यदि \(A={x:x\in \mathbb{Z}, x^2-4x+3=0}\) और \(B=\{1,3\}\), तो सही संबंध कौन सा है?
If \(A={x:x\in \mathbb{Z}, x^2-4x+3=0}\) and \(B=\{1,3\}\), which relation is correct?
#sets
#equal sets
#quadratic
#level 9
A (A=B)
B \(A\subset B\) लेकिन \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) लेकिन \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The equation gives ((x-1)(x-3)=0), so \(A=\{1,3\}\). Equal sets have the same elements, order is not important.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The equation gives ((x-1)(x-3)=0), so \(A=\{1,3\}\). Equal sets have the same elements, order is not important.
Step 3
Exam Tip
समीकरण से ((x-1)(x-3)=0), इसलिए \(A=\{1,3\}\)। बराबर समुच्चय में अवयव वही होते हैं, क्रम जरूरी नहीं।
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यदि \(A={x:x\in \mathbb{N}, x\le 4}\) और \(B={x:x\) 5 से छोटी प्राकृतिक संख्या है(}), तो कौन सा कथन सही है?
If \(A={x:x\in \mathbb{N}, x\le 4}\) and \(B={x:x\) is a natural number less than 5(}), which statement is correct?
#equal sets
#natural numbers
#inequality
A (A=B)
B \(A\subset B\) लेकिन \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) लेकिन \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Both descriptions give ({1,2,3,4}). Do not be confused by different forms of inequalities.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Both descriptions give ({1,2,3,4}). Do not be confused by different forms of inequalities.
Step 3
Exam Tip
दोनों वर्णन ({1,2,3,4}) देते हैं। असमानता के अलग रूपों से भ्रमित न हों।
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यदि \(A=\{a,b,c\}\) और \(B=\{b,c,d\}\), तो कौन सा कथन सही है?
If \(A=\{a,b,c\}\) and \(B=\{b,c,d\}\), which statement is correct?
#not subset
#equal sets
#comparison
A (A=B)
B \(A\subset B\)
C \(B\subset A\)
D न तो \(A\subseteq B\) और न ही \(B\subseteq A\) / Neither \(A\subseteq B\) nor \(B\subseteq A\)
Explanation opens after your attempt
Correct Answer
D. न तो \(A\subseteq B\) और न ही \(B\subseteq A\) / Neither \(A\subseteq B\) nor \(B\subseteq A\)
Step 1
Concept
(a) is not in (B), and (d) is not in (A). Hence neither set is a subset of the other.
Step 2
Why this answer is correct
The correct answer is D. न तो \(A\subseteq B\) और न ही \(B\subseteq A\) / Neither \(A\subseteq B\) nor \(B\subseteq A\). (a) is not in (B), and (d) is not in (A). Hence neither set is a subset of the other.
Step 3
Exam Tip
(a), (B) में नहीं है और (d), (A) में नहीं है। इसलिए कोई भी दूसरे का उपसमुच्चय नहीं है।
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यदि \(A={x:x\) 15 का धनात्मक भाजक है(}) और \(B=\{1,3,5,15\}\), तो कौन सा कथन सही है?
If \(A={x:x\) is a positive divisor of 15(}) and \(B=\{1,3,5,15\}\), which statement is correct?
#divisors
#equal sets
A (A=B)
B \(A\subset B\) लेकिन \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) लेकिन \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\{3,5\}\)
Explanation opens after your attempt
Step 1
Concept
The positive divisors of 15 are 1, 3, 5 and 15. Therefore the sets are equal.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive divisors of 15 are 1, 3, 5 and 15. Therefore the sets are equal.
Step 3
Exam Tip
15 के धनात्मक भाजक 1, 3, 5 और 15 हैं। इसलिए दोनों समुच्चय बराबर हैं।
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यदि \(A={x:x\in \mathbb{N}, 2x+1<10}\), तो (A) किसके बराबर है?
If \(A={x:x\in \mathbb{N}, 2x+1<10}\), what is (A) equal to?
#set builder
#inequality
#equal sets
A ({1,2,3,4})
B ({0,1,2,3,4})
C ({1,2,3,4,5})
D ({2,3,4})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4})
Step 1
Concept
From (2x+1<10), we get (x<4.5). The natural numbers are (1,2,3,4).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4}). From (2x+1<10), we get (x<4.5). The natural numbers are (1,2,3,4).
Step 3
Exam Tip
(2x+1<10) से (x<4.5) मिलता है। प्राकृतिक संख्याएं (1,2,3,4) हैं।
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यदि \(A=\{1,3,5,7\}\) और \(B={x:x\) 8 से छोटी धनात्मक विषम संख्या है(}), तो (A) और (B) कैसे संबंधित हैं?
If \(A=\{1,3,5,7\}\) and \(B={x:x\) is a positive odd number less than 8(}), how are (A) and (B) related?
