यदि \(A=\{2,5,7\}\) है तो (n(\mathcal{P}(A))) कितना होगा?
If \(A=\{2,5,7\}\) then what is (n(\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
Set (A) has (3) elements so its power set has \(2^3=8\) elements. Remember (n(\mathcal{P}(A))=2^{n(A)}) for exams.
Step 2
Why this answer is correct
The correct answer is C. (8). Set (A) has (3) elements so its power set has \(2^3=8\) elements. Remember (n(\mathcal{P}(A))=2^{n(A)}) for exams.
Step 3
Exam Tip
(A) में (3) तत्व हैं इसलिए घात समुच्चय में \(2^3=8\) तत्व होंगे। परीक्षा में (n(\mathcal{P}(A))=2^{n(A)}) याद रखें।
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यदि \(A=\{x,y\}\) है तो (\mathcal{P}(A)) में कौन सा तत्व अवश्य होगा?
If \(A=\{x,y\}\) then which element must be in (\mathcal{P}(A))?
#sets
#power_set
#subset
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A (x)
B ({x})
C (y)
D (xy)
Explanation opens after your attempt
Step 1
Concept
({x}) is a subset of (A) so it is an element of (\mathcal{P}(A)). A power set contains subsets not direct elements.
Step 2
Why this answer is correct
The correct answer is B. ({x}). ({x}) is a subset of (A) so it is an element of (\mathcal{P}(A)). A power set contains subsets not direct elements.
Step 3
Exam Tip
({x}) (A) का उपसमुच्चय है इसलिए यह (\mathcal{P}(A)) का तत्व है। घात समुच्चय में सीधे तत्व नहीं बल्कि उपसमुच्चय आते हैं।
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सार्वत्रिक समुच्चय (U) का उपयोग मुख्य रूप से किसे तय करने के लिए होता है?
The universal set (U) is mainly used to decide what?
#sets
#universal_set
#complement
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A पूरक समुच्चय / complement set
B केवल रिक्त समुच्चय / only empty set
C केवल समान समुच्चय / only equal sets
D केवल क्रमित युग्म / only ordered pairs
Explanation opens after your attempt
Correct Answer
A. पूरक समुच्चय / complement set
Step 1
Concept
A complement is always found with respect to a given universal set. Without (U) the complement is not clear.
Step 2
Why this answer is correct
The correct answer is A. पूरक समुच्चय / complement set. A complement is always found with respect to a given universal set. Without (U) the complement is not clear.
Step 3
Exam Tip
पूरक हमेशा किसी दिए गए सार्वत्रिक समुच्चय के संदर्भ में निकाला जाता है। बिना (U) के पूरक स्पष्ट नहीं होता।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और \(A=\{2,5,7\}\) है तो (A') क्या है?
If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{2,5,7\}\), what is (A')?
#sets
#universal_set
#complement
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A ({2,5,7})
B ({1,3,4,6})
C ({1,2,3,4})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({1,3,4,6})
Step 1
Concept
(A') contains elements of (U) that are not in (A). Here (1,3,4,6) remain.
Step 2
Why this answer is correct
The correct answer is B. ({1,3,4,6}). (A') contains elements of (U) that are not in (A). Here (1,3,4,6) remain.
Step 3
Exam Tip
(A') में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। यहां (1,3,4,6) बचते हैं।
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यदि (\mathcal{P}(A)) में (16) तत्व हैं तो (A) में कितने तत्व होंगे?
If (\mathcal{P}(A)) has (16) elements then how many elements are in (A)?
#sets
#power_set
#reverse_count
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Since \(16=2^4\), (n(A)=4). Match the power set size with \(2^n\).
Step 2
Why this answer is correct
The correct answer is C. (4). Since \(16=2^4\), (n(A)=4). Match the power set size with \(2^n\).
Step 3
Exam Tip
क्योंकि \(16=2^4\) इसलिए (n(A)=4) है। घात समुच्चय की संख्या को \(2^n\) से मिलाएं।
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यदि \(A=\{3\}\) है तो (\mathcal{P}(A)) कौन सा है?
If \(A=\{3\}\) then which is (\mathcal{P}(A))?
#sets
#power_set
#singleton
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A ({3})
B \({\emptyset,3}\)
C \({\emptyset,{3}}\)
D ({{3},3})
Explanation opens after your attempt
Correct Answer
C. \({\emptyset,{3}}\)
Step 1
Concept
A one element set has subsets \(\emptyset\) and ({3}). So the power set is \({\emptyset,{3}}\).
Step 2
Why this answer is correct
The correct answer is C. \({\emptyset,{3}}\). A one element set has subsets \(\emptyset\) and ({3}). So the power set is \({\emptyset,{3}}\).
Step 3
Exam Tip
एक तत्व वाले समुच्चय के उपसमुच्चय \(\emptyset\) और ({3}) हैं। इसलिए घात समुच्चय \({\emptyset,{3}}\) है।
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यदि \(U=\{a,b,c,d,e\}\) और \(B=\{b,e\}\) है तो (B') में कौन सा तत्व नहीं होगा?
If \(U=\{a,b,c,d,e\}\) and \(B=\{b,e\}\), which element will not be in (B')?
