ({40})
Explanation opens after your attempt
Step 1
Concept
({20}) is a subset of (A), so it will be in (\mathcal{P}(A)). Do not treat direct (20) as an element of the power set.
Step 2
Why this answer is correct
The correct answer is B. ({20}). ({20}) is a subset of (A), so it will be in (\mathcal{P}(A)). Do not treat direct (20) as an element of the power set.
Step 3
Exam Tip
({20}) (A) का एक उपसमुच्चय है इसलिए यह (\mathcal{P}(A)) में होगा। सीधे (20) को घात समुच्चय का तत्व न समझें।
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