यदि \(A={x:x\in\mathbb{Z}\) और \(x^2-4x+3=0}\) तथा \(B=\{1,3\}\) हैं तो सही संबंध कौन सा है?
If \(A={x:x\in\mathbb{Z}\) and \(x^2-4x+3=0}\) and \(B=\{1,3\}\), which relation is correct?
#sets
#equal_sets
#quadratic_roots
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A (A=B)
B (A) (B) का उचित उपसमुच्चय है / (A) is a proper subset of (B)
C (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The equation has roots (1) and (3), so both sets have the same elements. In equal sets order is not considered.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The equation has roots (1) and (3), so both sets have the same elements. In equal sets order is not considered.
Step 3
Exam Tip
समीकरण के हल (1) और (3) हैं इसलिए दोनों समुच्चयों में वही अवयव हैं। बराबर समुच्चय में क्रम नहीं देखा जाता।
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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
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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।
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यदि \(A=\{1,2,{3,4}\}\) है तो निम्न में से कौन (A) का उपसमुच्चय है?
If \(A=\{1,2,{3,4}\}\), which of the following is a subset of (A)?
#sets
#subsets
#nested_sets
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A ({1,3})
B ({2,{3,4}})
C ({{1,2},3})
D ({4,{3}})
Explanation opens after your attempt
Correct Answer
B. ({2,{3,4}})
Step 1
Concept
Both (2) and ({3,4}) are elements of (A). Changing braces can change the element.
Step 2
Why this answer is correct
The correct answer is B. ({2,{3,4}}). Both (2) and ({3,4}) are elements of (A). Changing braces can change the element.
Step 3
Exam Tip
(2) और ({3,4}) दोनों (A) के अवयव हैं। कोष्ठक बदलने से अवयव बदल सकता है।
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यदि (P(A)) में (64) अवयव हैं तो (A) के उचित उपसमुच्चयों की संख्या क्या होगी?
If (P(A)) has (64) elements, what is the number of proper subsets of (A)?
#sets
#power_set
#proper_subsets
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A (31)
B (32)
C (63)
D (64)
Explanation opens after your attempt
Step 1
Concept
From \(2^n=64\), (n=6), and proper subsets are \(2^6-1=63\). Keep the formulas for power set and proper subsets separate.
Step 2
Why this answer is correct
The correct answer is C. (63). From \(2^n=64\), (n=6), and proper subsets are \(2^6-1=63\). Keep the formulas for power set and proper subsets separate.
Step 3
Exam Tip
\(2^n=64\) से (n=6) है और उचित उपसमुच्चय \(2^6-1=63\) होंगे। पावर समुच्चय और उचित उपसमुच्चय के सूत्र अलग रखें।
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यदि \(A={x:x\) (42) का अभाज्य भाजक है(}) और \(B=\{2,3,7\}\) हैं तो कौन सा कथन सही है?
If \(A={x:x\) is a prime divisor of (42)(}) and \(B=\{2,3,7\}\), which statement is correct?
#sets
#equal_sets
#prime_divisors
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A (A=B)
B \(A=\{1,2,3,6,7,14,21,42\}\)
C (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The prime divisors of (42) are (2,3,7). Understand the difference between all divisors and prime divisors.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The prime divisors of (42) are (2,3,7). Understand the difference between all divisors and prime divisors.
Step 3
Exam Tip
(42) के अभाज्य भाजक (2,3,7) हैं। सभी भाजकों और अभाज्य भाजकों में अंतर समझें।
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यदि \(A={x:x\in\mathbb{N}\) और \(x\mid 18}\) तथा \(B=\{1,2,3,6,9,18\}\) हैं तो सही विकल्प चुनिए।
If \(A={x:x\in\mathbb{N}\) and \(x\mid 18}\) and \(B=\{1,2,3,6,9,18\}\), choose the correct option.
#sets
#equal_sets
#divisibility
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A (A=B)
B (A) में केवल अभाज्य भाजक हैं / (A) contains only prime divisors
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(18\notin A\)
Explanation opens after your attempt
Step 1
Concept
\(x\mid 18\) means (x) divides (18). A number itself is also its positive divisor.
Step 2
Why this answer is correct
The correct answer is A. (A=B). \(x\mid 18\) means (x) divides (18). A number itself is also its positive divisor.
Step 3
Exam Tip
\(x\mid 18\) का अर्थ है (x) (18) का भाजक है। संख्या स्वयं भी उसका धनात्मक भाजक होती है।
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यदि \(A=\{0,1,2,3\}\) है तो (A) के ऐसे उपसमुच्चयों की संख्या क्या है जिनमें (0) अवश्य हो?
If \(A=\{0,1,2,3\}\), how many subsets of (A) must contain (0)?
#sets
#subsets
#counting
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A (4)
B (6)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
Fixing (0), the remaining three elements are optional, so there are \(2^3=8\) subsets. For a fixed element, count choices for the remaining elements.
Step 2
Why this answer is correct
The correct answer is C. (8). Fixing (0), the remaining three elements are optional, so there are \(2^3=8\) subsets. For a fixed element, count choices for the remaining elements.
Step 3
Exam Tip
(0) को निश्चित रखने पर बाकी तीन अवयव स्वतंत्र हैं इसलिए \(2^3=8\) उपसमुच्चय मिलते हैं। निश्चित अवयव को चुनकर बाकी पर गिनती करें।
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यदि \(A=\{a,b,c,d,e\}\) है तो (A) के ऐसे उपसमुच्चयों की संख्या क्या है जिनमें (a) न हो?
If \(A=\{a,b,c,d,e\}\), how many subsets of (A) do not contain (a)?
#sets
#subsets
#counting_without_element
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A (8)
B (16)
C (24)
D (31)
Explanation opens after your attempt
Step 1
Concept
After excluding (a), four elements remain and they form \(2^4=16\) subsets. Remove the forbidden element first.
Step 2
Why this answer is correct
The correct answer is B. (16). After excluding (a), four elements remain and they form \(2^4=16\) subsets. Remove the forbidden element first.