#sets
#universal_set
#element_check
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A (a)
B (b)
C (c)
D (d)
Explanation opens after your attempt
Step 1
Concept
Elements of (B) do not appear in its complement. So (b) will not be in (B').
Step 2
Why this answer is correct
The correct answer is B. (b). Elements of (B) do not appear in its complement. So (b) will not be in (B').
Step 3
Exam Tip
पूरक में (B) के तत्व नहीं आते। इसलिए (b) (B') में नहीं होगा।
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यदि \(A=\{1,4,9\}\) है तो ({1,9}) के लिए सही कथन कौन सा है?
If \(A=\{1,4,9\}\), which statement is correct for ({1,9})?
#sets
#power_set
#element_relation
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A \({1,9}\in A\)
B \({1,9}\in \mathcal{P}(A)\)
C ({1,9}=U)
D \({1,9}\not\subseteq A\)
Explanation opens after your attempt
Correct Answer
B. \({1,9}\in \mathcal{P}(A)\)
Step 1
Concept
({1,9}) 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 B. \({1,9}\in \mathcal{P}(A)\). ({1,9}) is a subset of (A). Therefore it is an element of (\mathcal{P}(A)).
Step 3
Exam Tip
({1,9}) (A) का उपसमुच्चय है। इसलिए यह (\mathcal{P}(A)) का तत्व है।
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यदि \(U=\{0,1,2,3,4,5\}\) और \(A=\{0,1,5\}\) है तो (n(A')) कितना है?
If \(U=\{0,1,2,3,4,5\}\) and \(A=\{0,1,5\}\), what is (n(A'))?
#sets
#universal_set
#complement_count
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(A') contains (2,3,4). Therefore (n(A')=3).
Step 2
Why this answer is correct
The correct answer is B. (3). (A') contains (2,3,4). Therefore (n(A')=3).
Step 3
Exam Tip
(A') में (2,3,4) हैं। इसलिए (n(A')=3) है।
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रिक्त समुच्चय के घात समुच्चय में कितने तत्व होते हैं?
How many elements are in the power set of the empty set?
#sets
#power_set
#empty_set
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A (0)
B (1)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The empty set has only one subset which is \(\emptyset\). Hence (\mathcal{P}\(\emptyset\)) has (1) element.
Step 2
Why this answer is correct
The correct answer is B. (1). The empty set has only one subset which is \(\emptyset\). Hence (\mathcal{P}\(\emptyset\)) has (1) element.
Step 3
Exam Tip
रिक्त समुच्चय का केवल एक उपसमुच्चय \(\emptyset\) होता है। इसलिए (\mathcal{P}\(\emptyset\)) में (1) तत्व है।
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यदि \(A={\emptyset,1}\) है तो (n(\mathcal{P}(A))) कितना होगा?
If \(A={\emptyset,1}\) then what is (n(\mathcal{P}(A)))?
#sets
#power_set
#empty_element
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A (1)
B (2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here (A) has two elements which are \(\emptyset\) and (1). Therefore there are \(2^2=4\) subsets.
Step 2
Why this answer is correct
The correct answer is C. (4). Here (A) has two elements which are \(\emptyset\) and (1). Therefore there are \(2^2=4\) subsets.
Step 3
Exam Tip
यहां (A) में दो तत्व हैं जो \(\emptyset\) और (1) हैं। इसलिए \(2^2=4\) उपसमुच्चय होंगे।
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यदि (U) एक कक्षा के सभी विद्यार्थियों का समुच्चय है और (G) चश्मा पहनने वाले विद्यार्थियों का समुच्चय है तो (G') क्या दर्शाएगा?
If (U) is the set of all students in a class and (G) is the set of students wearing glasses, what does (G') represent?
#sets
#universal_set
#word_problem
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A चश्मा पहनने वाले विद्यार्थी / students wearing glasses
B चश्मा न पहनने वाले कक्षा के विद्यार्थी / class students not wearing glasses
C सभी शिक्षक / all teachers
D केवल अनुपस्थित विद्यार्थी / only absent students
Explanation opens after your attempt
Correct Answer
B. चश्मा न पहनने वाले कक्षा के विद्यार्थी / class students not wearing glasses
Step 1
Concept
A complement contains elements inside (U) that are not in the given set. Here (G') means students not wearing glasses.
Step 2
Why this answer is correct
The correct answer is B. चश्मा न पहनने वाले कक्षा के विद्यार्थी / class students not wearing glasses. A complement contains elements inside (U) that are not in the given set. Here (G') means students not wearing glasses.
Step 3
Exam Tip
पूरक में उसी (U) के अंदर वे तत्व आते हैं जो दिए गए समुच्चय में नहीं हैं। यहां (G') चश्मा न पहनने वाले विद्यार्थियों को दिखाता है।
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यदि \(A=\{p,q,r,s\}\) है तो (\mathcal{P}(A)) में कितने एक तत्व वाले उपसमुच्चय होंगे?
If \(A=\{p,q,r,s\}\), how many one element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#singleton_subsets
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A (1)
B (2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The four elements form four singleton subsets. So the number is (4).
Step 2
Why this answer is correct
The correct answer is C. (4). The four elements form four singleton subsets. So the number is (4).
