यदि \(A=\{1,2,3,4,5\}\), तो (\mathcal{P}(A)) के कितने तत्वों में (1) होगा, (2) नहीं होगा और ठीक (3) तत्व होंगे?
If \(A=\{1,2,3,4,5\}\), how many elements of (\mathcal{P}(A)) contain (1), do not contain (2), and have exactly (3) elements?
#sets
#power-set
#restricted-subsets
#exact-size
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(1) is fixed and (2) is excluded, so choose (2) elements from (3,4,5). The count is \(\binom{3}{2}=3\).
Step 2
Why this answer is correct
The correct answer is B. (3). (1) is fixed and (2) is excluded, so choose (2) elements from (3,4,5). The count is \(\binom{3}{2}=3\).
Step 3
Exam Tip
(1) निश्चित है और (2) नहीं लेना है, इसलिए (3,4,5) में से (2) तत्व चुनने होंगे। संख्या \(\binom{3}{2}=3\) है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5,6\}\), तो (\mathcal{P}(A)) के कितने तत्वों में (1) होगा और (6) नहीं होगा?
If \(A=\{1,2,3,4,5,6\}\), how many elements of (\mathcal{P}(A)) contain (1) and do not contain (6)?
#sets
#power-set
#restricted-subsets
A (8)
B (16)
C (32)
D (64)
Explanation opens after your attempt
Step 1
Concept
(1) is fixed and (6) is forbidden. The remaining four elements are free, so there are \(2^4=16\) subsets.
Step 2
Why this answer is correct
The correct answer is B. (16). (1) is fixed and (6) is forbidden. The remaining four elements are free, so there are \(2^4=16\) subsets.
Step 3
Exam Tip
(1) निश्चित है और (6) निषिद्ध है। शेष चार तत्व स्वतंत्र हैं, इसलिए \(2^4=16\) उपसमुच्चय होंगे।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{a,b,c,d,e\}\), तो (\mathcal{P}(A)) के कितने तत्वों में (a) होगा लेकिन (b) और (c) दोनों नहीं होंगे?
If \(A=\{a,b,c,d,e\}\), how many elements of (\mathcal{P}(A)) contain (a) but do not contain both (b) and (c)?
#sets
#power-set
#restricted-subsets
#counting
A (12)
B (16)
C (24)
D (32)
Explanation opens after your attempt
Step 1
Concept
(a) is fixed and (d,e) are free. For (b,c), remove the one case where both are chosen, so the count is \(3\times 2^2=12\).
Step 2
Why this answer is correct
The correct answer is A. (12). (a) is fixed and (d,e) are free. For (b,c), remove the one case where both are chosen, so the count is \(3\times 2^2=12\).
Step 3
Exam Tip
(a) निश्चित है और (d,e) स्वतंत्र हैं। (b,c) के लिए कुल (4) विकल्पों में से दोनों साथ वाला विकल्प हटेगा, इसलिए \(3\times 2^2=12\)।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4\}\), तो (\mathcal{P}(A)) के कितने तत्वों में (1) नहीं होगा और (4) होगा?
If \(A=\{1,2,3,4\}\), how many elements of (\mathcal{P}(A)) do not contain (1) and contain (4)?
#sets
#power-set
#restricted-subsets
A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(4) is fixed and (1) is excluded. The remaining (2,3) give \(2^2=4\) choices.
Step 2
Why this answer is correct
The correct answer is C. (4). (4) is fixed and (1) is excluded. The remaining (2,3) give \(2^2=4\) choices.
Step 3
Exam Tip
(4) निश्चित है और (1) नहीं लेना है। शेष (2,3) के लिए \(2^2=4\) विकल्प हैं।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5\}\), तो (\mathcal{P}(A)) के कितने तत्वों में (2) और (5) दोनों होंगे लेकिन (1) नहीं होगा?
If \(A=\{1,2,3,4,5\}\), how many elements of (\mathcal{P}(A)) contain both (2) and (5) but not (1)?