Step 3
Exam Tip
(a) हटाने के बाद चार अवयव बचते हैं और उनसे \(2^4=16\) उपसमुच्चय बनते हैं। निषिद्ध अवयव को पहले बाहर करें।
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यदि \(A={x:x\in\mathbb{Z}\) और \(-3\leq x<2}\) तो (A) के बराबर कौन सा समुच्चय है?
If \(A={x:x\in\mathbb{Z}\) and \(-3\leq x<2}\), which set is equal to (A)?
#sets
#equal_sets
#integer_interval
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A ({-3,-2,-1,0,1})
B ({-2,-1,0,1,2})
C ({-3,-2,-1,0,1,2})
D ({-2,-1,0,1})
Explanation opens after your attempt
Correct Answer
A. ({-3,-2,-1,0,1})
Step 1
Concept
(-3) is included and (2) is not included. Read open and closed ends of inequalities carefully.
Step 2
Why this answer is correct
The correct answer is A. ({-3,-2,-1,0,1}). (-3) is included and (2) is not included. Read open and closed ends of inequalities carefully.
Step 3
Exam Tip
(-3) शामिल है और (2) शामिल नहीं है। असमानता में खुले और बंद सिरों को ध्यान से पढ़ें।
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यदि \(A\subseteq B\), \(B\subseteq C\), और \(A\not=C\) है तो कौन सा कथन हमेशा सत्य है?
If \(A\subseteq B\), \(B\subseteq C\), and \(A\not=C\), which statement is always true?
#sets
#subset_transitivity
#proper_subset
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A \(A\subset C\) उचित रूप से / (A) is a proper subset of (C)
B (B=C) अवश्य / (B=C) necessarily
C (A=B) अवश्य / (A=B) necessarily
D \(C\subset A\)
Explanation opens after your attempt
Correct Answer
A. \(A\subset C\) उचित रूप से / (A) is a proper subset of (C)
Step 1
Concept
By transitivity \(A\subseteq C\), and since \(A\ne C\), (A) is a proper subset. The middle set may or may not be equal.
Step 2
Why this answer is correct
The correct answer is A. \(A\subset C\) उचित रूप से / (A) is a proper subset of (C). By transitivity \(A\subseteq C\), and since \(A\ne C\), (A) is a proper subset. The middle set may or may not be equal.
Step 3
Exam Tip
ट्रांजिटिव नियम से \(A\subseteq C\) और \(A\not=C\) होने से (A) उचित उपसमुच्चय है। बीच वाला समुच्चय बराबर भी हो सकता है।
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यदि \(A={x:x\) (25) से छोटे पूर्ण वर्ग हैं और (x>0}) तो कौन सा विकल्प (A) के बराबर है?
If \(A={x:x\) is a positive perfect square less than (25)(}), which option is equal to (A)?
#sets
#equal_sets
#perfect_squares
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A ({1,4,9,16})
B ({0,1,4,9,16})
C ({1,4,9,16,25})
D ({2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({1,4,9,16})
Step 1
Concept
The positive perfect squares are (1,4,9,16), and (25) is not included. Apply every condition together.
Step 2
Why this answer is correct
The correct answer is A. ({1,4,9,16}). The positive perfect squares are (1,4,9,16), and (25) is not included. Apply every condition together.
Step 3
Exam Tip
धनात्मक पूर्ण वर्ग (1,4,9,16) हैं और (25) सीमा में शामिल नहीं है। हर शर्त को साथ में लागू करें।
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यदि \(A=\{p,q,r,s\}\) है तो (A) के दो अवयवों वाले उपसमुच्चयों की संख्या क्या है?
If \(A=\{p,q,r,s\}\), how many subsets of (A) have exactly two elements?
#sets
#subsets
#combinations
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A (4)
B (6)
C (8)
D (12)
Explanation opens after your attempt
Step 1
Concept
The number of ways to choose two elements is \(\binom{4}{2}=6\). Order is not counted in subsets.
Step 2
Why this answer is correct
The correct answer is B. (6). The number of ways to choose two elements is \(\binom{4}{2}=6\). Order is not counted in subsets.
Step 3
Exam Tip
दो अवयव चुनने के तरीके \(\binom{4}{2}=6\) हैं। उपसमुच्चय में क्रम नहीं गिना जाता।
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यदि \(A={\varnothing,{\varnothing},1}\) है तो निम्न में से कौन (A) का उपसमुच्चय है?
If \(A={\varnothing,{\varnothing},1}\), which of the following is a subset of (A)?
#sets
#empty_set
#subset_test
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A \({\varnothing,1}\)
B ({0,1})
C \({{{\varnothing}}}\)
D \({2,\varnothing}\)
Explanation opens after your attempt
Correct Answer
A. \({\varnothing,1}\)
Step 1
Concept
Both \(\varnothing\) and (1) are elements of (A), so \({\varnothing,1}\) is a subset. (0) and \(\varnothing\) are different.
Step 2
Why this answer is correct
The correct answer is A. \({\varnothing,1}\). Both \(\varnothing\) and (1) are elements of (A), so \({\varnothing,1}\) is a subset. (0) and \(\varnothing\) are different.
Step 3
Exam Tip
\(\varnothing\) और (1) दोनों (A) के अवयव हैं इसलिए \({\varnothing,1}\) उपसमुच्चय है। (0) और \(\varnothing\) अलग हैं।
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यदि \(A={x:x\in\mathbb{N}\) और (x) (16) का गुणनखंड है पर (x) सम नहीं है(}) तो (A) क्या है?
If \(A={x:x\in\mathbb{N}\) and (x) is a factor of (16) but (x) is not even(}), what is (A)?
#sets
#set_builder
#odd_factor
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A ({1})
B ({2,4,8,16})
C ({1,2,4,8,16})
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Among the factors of (16), only (1) is odd. In questions with a negative condition, pay attention to the excluded elements.