Step 3
Exam Tip
चारों तत्वों से चार एकल उपसमुच्चय बनते हैं। इसलिए संख्या (4) है।
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यदि \(A=\{1,2,3\}\) है तो कौन सा (\mathcal{P}(A)) का तत्व नहीं है?
If \(A=\{1,2,3\}\), which is not an element of (\mathcal{P}(A))?
#sets
#power_set
#not_subset
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A ({1})
B ({2,3})
C \(\emptyset\)
D ({1,4})
Explanation opens after your attempt
Correct Answer
D. ({1,4})
Step 1
Concept
({1,4}) is not a subset of (A) because (4) is not in (A). So it will not be in the power set.
Step 2
Why this answer is correct
The correct answer is D. ({1,4}). ({1,4}) is not a subset of (A) because (4) is not in (A). So it will not be in the power set.
Step 3
Exam Tip
({1,4}) (A) का उपसमुच्चय नहीं है क्योंकि (4) (A) में नहीं है। इसलिए यह घात समुच्चय में नहीं आएगा।
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यदि \(A\subseteq U\) है तो \(A\cup A'\) किसके बराबर होता है?
If \(A\subseteq U\), then \(A\cup A'\) is equal to what?
#sets
#universal_set
#union_complement
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A (A)
B (A')
C (U)
D \(\emptyset\)
Explanation opens after your attempt
Step 1
Concept
The union of a set and its complement gives the whole universal set. Thus \(A\cup A'=U\).
Step 2
Why this answer is correct
The correct answer is C. (U). The union of a set and its complement gives the whole universal set. Thus \(A\cup A'=U\).
Step 3
Exam Tip
किसी समुच्चय और उसके पूरक का संघ पूरा सार्वत्रिक समुच्चय देता है। इसलिए \(A\cup A'=U\) है।
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यदि \(A\subseteq U\) है तो \(A\cap A'\) किसके बराबर होता है?
If \(A\subseteq U\), then \(A\cap A'\) is equal to what?
#sets
#universal_set
#intersection_complement
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A (U)
B (A)
C \(\emptyset\)
D (\mathcal{P}(A))
Explanation opens after your attempt
Correct Answer
C. \(\emptyset\)
Step 1
Concept
No element can be in both (A) and (A'). Therefore \(A\cap A'=\emptyset\).
Step 2
Why this answer is correct
The correct answer is C. \(\emptyset\). No element can be in both (A) and (A'). Therefore \(A\cap A'=\emptyset\).
Step 3
Exam Tip
किसी तत्व का (A) और (A') दोनों में होना संभव नहीं है। इसलिए \(A\cap A'=\emptyset\) होता है।
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यदि \(A=\{6,12\}\) है तो (\mathcal{P}(A)) में कुल कौन से तत्व हैं?
If \(A=\{6,12\}\), what are all the elements of (\mathcal{P}(A))?
#sets
#power_set
#list_subsets
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A \({\emptyset,{6},{12},{6,12}}\)
B ({6,12})
C ({{6},{12}})
D \({\emptyset,6,12}\)
Explanation opens after your attempt
Correct Answer
A. \({\emptyset,{6},{12},{6,12}}\)
Step 1
Concept
A two element set has four subsets. Include \(\emptyset\) and the whole set in the power set.
Step 2
Why this answer is correct
The correct answer is A. \({\emptyset,{6},{12},{6,12}}\). A two element set has four subsets. Include \(\emptyset\) and the whole set in the power set.
Step 3
Exam Tip
दो तत्वों वाले समुच्चय के चार उपसमुच्चय होते हैं। घात समुच्चय में \(\emptyset\) और पूरा समुच्चय भी लिखें।
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यदि \(U=\{1,2,3,4,5,6,8\}\) और \(A=\{2,4,6,8\}\) है तो (A') क्या है?
If \(U=\{1,2,3,4,5,6,8\}\) and \(A=\{2,4,6,8\}\), what is (A')?
#sets
#universal_set
#even_numbers
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A ({1,3,5})
B ({2,4,6,8})
C ({1,2,3,4})
D ({5,6,8})
Explanation opens after your attempt
Correct Answer
A. ({1,3,5})
Step 1
Concept
(A') contains the elements of (U) that are not in (A). Here (1,3,5) remain.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5}). (A') contains the elements of (U) that are not in (A). Here (1,3,5) remain.
Step 3
Exam Tip
(A') में (U) के वे तत्व होंगे जो (A) में नहीं हैं। यहां (1,3,5) बचते हैं।
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यदि \(A=\{a,b,c,d\}\) है तो (\mathcal{P}(A)) में कितने दो तत्व वाले उपसमुच्चय होंगे?
If \(A=\{a,b,c,d\}\), how many two element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#two_element_subsets
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
Choosing two elements from four gives (6) subsets. For easy checking list all pairs.
Step 2
Why this answer is correct
The correct answer is C. (6). Choosing two elements from four gives (6) subsets. For easy checking list all pairs.
Step 3
Exam Tip
चार तत्वों में से दो चुनने पर (6) उपसमुच्चय बनते हैं। आसान गिनती के लिए सभी जोड़े बनाकर जांचें।
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यदि \(U=\{1,2,3,4\}\) और (A'={1,4}) है तो (A) क्या है?