#odd numbers
#equal sets
A (A=B)
B \(A\subset B\) लेकिन \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) लेकिन \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The positive odd numbers less than 8 are 1, 3, 5 and 7. The list and rule give the same set.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive odd numbers less than 8 are 1, 3, 5 and 7. The list and rule give the same set.
Step 3
Exam Tip
8 से छोटी धनात्मक विषम संख्याएं 1, 3, 5 और 7 हैं। सूची और नियम दोनों समान समुच्चय देते हैं।
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यदि \(A={x:x\) 6 का गुणज है और (x<20)(}) तथा \(B=\{6,12,18\}\), तो कौन सा संबंध सही है?
If \(A={x:x\) is a multiple of 6 and (x<20)(}) and \(B=\{6,12,18\}\), which relation is correct?
#multiples
#equal sets
#set builder
A (A=B)
B \(A\subset B\) लेकिन \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) लेकिन \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D (A) अनंत है / (A) is infinite
Explanation opens after your attempt
Step 1
Concept
The positive multiples of 6 less than 20 are 6, 12 and 18. So the two sets are equal.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive multiples of 6 less than 20 are 6, 12 and 18. So the two sets are equal.
Step 3
Exam Tip
20 से छोटे धनात्मक 6 के गुणज 6, 12 और 18 हैं। इसलिए दोनों समुच्चय समान हैं।
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यदि \(A=\{0,1\}\) और \(B={x:x^2=x}\), तो सही संबंध क्या है?
If \(A=\{0,1\}\) and \(B={x:x^2=x}\), what is the correct relation?
#equal sets
#solution set
#algebra
A (A=B)
B \(A\subset B\) लेकिन \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B=\{1\}\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
From \(x^2=x\), (x(x-1)=0), so (x=0) or (x=1). Both sets are equal.
Step 2
Why this answer is correct
The correct answer is A. (A=B). From \(x^2=x\), (x(x-1)=0), so (x=0) or (x=1). Both sets are equal.
Step 3
Exam Tip
\(x^2=x\) से (x(x-1)=0), इसलिए (x=0) या (x=1)। दोनों समुच्चय समान हैं।
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यदि \(A={x:x^2-5x+6=0}\) और \(B=\{2,3\}\), तो सही कथन कौन सा है?
If \(A={x:x^2-5x+6=0}\) and \(B=\{2,3\}\), which statement is correct?
#quadratic
#equal sets
#set builder
A (A=B)
B \(A=\{6\}\)
C \(B\subset A\) लेकिन \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The equation gives ((x-2)(x-3)=0), so the solutions are 2 and 3. The solution set equals (B).
Step 2
Why this answer is correct
The correct answer is A. (A=B). The equation gives ((x-2)(x-3)=0), so the solutions are 2 and 3. The solution set equals (B).
Step 3
Exam Tip
समीकरण ((x-2)(x-3)=0) देता है, इसलिए हल 2 और 3 हैं। हलों का समुच्चय (B) के बराबर है।
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यदि \(A={x:x\) 10 से छोटी अभाज्य संख्या है(}) और \(B=\{2,3,5,7\}\), तो कौन सा कथन सही है?
If \(A={x:x\) is a prime number less than 10(}) and \(B=\{2,3,5,7\}\), which statement is correct?
#prime numbers
#equal sets
#common mistake
A (A=B)
B \(A\subset B\) और \(A\ne B\) / \(A\subset B\) and \(A\ne B\)
C \(B\subset A\) और \(A\ne B\) / \(B\subset A\) and \(A\ne B\)
D \(A=\{1,2,3,5,7\}\)
Explanation opens after your attempt
Step 1
Concept
The prime numbers less than 10 are 2, 3, 5 and 7. The number 1 is not prime.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The prime numbers less than 10 are 2, 3, 5 and 7. The number 1 is not prime.
Step 3
Exam Tip
10 से छोटी अभाज्य संख्याएं 2, 3, 5 और 7 हैं। 1 अभाज्य नहीं है।
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यदि \(A={x:x\) 12 का धनात्मक गुणनखंड है(}) और \(B=\{1,2,3,4,6,12\}\), तो क्या सत्य है?
If \(A={x:x\) is a positive factor of 12(}) and \(B=\{1,2,3,4,6,12\}\), what is true?
#factors
#equal sets
#set builder
A (A=B)
B \(A\subset B\) लेकिन \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) लेकिन \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D (A) अनंत है / (A) is infinite
Explanation opens after your attempt
Step 1
Concept
These six numbers are exactly the positive factors of 12. Set-builder form and roster form give the same set.
Step 2
Why this answer is correct
The correct answer is A. (A=B). These six numbers are exactly the positive factors of 12. Set-builder form and roster form give the same set.