Step 2
Why this answer is correct
The correct answer is A. ({1}). Among the factors of (16), only (1) is odd. In questions with a negative condition, pay attention to the excluded elements.
Step 3
Exam Tip
(16) के भाजकों में केवल (1) विषम है। नकारात्मक शर्त वाले प्रश्न में हटाए गए अवयवों पर ध्यान दें।
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यदि \(A=\{1,2,3,4,5\}\) है तो (A) के तीन या अधिक अवयवों वाले उपसमुच्चयों की संख्या क्या है?
If \(A=\{1,2,3,4,5\}\), how many subsets of (A) have three or more elements?
#sets
#subsets
#combinations
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A (10)
B (16)
C (20)
D (26)
Explanation opens after your attempt
Step 1
Concept
The number is \(\binom{5}{3}+\binom{5}{4}+\binom{5}{5}=16\). For size based counting, add the combinations.
Step 2
Why this answer is correct
The correct answer is B. (16). The number is \(\binom{5}{3}+\binom{5}{4}+\binom{5}{5}=16\). For size based counting, add the combinations.
Step 3
Exam Tip
तीन या अधिक अवयवों की संख्या \(\binom{5}{3}+\binom{5}{4}+\binom{5}{5}=16\) है। आकार आधारित गिनती में संयोजन जोड़ें।
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यदि \(A={x:x\) अंग्रेजी शब्द (LEVEL) के अलग अक्षर हैं(}) और \(B=\{L,E,V\}\) हैं तो सही निष्कर्ष क्या है?
If \(A={x:x\) is a distinct letter of the English word (LEVEL)(}) and \(B=\{L,E,V\}\), what is the correct conclusion?
#sets
#equal_sets
#repeated_letters
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A (A=B)
B \(A\ne B\) क्योंकि (L) दो बार आता है / \(A\ne B\) because (L) occurs twice
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{L,E,V,E,L\}\) और यह अलग है / \(A=\{L,E,V,E,L\}\) and it is different
Explanation opens after your attempt
Step 1
Concept
Repetition is not counted in a set, so the distinct letters are (L,E,V). In letter based questions count only distinct elements.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Repetition is not counted in a set, so the distinct letters are (L,E,V). In letter based questions count only distinct elements.
Step 3
Exam Tip
समुच्चय में दोहराव नहीं गिना जाता इसलिए अलग अक्षर (L,E,V) हैं। अक्षरों वाले प्रश्न में केवल अलग अवयव गिनें।
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यदि \(A={x:x\in\mathbb{Z}\) और \(x^2\leq 4}\) है तो (A) का कौन सा उपसमुच्चय उचित नहीं है?
If \(A={x:x\in\mathbb{Z}\) and \(x^2\leq 4}\), which subset of (A) is not proper?
#sets
#proper_subset
#integer_squares
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A ({-2,-1,0,1,2})
B ({-1,0,1})
C ({-2,2})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({-2,-1,0,1,2})
Step 1
Concept
Here \(A=\{-2,-1,0,1,2\}\), so the same set is a subset but not proper. A proper subset is not the whole set.
Step 2
Why this answer is correct
The correct answer is A. ({-2,-1,0,1,2}). Here \(A=\{-2,-1,0,1,2\}\), so the same set is a subset but not proper. A proper subset is not the whole set.
Step 3
Exam Tip
\(A=\{-2,-1,0,1,2\}\) है इसलिए वही समुच्चय उपसमुच्चय है पर उचित नहीं है। उचित उपसमुच्चय पूरा समुच्चय नहीं होता।
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यदि \(A=\{2,4,6,8\}\) और \(B={x:x=2n\) जहाँ \(n\in\mathbb{N}\) और \(1\leq n\leq 4}\) हैं तो कौन सा विकल्प सही है?
If \(A=\{2,4,6,8\}\) and \(B={x:x=2n\) where \(n\in\mathbb{N}\) and \(1\leq n\leq 4}\), which option is correct?
#sets
#equal_sets
#parametric_set
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A (A=B)
B \(A\subset B\) पर \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B=\{1,2,3,4\}\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Putting (n=1,2,3,4) gives (x=2,4,6,8). In parameter based sets, first find the values.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Putting (n=1,2,3,4) gives (x=2,4,6,8). In parameter based sets, first find the values.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (x=2,4,6,8) मिलता है। पैरामीटर वाले समुच्चय में पहले मान निकालें।
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यदि \(A=\{1,2,3\}\) और (B=P(A)) है तो निम्न में से कौन (B) का अवयव नहीं है?
If \(A=\{1,2,3\}\) and (B=P(A)), which of the following is not an element of (B)?
#sets
#power_set
#element_vs_subset
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A ({1,2})
B \(\varnothing\)
C ({3})
D (2)
Explanation opens after your attempt
Step 1
Concept
The elements of (P(A)) are subsets of (A), and (2) itself is not a subset. ({2}) and (2) are different.
Step 2
Why this answer is correct
The correct answer is D. (2). The elements of (P(A)) are subsets of (A), and (2) itself is not a subset. ({2}) and (2) are different.
Step 3
Exam Tip
(P(A)) के अवयव (A) के उपसमुच्चय होते हैं और (2) स्वयं उपसमुच्चय नहीं है। ({2}) और (2) अलग हैं।
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यदि \(A={x:x\in\mathbb{N}\) और (x<10}), \(B={x:x\) एक अंक की प्राकृतिक संख्या है(}) हैं तो क्या सत्य है?
If \(A={x:x\in\mathbb{N}\) and (x<10}), \(B={x:x\) is a one digit natural number(}), what is true?
#sets
#equal_sets
#natural_numbers
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A (A=B)
B (A) में (0) है और (B) में नहीं है / (A) contains (0) but (B) does not
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{0,1,2,3,4,5,6,7,8,9\}\)
Explanation opens after your attempt
Step 1
Concept
In Class (11), usually \(\mathbb{N}={1,2,3,\ldots}\), so both sets are (1) to (9). Read the given number system carefully.