If \(U=\{1,2,3,4\}\) and (A'={1,4}), what is (A)?
#sets
#universal_set
#find_set
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A ({1,4})
B ({2,3})
C ({1,2,3})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({2,3})
Step 1
Concept
If the complement is (1,4), then (A) contains the remaining elements of (U). So \(A=\{2,3\}\).
Step 2
Why this answer is correct
The correct answer is B. ({2,3}). If the complement is (1,4), then (A) contains the remaining elements of (U). So \(A=\{2,3\}\).
Step 3
Exam Tip
यदि पूरक (1,4) है तो (A) में (U) के बाकी तत्व होंगे। इसलिए \(A=\{2,3\}\) है।
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यदि \(A=\{10,20,30,40\}\) है तो (\mathcal{P}(A)) में पूरा (A) किस रूप में आता है?
If \(A=\{10,20,30,40\}\), in what form does the whole (A) appear in (\mathcal{P}(A))?
#sets
#power_set
#self_subset
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A तत्व के रूप में / as an element
B सार्वत्रिक समुच्चय के रूप में / as universal set
C असंभव रूप में / as impossible form
D केवल संख्या के रूप में / as a number only
Explanation opens after your attempt
Correct Answer
A. तत्व के रूप में / as an element
Step 1
Concept
Every set is a subset of itself so \(A\in\mathcal{P}(A)\). Understand it from \(A\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. तत्व के रूप में / as an element. Every set is a subset of itself so \(A\in\mathcal{P}(A)\). Understand it from \(A\subseteq A\).
Step 3
Exam Tip
हर समुच्चय स्वयं का उपसमुच्चय है इसलिए \(A\in\mathcal{P}(A)\) होता है। इसे \(A\subseteq A\) से समझें।
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यदि \(A=\{2,3,5\}\) है तो (2) और ({2}) में से (\mathcal{P}(A)) का तत्व कौन है?
If \(A=\{2,3,5\}\), which among (2) and ({2}) is an element of (\mathcal{P}(A))?
#sets
#power_set
#common_mistake
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A केवल (2) / only (2)
B केवल ({2}) / only ({2})
C दोनों / both
D कोई नहीं / none
Explanation opens after your attempt
Correct Answer
B. केवल ({2}) / only ({2})
Step 1
Concept
(\mathcal{P}(A)) contains subsets so ({2}) is correct. (2) is an element of (A) but not of the power set.
Step 2
Why this answer is correct
The correct answer is B. केवल ({2}) / only ({2}). (\mathcal{P}(A)) contains subsets so ({2}) is correct. (2) is an element of (A) but not of the power set.
Step 3
Exam Tip
(\mathcal{P}(A)) में उपसमुच्चय होते हैं इसलिए ({2}) सही है। (2) (A) का तत्व है लेकिन घात समुच्चय का तत्व नहीं।
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यदि \(U=\{सूर्य,चंद्र,तारा\}\) और \(A=\{सूर्य\}\) है तो (A') कौन सा है?
If \(U=\{sun,moon,star\}\) and \(A=\{sun\}\), which is (A')?
#sets
#universal_set
#real_context
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A ({सूर्य}) / ({sun})
B ({चंद्र,तारा}) / ({moon,star})
C ({तारा}) / ({star})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({चंद्र,तारा}) / ({moon,star})
Step 1
Concept
A complement contains the elements left after removing (A) from (U). Here moon and star remain.
Step 2
Why this answer is correct
The correct answer is B. ({चंद्र,तारा}) / ({moon,star}). A complement contains the elements left after removing (A) from (U). Here moon and star remain.
Step 3
Exam Tip
पूरक में (U) से (A) के तत्व हटाकर बचे तत्व आते हैं। यहां चंद्र और तारा बचते हैं।
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यदि \(A=\{1,2,3,4,5\}\) है तो (\mathcal{P}(A)) में कितने चार तत्व वाले उपसमुच्चय होंगे?
If \(A=\{1,2,3,4,5\}\), how many four element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#four_element_subsets
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A (4)
B (5)
C (10)
D (16)
Explanation opens after your attempt
Step 1
Concept
There are (5) ways to choose four elements from five. Each time one different element is left out.
Step 2
Why this answer is correct
The correct answer is B. (5). There are (5) ways to choose four elements from five. Each time one different element is left out.
Step 3
Exam Tip
पांच तत्वों में से चार चुनने के (5) तरीके हैं। हर बार एक अलग तत्व छोड़ा जाता है।
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यदि \(A=\{r,s,t\}\) है तो (\mathcal{P}(A)) में \(\emptyset\) क्यों होता है?
If \(A=\{r,s,t\}\), why is \(\emptyset\) in (\mathcal{P}(A))?
#sets
#power_set
#empty_subset
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A क्योंकि \(\emptyset\subseteq A\) / because \(\emptyset\subseteq A\)
B क्योंकि \(\emptyset=A\) / because \(\emptyset=A\)
C क्योंकि \(\emptyset=U\) / because \(\emptyset=U\)
D क्योंकि \(\emptyset\) संख्या है / because \(\emptyset\) is a number
Explanation opens after your attempt
Correct Answer
A. क्योंकि \(\emptyset\subseteq A\) / because \(\emptyset\subseteq A\)
Step 1
Concept
The empty set is a subset of every set. Therefore it appears as an element in every power set.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(\emptyset\subseteq A\) / because \(\emptyset\subseteq A\). The empty set is a subset of every set. Therefore it appears as an element in every power set.