Step 3
Exam Tip
12 के सभी धनात्मक गुणनखंड यही छह हैं। वर्णनात्मक रूप और सूची रूप एक ही समुच्चय दे रहे हैं।
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समुच्चय \(A={x:x^2=4,\ x\in \mathbb{Z}}\) और \(B=\{-2,2\}\) के लिए सही कथन चुनिए।
Choose the correct statement for \(A={x:x^2=4,\ x\in \mathbb{Z}}\) and \(B=\{-2,2\}\).
#equal sets
#roster form
#set builder
A (A=B)
B \(A=\{2\}\) इसलिए \(A\ne B\) / \(A=\{2\}\) so \(A\ne B\)
C \(B\subset A\) लेकिन \(A\not\subset B\) / \(B\subset A\) but \(A\not\subset B\)
D \(A=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
In integers, the solutions of \(x^2=4\) are (-2) and 2. Both sets are equal.
Step 2
Why this answer is correct
The correct answer is A. (A=B). In integers, the solutions of \(x^2=4\) are (-2) and 2. Both sets are equal.
Step 3
Exam Tip
पूर्णांकों में \(x^2=4\) के हल (-2) और 2 हैं। दोनों समुच्चय बराबर हैं।
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यदि ({x,5}={3,y}), तो निम्न में से कौन सा युग्म सही हो सकता है?
If ({x,5}={3,y}), which pair can be correct?
#equal sets
#variables
#reasoning
A (x=3,y=5)
B (x=5,y=3)
C (x=3,y=3)
D (x=5,y=5)
Explanation opens after your attempt
Correct Answer
A. (x=3,y=5)
Step 1
Concept
Equal sets must contain exactly the same elements, so 3 and 5 must appear on both sides. Do not be confused by order.
Step 2
Why this answer is correct
The correct answer is A. (x=3,y=5). Equal sets must contain exactly the same elements, so 3 and 5 must appear on both sides. Do not be confused by order.
Step 3
Exam Tip
बराबर समुच्चयों में वही अवयव होने चाहिए, इसलिए 3 और 5 दोनों ओर होने चाहिए। ऐसे प्रश्नों में क्रम से भ्रमित न हों।
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समुच्चय \(A=\{1,1,2,3\}\) और \(B=\{3,2,1\}\) के लिए कौन सा निष्कर्ष सही है?
For the sets \(A=\{1,1,2,3\}\) and \(B=\{3,2,1\}\), which conclusion is correct?
#sets
#duplicate elements
#equal sets
A \(A\ne B\) क्योंकि 1 दो बार लिखा है / \(A\ne B\) because 1 is written twice
B (A=B)
C \(A\subset B\) लेकिन \(B\not\subset A\) / \(A\subset B\) but \(B\not\subset A\)
D \(B\subset A\) लेकिन \(A\not\subset B\) / \(B\subset A\) but \(A\not\subset B\)
Explanation opens after your attempt
Step 1
Concept
Repeated elements are not counted in a set. In exams, first list the distinct elements.
Step 2
Why this answer is correct
The correct answer is B. (A=B). Repeated elements are not counted in a set. In exams, first list the distinct elements.
Step 3
Exam Tip
समुच्चय में किसी अवयव की पुनरावृत्ति नहीं गिनी जाती। परीक्षा में पहले वास्तविक अलग-अलग अवयव लिखें।
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यदि \(A=\{2,4,6\}\) और \(B={x:x\) संख्या 8 से छोटी धनात्मक सम संख्या है(}), तो सही कथन कौन सा है?
If \(A=\{2,4,6\}\) and \(B={x:x\) is a positive even number less than 8(}), which statement is correct?
#sets
#equal sets
#subset
#class 11
A (A=B)
B \(A\subset B\) लेकिन \(A\ne B\) / \(A\subset B\) but \(A\ne B\)
C \(B\subset A\) लेकिन \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Both sets have exactly the elements 2, 4 and 6. Order or description does not change a set.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Both sets have exactly the elements 2, 4 and 6. Order or description does not change a set.
Step 3
Exam Tip
दोनों समुच्चयों के सभी अवयव 2, 4 और 6 हैं। क्रम या वर्णन बदलने से समुच्चय नहीं बदलता।
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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
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 \(A={x:x\in\mathbb{Z}\) 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
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 \(A={x:x\) (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
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 \(A={x:x\) (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
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 \(A={x:x\in\mathbb{Z}\) 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
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 \(A={x:x\) (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
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 \(A=\{1,2,3\}\), \(B=\{1,2,3,4\}\), 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
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 \(A={x:x\) \(x^2-1=0\) 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
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 \(A={x:x\) (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
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 \(A={x:x\) (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
#equal_sets
#even_prime
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 \(A={x:x\in\mathbb{Z}\) 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
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 \(A=\{a,b\}\) 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
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 \(A={x:x\in\mathbb{N}\) 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
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 \(A=\{2,4,6,8\}\) 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
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 \(A={x:x\) 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
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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