Step 2
Why this answer is correct
The correct answer is A. (A=B). In Class (11), usually \(\mathbb{N}={1,2,3,\ldots}\), so both sets are (1) to (9). Read the given number system carefully.
Step 3
Exam Tip
कक्षा (11) में सामान्यतः \(\mathbb{N}={1,2,3,\ldots}\) लिया जाता है इसलिए दोनों (1) से (9) तक हैं। संकेत में दी गई संख्या पद्धति को ध्यान से देखें।
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यदि \(A={x:x\) (60) का धनात्मक भाजक है और (x) (15) का भाजक भी है(}) तो (A) कौन सा है?
If \(A={x:x\) is a positive divisor of (60) and also a divisor of (15)(}), what is (A)?
#sets
#set_builder
#common_divisors
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A ({1,3,5,15})
B ({2,4,6,10,12,20,30,60})
C ({15,30,45,60})
D ({3,5})
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,15})
Step 1
Concept
The common positive divisors of both numbers are (1,3,5,15). For an and condition, choose common elements.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,15}). The common positive divisors of both numbers are (1,3,5,15). For an and condition, choose common elements.
Step 3
Exam Tip
दोनों संख्याओं के सामान्य धनात्मक भाजक (1,3,5,15) हैं। और की शर्त में समान अवयव चुनें।
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यदि \(A=\{a,b\}\) है तो (P(A)) के बराबर कौन सा समुच्चय है?
If \(A=\{a,b\}\), which set is equal to (P(A))?
#sets
#power_set
#equal_sets
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A \({\varnothing,{a},{b},{a,b}}\)
B ({a,b,{a,b}})
C ({{a},{b}})
D \({\varnothing,a,b}\)
Explanation opens after your attempt
Correct Answer
A. \({\varnothing,{a},{b},{a,b}}\)
Step 1
Concept
A power set lists all subsets as elements. It contains ({a}), not (a) as the singleton subset.
Step 2
Why this answer is correct
The correct answer is A. \({\varnothing,{a},{b},{a,b}}\). A power set lists all subsets as elements. It contains ({a}), not (a) as the singleton subset.
Step 3
Exam Tip
पावर समुच्चय में सभी उपसमुच्चय अवयव के रूप में लिखे जाते हैं। (a) नहीं बल्कि ({a}) उसका अवयव होगा।
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यदि \(A={x:x\in\mathbb{Z}\) और \(|x|\leq 2}\) तथा \(B=\{-2,-1,0,1,2\}\) हैं तो कौन सा निष्कर्ष सही है?
If \(A={x:x\in\mathbb{Z}\) and \(|x|\leq 2}\) and \(B=\{-2,-1,0,1,2\}\), which conclusion is correct?
#sets
#equal_sets
#modulus
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A (A=B)
B \(A=\{0,1,2\}\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{-2,2\}\)
Explanation opens after your attempt
Step 1
Concept
The condition \(|x|\leq 2\) includes all integers from (-2) to (2). In modulus, check both positive and negative sides.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The condition \(|x|\leq 2\) includes all integers from (-2) to (2). In modulus, check both positive and negative sides.
Step 3
Exam Tip
\(|x|\leq 2\) में (-2) से (2) तक के सभी पूर्णांक आते हैं। मापांक में धन और ऋण दोनों पक्ष देखें।
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यदि \(A=\{1,2,3,4\}\) है तो (A) के ऐसे उपसमुच्चयों की संख्या क्या है जिनमें (1) हो और (4) न हो?
If \(A=\{1,2,3,4\}\), how many subsets of (A) contain (1) and do not contain (4)?
#sets
#subsets
#restricted_counting
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(1) is fixed and (4) is forbidden, so (2,3) are free. Hence \(2^2=4\) subsets are possible.
Step 2
Why this answer is correct
The correct answer is B. (4). (1) is fixed and (4) is forbidden, so (2,3) are free. Hence \(2^2=4\) subsets are possible.
Step 3
Exam Tip
(1) निश्चित और (4) निषिद्ध है इसलिए (2,3) स्वतंत्र हैं। अतः \(2^2=4\) उपसमुच्चय बनते हैं।
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यदि \(A={x:x\) (10) से छोटे सम अभाज्य हैं(}) तो कौन सा समुच्चय (A) के बराबर है?
If \(A={x:x\) is an even prime less than (10)(}), which set is equal to (A)?
#sets
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#even_prime
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A ({2})
B ({2,4,6,8})
C ({2,3,5,7})
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Only (2) is an even prime number. In combined conditions, both properties must hold together.
Step 2
Why this answer is correct
The correct answer is A. ({2}). Only (2) is an even prime number. In combined conditions, both properties must hold together.
Step 3
Exam Tip
केवल (2) ही सम अभाज्य संख्या है। संयुक्त शर्तों में दोनों गुण एक साथ चाहिए।
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यदि \(A=\{1,2,3\}\) और \(B=\{1,2,3,4,5\}\) हैं तो (B) के कितने उपसमुच्चय (A) के भी उपसमुच्चय हैं?
If \(A=\{1,2,3\}\) and \(B=\{1,2,3,4,5\}\), how many subsets of (B) are also subsets of (A)?
#sets
#subsets
#common_subsets
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A (3)
B (6)
C (8)
D (32)
Explanation opens after your attempt
Step 1
Concept
The subsets lying inside (A) are subsets of both, and their number is \(2^3=8\). Decide the common limit using the smaller set.
Step 2
Why this answer is correct
The correct answer is C. (8). The subsets lying inside (A) are subsets of both, and their number is \(2^3=8\). Decide the common limit using the smaller set.
Step 3
Exam Tip
जो उपसमुच्चय (A) के अंदर हैं वही दोनों के लिए उपसमुच्चय होंगे और उनकी संख्या \(2^3=8\) है। साझा सीमा को छोटे समुच्चय से तय करें।
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यदि \(A={x:x\in\mathbb{N}\) और \(x^2<50}\) तो (A) का कौन सा उपसमुच्चय नहीं है?