Step 3
Exam Tip
रिक्त समुच्चय हर समुच्चय का उपसमुच्चय होता है। इसलिए वह हर घात समुच्चय में तत्व के रूप में आता है।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,3,6\}\) है तो (\mathcal{P}(A')) में कितने तत्व होंगे?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,3,6\}\), how many elements will be in (\mathcal{P}(A'))?
#sets
#power_set
#universal_set
#complement_power
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A (4)
B (6)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
First (A'={2,4,5}), which has (3) elements. So (\mathcal{P}(A')) has \(2^3=8\) elements.
Step 2
Why this answer is correct
The correct answer is C. (8). First (A'={2,4,5}), which has (3) elements. So (\mathcal{P}(A')) has \(2^3=8\) elements.
Step 3
Exam Tip
पहले (A'={2,4,5}) मिलेगा जिसमें (3) तत्व हैं। इसलिए (\mathcal{P}(A')) में \(2^3=8\) तत्व होंगे।
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यदि \(A=\{{1},2\}\) है तो (n(A)) कितना है?
If \(A=\{{1},2\}\), what is (n(A))?
#sets
#power_set
#nested_set
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
({1}) is one element and (2) is another element. Therefore (A) has (2) elements.
Step 2
Why this answer is correct
The correct answer is B. (2). ({1}) is one element and (2) is another element. Therefore (A) has (2) elements.
Step 3
Exam Tip
({1}) एक तत्व है और (2) दूसरा तत्व है। इसलिए (A) में कुल (2) तत्व हैं।
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यदि \(A=\{{1},2\}\) है तो (n(\mathcal{P}(A))) कितना होगा?
If \(A=\{{1},2\}\), what is (n(\mathcal{P}(A)))?
#sets
#power_set
#nested_cardinality
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Set (A) has two elements so its power set has \(2^2=4\) elements. Count elements carefully using brackets.
Step 2
Why this answer is correct
The correct answer is C. (4). Set (A) has two elements so its power set has \(2^2=4\) elements. Count elements carefully using brackets.
Step 3
Exam Tip
(A) में दो तत्व हैं इसलिए घात समुच्चय में \(2^2=4\) तत्व होंगे। अंदर के कोष्ठकों को देखकर तत्व गिनें।
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यदि \(U=\{1,2,3,4,5\}\) और \(A=\{2,3\}\) है तो (A') का घात समुच्चय किस पर आधारित होगा?
If \(U=\{1,2,3,4,5\}\) and \(A=\{2,3\}\), the power set of (A') will be based on which set?
#sets
#power_set
#complement_basis
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A ({2,3})
B ({1,4,5})
C ({1,2,3,4,5})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({1,4,5})
Step 1
Concept
First find (A'), which is ({1,4,5}). Then (\mathcal{P}(A')) is made from subsets of this set.
Step 2
Why this answer is correct
The correct answer is B. ({1,4,5}). First find (A'), which is ({1,4,5}). Then (\mathcal{P}(A')) is made from subsets of this set.
Step 3
Exam Tip
पहले (A') निकालते हैं जो ({1,4,5}) है। फिर (\mathcal{P}(A')) इसी समुच्चय के उपसमुच्चयों से बनेगा।
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यदि \(A=\{2,4,6,8\}\) है तो (\mathcal{P}(A)) में शून्य तत्व वाला उपसमुच्चय कितने हैं?
If \(A=\{2,4,6,8\}\), how many zero element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#zero_element_subset
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A (0)
B (1)
C (4)
D (16)
Explanation opens after your attempt
Step 1
Concept
The only zero element subset is \(\emptyset\). So any set has exactly one such subset.
Step 2
Why this answer is correct
The correct answer is B. (1). The only zero element subset is \(\emptyset\). So any set has exactly one such subset.
Step 3
Exam Tip
शून्य तत्व वाला केवल \(\emptyset\) होता है। इसलिए किसी भी समुच्चय में ऐसा उपसमुच्चय एक ही होता है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{1,2,3,4\}\) है तो (A') में सबसे छोटी संख्या कौन सी है?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,2,3,4\}\), what is the smallest number in (A')?
#sets
#universal_set
#smallest_element
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A (1)
B (4)
C (5)
D (8)
Explanation opens after your attempt
Step 1
Concept
(A') contains (5,6,7,8). The smallest among them is (5).
Step 2
Why this answer is correct
The correct answer is C. (5). (A') contains (5,6,7,8). The smallest among them is (5).
Step 3
Exam Tip
(A') में (5,6,7,8) हैं। इनमें सबसे छोटी संख्या (5) है।
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यदि \(A=\{क,ख,ग\}\) है तो (\mathcal{P}(A)) में ({क,ग}) किस कारण से होगा?
If \(A=\{a,b,c\}\), why will ({a,c}) be in (\mathcal{P}(A))?
