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
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 \(A=\{p,q,r,s\}\), तो (A) के 2 अवयव वाले उपसमुच्चयों की संख्या कितनी है?
If \(A=\{p,q,r,s\}\), how many 2-element subsets of (A) are there?
#subset count
#combination
#hard
A 4
B 5
C 6
D 8
Explanation opens after your attempt
Step 1
Concept
The number of ways to choose 2 elements is \(\binom{4}{2}=6\). Order is not counted in subsets.
Step 2
Why this answer is correct
The correct answer is C. 6. The number of ways to choose 2 elements is \(\binom{4}{2}=6\). Order is not counted in subsets.
Step 3
Exam Tip
2 अवयव चुनने के तरीके \(\binom{4}{2}=6\) हैं। उपसमुच्चयों में क्रम नहीं गिना जाता।
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यदि \(A=\varnothing\), तो (A) के उपसमुच्चयों की संख्या कितनी है?
If \(A=\varnothing\), how many subsets does (A) have?
#empty set
#subset count
#power set
A 0
B 1
C 2
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
The empty set has exactly one subset, the empty set itself. Remember \(2^0=1\).
Step 2
Why this answer is correct
The correct answer is B. 1. The empty set has exactly one subset, the empty set itself. Remember \(2^0=1\).
Step 3
Exam Tip
रिक्त समुच्चय का एक ही उपसमुच्चय है, वह स्वयं रिक्त समुच्चय है। \(2^0=1\) याद रखें।
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4 अवयव वाले समुच्चय के उचित उपसमुच्चयों की संख्या क्या है?
What is the number of proper subsets of a 4-element set?
#proper subset
#subset count
A 15
B 16
C 8
D 14
Explanation opens after your attempt
Step 1
Concept
Total subsets are \(2^4=16\), and the set itself is not a proper subset. So the number is 15.
Step 2
Why this answer is correct
The correct answer is A. 15. Total subsets are \(2^4=16\), and the set itself is not a proper subset. So the number is 15.
Step 3
Exam Tip
कुल उपसमुच्चय \(2^4=16\) हैं और समुच्चय स्वयं उचित उपसमुच्चय नहीं है। इसलिए संख्या 15 है।
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यदि (A) के कुल उपसमुच्चय 64 हैं, तो (A) में कितने अवयव हैं?
If (A) has 64 subsets, how many elements does (A) have?
#power set
#subset count
#exam
A 5
B 6
C 7
D 8
Explanation opens after your attempt
Step 1
Concept
Total subsets are \(2^n=64\), so (n=6). Recognising powers is the quick method.
Step 2
Why this answer is correct
The correct answer is B. 6. Total subsets are \(2^n=64\), so (n=6). Recognising powers is the quick method.
Step 3
Exam Tip
कुल उपसमुच्चय \(2^n=64\) हैं, इसलिए (n=6)। घातों को पहचानना तेज तरीका है।
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यदि \(A=\varnothing\) है तो (A) के उपसमुच्चयों की संख्या क्या है?
If \(A=\varnothing\) then what is the number of subsets of (A)?
#sets
#empty-set
#subset-count
A (0)
B (1)
C (2)
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
The empty set has exactly one subset which is \(\varnothing\). Remember the formula \(2^0=1\).
Step 2
Why this answer is correct
The correct answer is B. (1). The empty set has exactly one subset which is \(\varnothing\). Remember the formula \(2^0=1\).
Step 3
Exam Tip
रिक्त समुच्चय का केवल एक उपसमुच्चय \(\varnothing\) ही होता है। सूत्र \(2^0=1\) याद रखें।
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यदि \(A={x\in N:x\leq 4}\), तो (A) के उपसमुच्चयों की संख्या क्या है?
If \(A={x\in N:x\leq 4}\), what is the number of subsets of (A)?
#sets
#subset count
#natural numbers
A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(A=\{1,2,3,4\}\), so it has (4) elements.
Step 2
Why this answer is correct
The number of subsets is \(2^4=16\).
Step 3
Exam Tip
First writing the set in roster form makes counting easier. चरण 1: \(A=\{1,2,3,4\}\), इसलिए इसमें (4) अवयव हैं। चरण 2: उपसमुच्चयों की संख्या \(2^4=16\) होगी। चरण 3: पहले समुच्चय को रोस्टर रूप में लिखना गिनती आसान कर देता है।
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यदि किसी समुच्चय के (16) उपसमुच्चय हैं, तो उसमें कितने अवयव होंगे?
If a set has (16) subsets, how many elements does it have?
#sets
#subset count
#powers
A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The number of subsets is \(2^n\).
Step 2
Why this answer is correct
Since \(2^n=16=2^4\), we get (n=4).
Step 3
Exam Tip
Match powers of (2) to find the number of elements quickly. चरण 1: उपसमुच्चयों की संख्या \(2^n\) होती है। चरण 2: \(2^n=16=2^4\), इसलिए (n=4) है। चरण 3: घातों को बराबर करके अवयवों की संख्या जल्दी मिलती है।
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