If \(A={x:x\in\mathbb{N}\) and \(x^2<50}\), which is not a subset of (A)?
#sets
#subset_test
#square_inequality
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A ({1,3,7})
B ({2,4,6})
C ({1,5,8})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
C. ({1,5,8})
Step 1
Concept
Here \(A=\{1,2,3,4,5,6,7\}\), and (8) is not in it. One outside element makes the subset statement false.
Step 2
Why this answer is correct
The correct answer is C. ({1,5,8}). Here \(A=\{1,2,3,4,5,6,7\}\), and (8) is not in it. One outside element makes the subset statement false.
Step 3
Exam Tip
\(A=\{1,2,3,4,5,6,7\}\) है और (8) इसमें नहीं है। एक बाहरी अवयव पूरा उपसमुच्चय कथन गलत कर देता है।
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यदि \(A={x:x\) (24) और (36) दोनों के अभाज्य भाजक हैं(}) तो (A) क्या है?
If \(A={x:x\) is a prime divisor of both (24) and (36)(}), what is (A)?
#sets
#equal_sets
#common_prime_divisors
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A ({2,3})
B ({2,3,5})
C ({1,2,3,6,12})
D ({6,12})
Explanation opens after your attempt
Correct Answer
A. ({2,3})
Step 1
Concept
The common prime divisors of both numbers are (2) and (3). Common divisors and common prime divisors can be different.
Step 2
Why this answer is correct
The correct answer is A. ({2,3}). The common prime divisors of both numbers are (2) and (3). Common divisors and common prime divisors can be different.
Step 3
Exam Tip
दोनों संख्याओं के सामान्य अभाज्य भाजक (2) और (3) हैं। सामान्य भाजक और सामान्य अभाज्य भाजक अलग हो सकते हैं।
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यदि \(A=\{1,2,{1,2}\}\) है तो (A) के कुल अवयव कितने हैं?
If \(A=\{1,2,{1,2}\}\), how many elements does (A) have?
#sets
#nested_sets
#cardinality
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Here (1), (2), and ({1,2}) are three distinct elements. A whole set can be an element of a larger set.
Step 2
Why this answer is correct
The correct answer is B. (3). Here (1), (2), and ({1,2}) are three distinct elements. A whole set can be an element of a larger set.
Step 3
Exam Tip
यहाँ (1), (2), और ({1,2}) तीन अलग अवयव हैं। पूरा समुच्चय भी किसी बड़े समुच्चय का अवयव हो सकता है।
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यदि \(A={x:x\in\mathbb{Z}\) और \(x^2=9}\) तथा \(B=\{-3,3,9\}\) हैं तो सही संबंध क्या है?
If \(A={x:x\in\mathbb{Z}\) and \(x^2=9}\) and \(B=\{-3,3,9\}\), what is the correct relation?
#sets
#proper_subset
#integer_roots
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A (A=B)
B (A) (B) का उचित उपसमुच्चय है / (A) is a proper subset of (B)
C (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A)
D \(A=\{9\}\)
Explanation opens after your attempt
Correct Answer
B. (A) (B) का उचित उपसमुच्चय है / (A) is a proper subset of (B)
Step 1
Concept
Here \(A=\{-3,3\}\), and (B) has the extra element (9). Distinguish roots of an equation from constants in it.
Step 2
Why this answer is correct
The correct answer is B. (A) (B) का उचित उपसमुच्चय है / (A) is a proper subset of (B). Here \(A=\{-3,3\}\), and (B) has the extra element (9). Distinguish roots of an equation from constants in it.
Step 3
Exam Tip
\(A=\{-3,3\}\) है और (B) में अतिरिक्त (9) है। समीकरण के हल और समीकरण में आए स्थिरांक को अलग समझें।
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यदि \(A={x:x\) (100) से छोटे (25) के धनात्मक गुणज हैं(}) तो (A) के उपसमुच्चयों की संख्या क्या है?
If \(A={x:x\) is a positive multiple of (25) less than (100)(}), how many subsets does (A) have?
#sets
#subsets
#multiples
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A (4)
B (6)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(A=\{25,50,75\}\) has (3) elements, so it has \(2^3=8\) subsets. The boundary (100) is not included.
Step 2
Why this answer is correct
The correct answer is C. (8). \(A=\{25,50,75\}\) has (3) elements, so it has \(2^3=8\) subsets. The boundary (100) is not included.
Step 3
Exam Tip
\(A=\{25,50,75\}\) में (3) अवयव हैं इसलिए \(2^3=8\) उपसमुच्चय होंगे। सीमा में (100) शामिल नहीं है।
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यदि \(A={x:x\) \(x^2-1=0\) का पूर्णांक हल है(}) और \(B={x:x\in\mathbb{Z}\) तथा (-2<x<2) और \(x\ne0}\) हैं तो क्या सत्य है?
If \(A={x:x\) is an integer solution of \(x^2-1=0\)(}) and \(B={x:x\in\mathbb{Z}\) with (-2<x<2) and \(x\ne0}\), what is true?
#sets
#equal_sets
#multiple_descriptions
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A (A=B)
B \(A=\{1\}\) और \(B=\{-1,1\}\) / \(A=\{1\}\) and \(B=\{-1,1\}\)
C \(B=\varnothing\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Both sets contain only (-1) and (1). Different descriptions can give equal sets.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Both sets contain only (-1) and (1). Different descriptions can give equal sets.
Step 3
Exam Tip
दोनों समुच्चयों में (-1) और (1) ही आते हैं। अलग वर्णन बराबर समुच्चय दे सकते हैं।
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यदि \(A=\{1,2,3,4,5,6\}\) और \(B=\{2,3,5\}\) हैं तो (B) के तीन अवयवों वाले उपसमुच्चय के बारे में क्या सही है?
If \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,3,5\}\), what is true about the three element subset of (B)?