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#power_set
#reasoning
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A क्योंकि यह (A) का उपसमुच्चय है / because it is a subset of (A)
B क्योंकि यह (A) का पूरक है / because it is the complement of (A)
C क्योंकि यह (U) है / because it is (U)
D क्योंकि यह रिक्त है / because it is empty
Explanation opens after your attempt
Correct Answer
A. क्योंकि यह (A) का उपसमुच्चय है / because it is a subset of (A)
Step 1
Concept
All elements of ({a,c}) are in (A), so it is a subset. Elements of a power set are subsets.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि यह (A) का उपसमुच्चय है / because it is a subset of (A). All elements of ({a,c}) are in (A), so it is a subset. Elements of a power set are subsets.
Step 3
Exam Tip
({क,ग}) के सभी तत्व (A) में हैं इसलिए यह उपसमुच्चय है। घात समुच्चय के तत्व उपसमुच्चय होते हैं।
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यदि \(U=\{1,2,3,4,5\}\) और \(A=\{1,2,3,4,5\}\) है तो (A') में कितने तत्व हैं?
If \(U=\{1,2,3,4,5\}\) and \(A=\{1,2,3,4,5\}\), how many elements are in (A')?
#sets
#universal_set
#empty_complement
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A (0)
B (1)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
When (A=U), the complement is empty. Therefore (A') has (0) elements.
Step 2
Why this answer is correct
The correct answer is A. (0). When (A=U), the complement is empty. Therefore (A') has (0) elements.
Step 3
Exam Tip
जब (A=U) हो तो पूरक रिक्त होता है। इसलिए (A') में (0) तत्व हैं।
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यदि \(U=\{1,2,3,4\}\) और \(A=\emptyset\) है तो (\mathcal{P}(A')) में कितने तत्व होंगे?
If \(U=\{1,2,3,4\}\) and \(A=\emptyset\), how many elements will be in (\mathcal{P}(A'))?
#sets
#power_set
#empty_set_complement
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A (1)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
When \(A=\emptyset\), (A'=U). Here (U) has (4) elements so the power set has \(2^4=16\) elements.
Step 2
Why this answer is correct
The correct answer is D. (16). When \(A=\emptyset\), (A'=U). Here (U) has (4) elements so the power set has \(2^4=16\) elements.
Step 3
Exam Tip
जब \(A=\emptyset\) हो तो (A'=U) होता है। यहां (U) में (4) तत्व हैं इसलिए \(2^4=16\) तत्व मिलेंगे।
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यदि \(A=\{1,2,3\}\) है तो (\mathcal{P}(A)) में कुल कितने समुच्चय (1) को रखते हैं?
If \(A=\{1,2,3\}\), how many sets in (\mathcal{P}(A)) contain (1)?
#sets
#power_set
#contains_element
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Keep (1) fixed and choose or not choose the remaining (2) elements in \(2^2=4\) ways. So there are (4) such subsets.
Step 2
Why this answer is correct
The correct answer is C. (4). Keep (1) fixed and choose or not choose the remaining (2) elements in \(2^2=4\) ways. So there are (4) such subsets.
Step 3
Exam Tip
(1) को स्थिर रखकर बाकी (2) तत्वों को चुनने या न चुनने के \(2^2=4\) तरीके हैं। इसलिए ऐसे (4) उपसमुच्चय हैं।
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यदि \(U=\{काला,सफेद,लाल,पीला\}\) और \(A=\{काला,पीला\}\) है तो (A') क्या है?
If \(U=\{black,white,red,yellow\}\) and \(A=\{black,yellow\}\), what is (A')?
#sets
#universal_set
#color_context
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A ({काला,पीला}) / ({black,yellow})
B ({सफेद,लाल}) / ({white,red})
C ({लाल,पीला}) / ({red,yellow})
D ({काला,सफेद}) / ({black,white})
Explanation opens after your attempt
Correct Answer
B. ({सफेद,लाल}) / ({white,red})
Step 1
Concept
After removing the colors of (A), white and red remain in (U). Hence (A'={white,red}).
Step 2
Why this answer is correct
The correct answer is B. ({सफेद,लाल}) / ({white,red}). After removing the colors of (A), white and red remain in (U). Hence (A'={white,red}).
Step 3
Exam Tip
(A) के रंग हटाने पर (U) में सफेद और लाल बचते हैं। इसलिए (A'={सफेद,लाल}) है।
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यदि \(A=\{5,10,15\}\) है तो (\mathcal{P}(A)) में कितने उपसमुच्चय (15) को नहीं रखते?
If \(A=\{5,10,15\}\), how many subsets in (\mathcal{P}(A)) do not contain (15)?
#sets
#power_set
#without_element
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
Without (15), the remaining (2) elements form \(2^2=4\) subsets. In exams count the elements left after removing the fixed element.
Step 2
Why this answer is correct
The correct answer is C. (4). Without (15), the remaining (2) elements form \(2^2=4\) subsets. In exams count the elements left after removing the fixed element.
Step 3
Exam Tip
(15) को न लेकर बाकी (2) तत्वों से \(2^2=4\) उपसमुच्चय बनते हैं। परीक्षा में हटे हुए तत्व के बाद बचे तत्व गिनें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(M=\{2,4,6,8,10\}\) है तो (M') में कौन सा तत्व होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(M=\{2,4,6,8,10\}\), which element will be in (M')?