#sets
#power-set
#restricted-subsets
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(2,5) are fixed and (1) is forbidden. The remaining (3,4) are free, so there are \(2^2=4\) subsets.
Step 2
Why this answer is correct
The correct answer is B. (4). (2,5) are fixed and (1) is forbidden. The remaining (3,4) are free, so there are \(2^2=4\) subsets.
Step 3
Exam Tip
(2,5) निश्चित हैं और (1) निषिद्ध है। शेष (3,4) स्वतंत्र हैं, इसलिए \(2^2=4\) उपसमुच्चय होंगे।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5,6\}\) है, तो (A) के ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (1), (2) और (3) में से कोई भी न हो?
If \(A=\{1,2,3,4,5,6\}\), how many subsets of (A) contain none of (1), (2), and (3)?
#sets
#power set
#restricted subsets
#class 11
A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
After excluding (1,2,3), the elements (4,5,6) remain. Their subsets are \(2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). After excluding (1,2,3), the elements (4,5,6) remain. Their subsets are \(2^3=8\).
Step 3
Exam Tip
(1,2,3) हटाने पर (4,5,6) बचते हैं। इनके \(2^3=8\) उपसमुच्चय होंगे।
Login to save your score, XP, coins and progress. Login
यदि (A) में (5) तत्व हैं, तो (A) के ऐसे उपसमुच्चयों की संख्या कितनी होगी जिनमें दो निश्चित तत्व न हों?
If (A) has (5) elements, how many subsets of (A) do not contain two fixed elements?
#sets
#power set
#restricted subsets
#class 11
A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
After excluding two fixed elements, (3) elements remain. Their subsets are \(2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). After excluding two fixed elements, (3) elements remain. Their subsets are \(2^3=8\).
Step 3
Exam Tip
दो निश्चित तत्व हटाने पर (3) तत्व बचते हैं। इनके उपसमुच्चय \(2^3=8\) होंगे।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5\}\) है, तो (A) के ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (1) या (2) में से कोई भी न हो?
If \(A=\{1,2,3,4,5\}\), how many subsets of (A) contain neither (1) nor (2)?
#sets
#power set
#restricted subsets
#class 11
A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
After excluding (1) and (2), the elements (3,4,5) remain. Their subsets are \(2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). After excluding (1) and (2), the elements (3,4,5) remain. Their subsets are \(2^3=8\).
Step 3
Exam Tip
(1) और (2) को हटाने के बाद (3,4,5) बचते हैं। इनके \(2^3=8\) उपसमुच्चय होंगे।
Login to save your score, XP, coins and progress. Login
यदि \(A={X:X\subseteq{1,2,3,4},{1,4}\subseteq X\) और \(2\notin X}\) है तो (A) के बराबर कौन सा समुच्चय है?
If \(A={X:X\subseteq{1,2,3,4},{1,4}\subseteq X\) and \(2\notin X}\), which set is equal to (A)?
#sets
#equal_sets
#restricted_subsets
A ({{1,4},{1,3,4}})
B ({{1,2,4},{1,3,4}})
C ({{1,4},{2,4},{1,2,3,4}})
D ({{1},{4},{1,4}})
Explanation opens after your attempt
Correct Answer
A. ({{1,4},{1,3,4}})
Step 1
Concept
Every (X) must contain (1) and (4), and must not contain (2), so only (3) is optional. In such questions, fix required and forbidden elements first.
Step 2
Why this answer is correct
The correct answer is A. ({{1,4},{1,3,4}}). Every (X) must contain (1) and (4), and must not contain (2), so only (3) is optional. In such questions, fix required and forbidden elements first.
Step 3
Exam Tip
हर (X) में (1) और (4) होना चाहिए तथा (2) नहीं होना चाहिए, इसलिए केवल (3) वैकल्पिक है। ऐसे प्रश्नों में अनिवार्य और निषिद्ध अवयव पहले तय करें।
Login to save your score, XP, coins and progress. Login