#sets
#subsets
#reasoning
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A वह (B) ही है और (A) का उपसमुच्चय भी है / It is (B) itself and also a subset of (A)
B वह (A) के बराबर है / It is equal to (A)
C ऐसा कोई उपसमुच्चय नहीं है / No such subset exists
D वह उचित उपसमुच्चय नहीं हो सकता किसी भी समुच्चय का / It cannot be a proper subset of any set
Explanation opens after your attempt
Correct Answer
A. वह (B) ही है और (A) का उपसमुच्चय भी है / It is (B) itself and also a subset of (A)
Step 1
Concept
The only three element subset of (B) is (B) itself. Since \(B\subset A\), it is also a subset of (A).
Step 2
Why this answer is correct
The correct answer is A. वह (B) ही है और (A) का उपसमुच्चय भी है / It is (B) itself and also a subset of (A). The only three element subset of (B) is (B) itself. Since \(B\subset A\), it is also a subset of (A).
Step 3
Exam Tip
तीन अवयवों वाला (B) का केवल उपसमुच्चय (B) स्वयं है। क्योंकि \(B\subset A\) है इसलिए यह (A) का उपसमुच्चय भी है।
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यदि \(A={x:x\) (12) से छोटे (2) या (3) के धनात्मक गुणज हैं(}) तो (A) कौन सा है?
If \(A={x:x\) is a positive multiple of (2) or (3) less than (12)(}), what is (A)?
#sets
#set_builder
#multiples
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A ({2,3,4,6,8,9,10})
B ({6})
C ({2,4,6,8,10,12})
D ({3,6,9,12})
Explanation opens after your attempt
Correct Answer
A. ({2,3,4,6,8,9,10})
Step 1
Concept
Combining multiples of (2) or (3) gives (2,3,4,6,8,9,10). For an or condition, think like a union.
Step 2
Why this answer is correct
The correct answer is A. ({2,3,4,6,8,9,10}). Combining multiples of (2) or (3) gives (2,3,4,6,8,9,10). For an or condition, think like a union.
Step 3
Exam Tip
(2) या (3) के गुणजों को मिलाने पर (2,3,4,6,8,9,10) मिलते हैं। या की शर्त में संघ जैसी सोच रखें।
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यदि \(A=\{1,2,3\}\), \(B=\{1,2,3,4\}\), और \(C=\{1,2,3,4\}\) हैं तो कौन सा कथन सत्य है?
If \(A=\{1,2,3\}\), \(B=\{1,2,3,4\}\), and \(C=\{1,2,3,4\}\), which statement is true?
#sets
#equal_sets
#proper_subset
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A (B=C) और (A) (B) का उचित उपसमुच्चय है / (B=C) and (A) is a proper subset of (B)
B (A=B=C)
C (C) (A) का उचित उपसमुच्चय है / (C) is a proper subset of (A)
D \(A\not\subset C\)
Explanation opens after your attempt
Correct Answer
A. (B=C) और (A) (B) का उचित उपसमुच्चय है / (B=C) and (A) is a proper subset of (B)
Step 1
Concept
(B) and (C) have the same elements, and (A) does not contain (4). Check equality and proper subset separately.
Step 2
Why this answer is correct
The correct answer is A. (B=C) और (A) (B) का उचित उपसमुच्चय है / (B=C) and (A) is a proper subset of (B). (B) and (C) have the same elements, and (A) does not contain (4). Check equality and proper subset separately.
Step 3
Exam Tip
(B) और (C) में वही अवयव हैं और (A) में (4) नहीं है। समानता और उचित उपसमुच्चय दोनों अलग-अलग जांचें।
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यदि किसी समुच्चय के (15) उचित उपसमुच्चय हैं तो उसके पावर समुच्चय में कितने अवयव होंगे?
If a set has (15) proper subsets, how many elements are in its power set?
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#proper_subsets
#power_set
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A (15)
B (16)
C (30)
D (31)
Explanation opens after your attempt
Step 1
Concept
From proper subsets \(2^n-1=15\), we get \(2^n=16\). A power set has \(2^n\) elements.
Step 2
Why this answer is correct
The correct answer is B. (16). From proper subsets \(2^n-1=15\), we get \(2^n=16\). A power set has \(2^n\) elements.
Step 3
Exam Tip
उचित उपसमुच्चय \(2^n-1=15\) से \(2^n=16\) मिलता है। पावर समुच्चय में कुल \(2^n\) अवयव होते हैं।
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यदि \(A={x:x\in\mathbb{N}\) और \(x\leq 6}\) तथा \(B={x:x\) (6) का धनात्मक भाजक है(}) हैं तो संबंध क्या है?
If \(A={x:x\in\mathbb{N}\) and \(x\leq 6}\) and \(B={x:x\) is a positive divisor of (6)(}), what is the relation?
#sets
#proper_subset
#divisors
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A (A=B)
B (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A)
C (A) (B) का उचित उपसमुच्चय है / (A) is a proper subset of (B)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A)
Step 1
Concept
\(A=\{1,2,3,4,5,6\}\) and \(B=\{1,2,3,6\}\). All elements of (B) are in (A), but (A) is larger.
Step 2
Why this answer is correct
The correct answer is B. (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A). \(A=\{1,2,3,4,5,6\}\) and \(B=\{1,2,3,6\}\). All elements of (B) are in (A), but (A) is larger.
Step 3
Exam Tip
\(A=\{1,2,3,4,5,6\}\) और \(B=\{1,2,3,6\}\) है। (B) के सभी अवयव (A) में हैं पर (A) बड़ा है।
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यदि \(A=\{{1},{2},{1,2}\}\) है तो (A) के अवयवों में कौन सा शामिल है?
If \(A=\{{1},{2},{1,2}\}\), which one is included as an element of (A)?
#sets
#nested_sets
#elements
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A ({1,2})
B (1)
C (2)
D ({{1},{2}})
Explanation opens after your attempt
Correct Answer
A. ({1,2})
Step 1
Concept
The elements of (A) are written as sets, and ({1,2}) is one of them. The inner (1) and (2) are not directly elements of (A).