#sets
#universal_set
#element_membership
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A (2)
B (6)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
(9) is in (U) but not in (M). So (9) will be in (M').
Step 2
Why this answer is correct
The correct answer is C. (9). (9) is in (U) but not in (M). So (9) will be in (M').
Step 3
Exam Tip
(9) (U) में है लेकिन (M) में नहीं है। इसलिए (9) (M') में होगा।
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यदि \(A=\{a,e,i\}\) है तो (\mathcal{P}(A)) में कितने तीन तत्व वाले उपसमुच्चय होंगे?
If \(A=\{a,e,i\}\), how many three element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#whole_subset_count
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A (1)
B (2)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
The only three element subset of a three element set is the whole set itself. So the number is (1).
Step 2
Why this answer is correct
The correct answer is A. (1). The only three element subset of a three element set is the whole set itself. So the number is (1).
Step 3
Exam Tip
तीन तत्वों वाले समुच्चय का तीन तत्व वाला उपसमुच्चय केवल वही पूरा समुच्चय होता है। इसलिए संख्या (1) है।
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यदि \(A=\{1,2\}\) है तो कौन सा कथन सही है?
If \(A=\{1,2\}\), which statement is correct?
#sets
#power_set
#statement
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A \({1}\subseteq A\) और \({1}\in\mathcal{P}(A)\) / \({1}\subseteq A\) and \({1}\in\mathcal{P}(A)\)
B \(1\in\mathcal{P}(A)\) केवल / \(1\in\mathcal{P}(A)\) only
C \({3}\in\mathcal{P}(A)\)
D (\mathcal{P}(A)=A)
Explanation opens after your attempt
Correct Answer
A. \({1}\subseteq A\) और \({1}\in\mathcal{P}(A)\) / \({1}\subseteq A\) and \({1}\in\mathcal{P}(A)\)
Step 1
Concept
({1}) is a subset of (A), so it is an element of the power set. Do not treat direct (1) as an element of (\mathcal{P}(A)).
Step 2
Why this answer is correct
The correct answer is A. \({1}\subseteq A\) और \({1}\in\mathcal{P}(A)\) / \({1}\subseteq A\) and \({1}\in\mathcal{P}(A)\). ({1}) is a subset of (A), so it is an element of the power set. Do not treat direct (1) as an element of (\mathcal{P}(A)).
Step 3
Exam Tip
({1}) (A) का उपसमुच्चय है इसलिए वह घात समुच्चय का तत्व है। सीधे (1) को (\mathcal{P}(A)) का तत्व न मानें।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और \(A=\{2,3,5,7\}\) है तो (A') में कितने तत्व (4) से छोटे हैं?
If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{2,3,5,7\}\), how many elements of (A') are less than (4)?
#sets
#universal_set
#comparison
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(A'={1,4,6}). Among these, only (1) is less than (4).
Step 2
Why this answer is correct
The correct answer is A. (1). (A'={1,4,6}). Among these, only (1) is less than (4).
Step 3
Exam Tip
(A'={1,4,6}) है। इनमें (4) से छोटा केवल (1) है।
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यदि \(A=\{0,1\}\) है तो (\mathcal{P}(\mathcal{P}(A))) में कितने तत्व होंगे?
If \(A=\{0,1\}\), how many elements are in (\mathcal{P}(\mathcal{P}(A)))?
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#power_set
#double_power_set
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
First (n(\mathcal{P}(A))=22 =4). Then (\mathcal{P}(\mathcal{P}(A))) has \(2^4=16\) elements.
Step 2
Why this answer is correct
The correct answer is C. (16). First (n(\mathcal{P}(A))=22 =4). Then (\mathcal{P}(\mathcal{P}(A))) has \(2^4=16\) elements.
Step 3
Exam Tip
पहले (n(\mathcal{P}(A))=22 =4) है। फिर (\mathcal{P}(\mathcal{P}(A))) में \(2^4=16\) तत्व होंगे।
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यदि \(U=\{1,2,3,4,5\}\) और \(A=\{1,5\}\) है तो ((A')') क्या है?
If \(U=\{1,2,3,4,5\}\) and \(A=\{1,5\}\), what is ((A')')?
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#universal_set
#double_complement
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A ({1,5})
B ({2,3,4})
C ({1,2,3,4,5})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. ({1,5})
Step 1
Concept
The complement of the complement of a set is the original set. Hence ((A')'=A={1,5}).
Step 2
Why this answer is correct
The correct answer is A. ({1,5}). The complement of the complement of a set is the original set. Hence ((A')'=A={1,5}).
Step 3
Exam Tip
किसी समुच्चय के पूरक का पूरक वही मूल समुच्चय होता है। इसलिए ((A')'=A={1,5}) है।
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यदि \(A=\{2,4,6\}\) है तो (\mathcal{P}(A)) में कुल कितने उपसमुच्चय ({2,4}) को शामिल करेंगे?
If \(A=\{2,4,6\}\), how many subsets in (\mathcal{P}(A)) will include ({2,4})?
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#power_set
#include_subset
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Keeping (2) and (4) is compulsory and (6) can be taken or not taken in (2) ways. So there are (2) such subsets.