Step 2
Why this answer is correct
The correct answer is A. ({1,2}). The elements of (A) are written as sets, and ({1,2}) is one of them. The inner (1) and (2) are not directly elements of (A).
Step 3
Exam Tip
(A) में अवयव समुच्चय के रूप में लिखे हैं और ({1,2}) उनमें से एक है। अंदर के (1) और (2) सीधे (A) के अवयव नहीं हैं।
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यदि \(A={x:x\) (40) का धनात्मक भाजक है और \(x\leq 10}\) तो कौन सा विकल्प (A) के बराबर है?
If \(A={x:x\) is a positive divisor of (40) and \(x\leq 10}\), which option is equal to (A)?
#sets
#equal_sets
#divisors
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A ({1,2,4,5,8,10})
B ({1,2,4,5,8,10,20,40})
C ({2,4,5,8})
D ({10,20,40})
Explanation opens after your attempt
Correct Answer
A. ({1,2,4,5,8,10})
Step 1
Concept
The positive divisors of (40) up to (10) are (1,2,4,5,8,10). Apply the boundary condition to the divisor list.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4,5,8,10}). The positive divisors of (40) up to (10) are (1,2,4,5,8,10). Apply the boundary condition to the divisor list.
Step 3
Exam Tip
(40) के (10) तक के धनात्मक भाजक (1,2,4,5,8,10) हैं। सीमा की शर्त को भाजक सूची पर लगाएं।
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यदि \(A=\{1,2,3,4\}\) है तो (A) के ऐसे उपसमुच्चयों की संख्या क्या है जिनमें (2) और (3) दोनों हों?
If \(A=\{1,2,3,4\}\), how many subsets of (A) contain both (2) and (3)?
#sets
#subsets
#restricted_counting
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(2) and (3) are fixed, while (1,4) are optional, so \(2^2=4\) subsets are obtained. Include fixed elements first.
Step 2
Why this answer is correct
The correct answer is B. (4). (2) and (3) are fixed, while (1,4) are optional, so \(2^2=4\) subsets are obtained. Include fixed elements first.
Step 3
Exam Tip
(2) और (3) निश्चित हैं तथा (1,4) स्वतंत्र हैं इसलिए \(2^2=4\) उपसमुच्चय मिलते हैं। निश्चित अवयवों को पहले शामिल करें।
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यदि \(A={x:x\in\mathbb{Z}\) और \(x^2-2x=0}\) तथा \(B=\{0,2\}\) हैं तो क्या सत्य है?
If \(A={x:x\in\mathbb{Z}\) and \(x^2-2x=0}\) and \(B=\{0,2\}\), what is true?
#sets
#equal_sets
#zero_root
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A (A=B)
B \(A=\{2\}\)
C (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
(x-2 -2x=x(x-2)), so the roots are (0) and (2). Do not forget zero as a root.
Step 2
Why this answer is correct
The correct answer is A. (A=B). (x-2 -2x=x(x-2)), so the roots are (0) and (2). Do not forget zero as a root.
Step 3
Exam Tip
(x-2 -2x=x(x-2)) इसलिए हल (0) और (2) हैं। शून्य को हल मानने में गलती न करें।
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यदि \(A={x:x\) (1) से (20) तक की अभाज्य संख्याएं हैं(}) और \(B=\{2,3,5,7,11,13,17,19\}\) हैं तो निष्कर्ष क्या है?
If \(A={x:x\) is a prime number from (1) to (20)(}) and \(B=\{2,3,5,7,11,13,17,19\}\), what is the conclusion?
#sets
#equal_sets
#prime_numbers
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A (A=B)
B \(A\ne B\) क्योंकि (1) छूट गया / \(A\ne B\) because (1) is missing
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{1,2,3,5,7,11,13,17,19\}\)
Explanation opens after your attempt
Step 1
Concept
The number (1) is not prime, and the primes up to (20) are exactly those in (B). Remember the definition of a prime number.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The number (1) is not prime, and the primes up to (20) are exactly those in (B). Remember the definition of a prime number.
Step 3
Exam Tip
(1) अभाज्य नहीं है और (20) तक अभाज्य संख्याएं वही हैं जो (B) में हैं। अभाज्य संख्या की परिभाषा याद रखें।
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यदि (A) में (5) अवयव हैं तो (A) के ऐसे उपसमुच्चयों की संख्या क्या है जो (A) के बराबर नहीं हैं?
If (A) has (5) elements, how many subsets of (A) are not equal to (A)?
#sets
#proper_subsets
#counting
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A (16)
B (30)
C (31)
D (32)
Explanation opens after your attempt
Step 1
Concept
Subsets not equal to (A) are proper subsets, and their number is \(2^5-1=31\). Only the whole set is removed once.
Step 2
Why this answer is correct
The correct answer is C. (31). Subsets not equal to (A) are proper subsets, and their number is \(2^5-1=31\). Only the whole set is removed once.
Step 3
Exam Tip
बराबर नहीं होने वाले उपसमुच्चय ही उचित उपसमुच्चय हैं और उनकी संख्या \(2^5-1=31\) है। पूरा समुच्चय केवल एक बार हटता है।
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यदि \(A={x:x\in\mathbb{R}\) और \(x^2+1=0}\) है तो वास्तविक संख्याओं में (A) क्या है?
If \(A={x:x\in\mathbb{R}\) and \(x^2+1=0}\), what is (A) in real numbers?
#sets
#empty_set
#real_numbers
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A \(\varnothing\)
B ({1,-1})
C ({0})
D ({i,-i})
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
For no real (x), \(x^2+1=0\) is possible. The number system condition can change the answer.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). For no real (x), \(x^2+1=0\) is possible. The number system condition can change the answer.
Step 3
Exam Tip
किसी वास्तविक (x) के लिए \(x^2+1=0\) संभव नहीं है। संख्या पद्धति की शर्त उत्तर बदल सकती है।
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यदि \(A={x:x\) (30) से छोटे (5) के धनात्मक गुणज हैं(}) और \(B=\{5,10,15,20,25\}\) हैं तो संबंध क्या है?
If \(A={x:x\) is a positive multiple of (5) less than (30)(}) and \(B=\{5,10,15,20,25\}\), what is the relation?
#sets
#equal_sets
#multiples
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A (A=B)
B \(A=\{5,10,15,20,25,30\}\)
C (B) (A) का उचित उपसमुच्चय है / (B) is a proper subset of (A)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Multiples less than (30) do not include (30). Therefore (A) and (B) are equal.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Multiples less than (30) do not include (30). Therefore (A) and (B) are equal.
Step 3
Exam Tip
(30) से छोटे गुणजों में (30) शामिल नहीं होता। इसलिए (A) और (B) समान हैं।
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यदि \(A=\{{1,2},3,4\}\) है तो निम्न में से कौन (A) का उपसमुच्चय नहीं है?
If \(A=\{{1,2},3,4\}\), which of the following is not a subset of (A)?
#sets
#nested_sets
#subset_error
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A ({3,4})
B ({{1,2}})
C ({{1,2},4})
D ({1,2})
Explanation opens after your attempt
Correct Answer
D. ({1,2})
Step 1
Concept
In (A), ({1,2}) is one element, but (1) and (2) are not separate elements. So ({1,2}) is not a subset.
Step 2
Why this answer is correct
The correct answer is D. ({1,2}). In (A), ({1,2}) is one element, but (1) and (2) are not separate elements. So ({1,2}) is not a subset.
Step 3
Exam Tip
(A) में ({1,2}) एक अवयव है पर (1) और (2) अलग से अवयव नहीं हैं। इसलिए ({1,2}) उपसमुच्चय नहीं है।
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यदि \(A={x:x\in\mathbb{N}\) और \(x\leq 3}\) तो (P(A)) में कितने ऐसे अवयव हैं जो एक-अवयवी समुच्चय हैं?
If \(A={x:x\in\mathbb{N}\) and \(x\leq 3}\), how many elements of (P(A)) are singleton sets?
#sets
#power_set
#singleton_subsets
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A (1)
B (2)
C (3)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here \(A=\{1,2,3\}\), and it has (3) singleton subsets. These subsets become elements of the power set.
Step 2
Why this answer is correct
The correct answer is C. (3). Here \(A=\{1,2,3\}\), and it has (3) singleton subsets. These subsets become elements of the power set.
Step 3
Exam Tip
\(A=\{1,2,3\}\) है और इसके एक-अवयवी उपसमुच्चय (3) हैं। पावर समुच्चय में ये उपसमुच्चय अवयव बनते हैं।
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यदि \(A=\{2,3,4\}\), \(B=\{2,3,4,5\}\), और \(C=\{3,4\}\) हैं तो कौन सा कथन सही है?
If \(A=\{2,3,4\}\), \(B=\{2,3,4,5\}\), and \(C=\{3,4\}\), which statement is correct?
#sets
#subset_chain
#proper_subset
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A \(C\subset A\subset B\) उचित रूप से / \(C\subset A\subset B\) properly
B \(B\subset A\subset C\) उचित रूप से / \(B\subset A\subset C\) properly
C (A=C)
D \(C\not\subset B\)
Explanation opens after your attempt
Correct Answer
A. \(C\subset A\subset B\) उचित रूप से / \(C\subset A\subset B\) properly
Step 1
Concept
All elements of (C) are in (A), and all elements of (A) are in (B). Each step is proper because there is an extra element.
Step 2
Why this answer is correct
The correct answer is A. \(C\subset A\subset B\) उचित रूप से / \(C\subset A\subset B\) properly. All elements of (C) are in (A), and all elements of (A) are in (B). Each step is proper because there is an extra element.
Step 3
Exam Tip
(C) के सभी अवयव (A) में हैं और (A) के सभी अवयव (B) में हैं। प्रत्येक चरण में अतिरिक्त अवयव होने से संबंध उचित है।
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यदि \(A={x:x\in\mathbb{Z}\) और \(0<x^2<10}\) तो (A) के बराबर कौन सा समुच्चय है?
If \(A={x:x\in\mathbb{Z}\) and \(0<x^2<10}\), which set is equal to (A)?
#sets
#equal_sets
#square_inequality
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A ({-3,-2,-1,1,2,3})
B ({0,1,2,3})
C ({-2,-1,0,1,2})
D ({-4,-3,-2,-1,1,2,3,4})
Explanation opens after your attempt
Correct Answer
A. ({-3,-2,-1,1,2,3})
Step 1
Concept
\(x^2\) can be (1,4,9), so \(x=\pm1,\pm2,\pm3\). Since \(0<x^2\), (0) is not included.
Step 2
Why this answer is correct
The correct answer is A. ({-3,-2,-1,1,2,3}). \(x^2\) can be (1,4,9), so \(x=\pm1,\pm2,\pm3\). Since \(0<x^2\), (0) is not included.
Step 3
Exam Tip
\(x^2\) (1,4,9) हो सकता है इसलिए \(x=\pm1,\pm2,\pm3\) हैं। \(0<x^2\) होने से (0) शामिल नहीं है।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{1,3\}\) हैं तो (A) के कितने उपसमुच्चय (B) को उपसमुच्चय के रूप में रखते हैं?
If \(A=\{1,2,3,4\}\) and \(B=\{1,3\}\), how many subsets of (A) contain (B) as a subset?
#sets
#subsets
#contain_subset
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(1) and (3) are fixed, while (2,4) are optional, so there are \(2^2=4\) subsets. When a subset must be contained, fix its elements first.
Step 2
Why this answer is correct
The correct answer is B. (4). (1) and (3) are fixed, while (2,4) are optional, so there are \(2^2=4\) subsets. When a subset must be contained, fix its elements first.
Step 3
Exam Tip
(1) और (3) निश्चित हैं तथा (2,4) स्वतंत्र हैं इसलिए \(2^2=4\) उपसमुच्चय होंगे। किसी उपसमुच्चय को शामिल रखना हो तो उसके अवयव पहले तय करें।
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