Step 2
Why this answer is correct
The correct answer is B. (2). Keeping (2) and (4) is compulsory and (6) can be taken or not taken in (2) ways. So there are (2) such subsets.
Step 3
Exam Tip
(2) और (4) को रखना अनिवार्य है और (6) को लेने या न लेने के (2) तरीके हैं। इसलिए ऐसे (2) उपसमुच्चय हैं।
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यदि \(U=\{सभी अंक\}\) और \(A=\{0,2,4,6,8\}\) है तो (A') क्या होगा?
If \(U=\{all digits\}\) and \(A=\{0,2,4,6,8\}\), what will (A') be?
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#universal_set
#digits
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A ({1,3,5,7,9})
B ({0,2,4,6,8})
C ({2,4,6})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7,9})
Step 1
Concept
All digits are from (0) to (9), and (A) contains even digits. The remaining odd digits are (1,3,5,7,9).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7,9}). All digits are from (0) to (9), and (A) contains even digits. The remaining odd digits are (1,3,5,7,9).
Step 3
Exam Tip
सभी अंक (0) से (9) तक होते हैं और (A) में सम अंक हैं। बचे हुए विषम अंक (1,3,5,7,9) हैं।
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यदि \(A=\{1,2,3,4\}\) है तो (\mathcal{P}(A)) में कितने उपसमुच्चय (1) को रखते और (4) को नहीं रखते?
If \(A=\{1,2,3,4\}\), how many subsets in (\mathcal{P}(A)) contain (1) and do not contain (4)?
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#power_set
#condition_count
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
Keeping (1) and excluding (4) are fixed. For remaining (2,3), there are \(2^2=4\) choices.
Step 2
Why this answer is correct
The correct answer is B. (4). Keeping (1) and excluding (4) are fixed. For remaining (2,3), there are \(2^2=4\) choices.
Step 3
Exam Tip
(1) को रखना और (4) को हटाना तय है। बाकी (2,3) के लिए \(2^2=4\) विकल्प हैं।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\) और (B=A') है तो (B') क्या है?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\) and (B=A'), what is (B')?
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A ({1,2,3})
B ({4,5,6})
C ({1,2,3,4,5,6})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. ({1,2,3})
Step 1
Concept
If (B=A'), then (B'=(A')'=A). So (B'={1,2,3}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3}). If (B=A'), then (B'=(A')'=A). So (B'={1,2,3}).
Step 3
Exam Tip
यदि (B=A') है तो (B'=(A')'=A) होगा। इसलिए (B'={1,2,3}) है।
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यदि \(A={\emptyset,{\emptyset}}\) है तो (n(\mathcal{P}(A))) कितना होगा?
If \(A={\emptyset,{\emptyset}}\), what is (n(\mathcal{P}(A)))?
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#nested_empty
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(A) has two distinct elements \(\emptyset\) and \({\emptyset}\). Therefore (n(\mathcal{P}(A))=22 =4).
Step 2
Why this answer is correct
The correct answer is B. (4). (A) has two distinct elements \(\emptyset\) and \({\emptyset}\). Therefore (n(\mathcal{P}(A))=22 =4).
Step 3
Exam Tip
(A) में दो अलग तत्व \(\emptyset\) और \({\emptyset}\) हैं। इसलिए (n(\mathcal{P}(A))=22 =4) है।
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यदि \(U=\{2,4,6,8,10,12\}\) और \(A=\{4,8,12\}\) है तो (A') क्या है?
If \(U=\{2,4,6,8,10,12\}\) and \(A=\{4,8,12\}\), what is (A')?
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#complement
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A ({2,6,10})
B ({4,8,12})
C ({2,4,6})
D ({10,12})
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Correct Answer
A. ({2,6,10})
Step 1
Concept
After removing (4,8,12) from (U), (2,6,10) remain. So this is the complement.
Step 2
Why this answer is correct
The correct answer is A. ({2,6,10}). After removing (4,8,12) from (U), (2,6,10) remain. So this is the complement.
Step 3
Exam Tip
(U) से (4,8,12) हटाने पर (2,6,10) बचते हैं। इसलिए यही पूरक है।
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यदि \(A=\{1,3,5,7\}\) है तो (\mathcal{P}(A)) में कुल उपसमुच्चयों की संख्या और एक तत्व वाले उपसमुच्चयों की संख्या क्रमशः क्या है?
If \(A=\{1,3,5,7\}\), what are the total number of subsets and the number of one element subsets in (\mathcal{P}(A)) respectively?
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A (8) और (4) / (8) and (4)
B (16) और (4) / (16) and (4)
C (16) और (8) / (16) and (8)
D (4) और (16) / (4) and (16)
Explanation opens after your attempt
Correct Answer
B. (16) और (4) / (16) and (4)
Step 1
Concept
A set with four elements has \(2^4=16\) total subsets. The number of one element subsets is (4).
Step 2
Why this answer is correct
The correct answer is B. (16) और (4) / (16) and (4). A set with four elements has \(2^4=16\) total subsets. The number of one element subsets is (4).
Step 3
Exam Tip
चार तत्वों वाले समुच्चय के कुल \(2^4=16\) उपसमुच्चय होते हैं। एक तत्व वाले उपसमुच्चय (4) होते हैं।
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