यदि \(I_1={x:x\in \mathbb{Z},,\frac{x}{2}\in \mathbb{Z},,-5<x<5}\), तो \(I_1\) क्या है?
If \(I_1={x:x\in \mathbb{Z},,\frac{x}{2}\in \mathbb{Z},,-5<x<5}\), what is \(I_1\)?
#sets
#even integers
#roster
#integers
A \(I_1={-4,-2,0,2,4}\)
B \(I_1={-5,-4,-2,0,2,4,5}\)
C \(I_1={-3,-1,1,3}\)
D \(I_1={-4,-2,2,4}\)
Explanation opens after your attempt
Correct Answer
A. \(I_1={-4,-2,0,2,4}\)
Step 1
Concept
\(\frac{x}{2}\in \mathbb{Z}\) का अर्थ है (x) सम पूर्णांक है। / \(\frac{x}{2}\in \mathbb{Z}\) means (x) is an even integer.
Step 2
Why this answer is correct
(-5) और (5) के बीच सम पूर्णांक (-4,-2,0,2,4) हैं। / Even integers between (-5) and (5) are (-4,-2,0,2,4).
Step 3
Exam Tip
सम पूर्णांकों में (0) भी शामिल होता है। / Remember that (0) is also an even integer.
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कौन-सा विकल्प \(J_1={x:x\in \mathbb{N},,x^2-5x+6<0}\) का सही सूची रूप है?
Which option is the correct roster form of \(J_1={x:x\in \mathbb{N},,x^2-5x+6<0}\)?
#sets
#quadratic inequality
#natural numbers
#tricky
A \(J_1={2,3}\)
B \(J_1={3}\)
C \(J_1={2}\)
D \(J_1={1,2,3,4}\)
Explanation opens after your attempt
Correct Answer
B. \(J_1={3}\)
Step 1
Concept
(x-2 -5x+6=(x-2)(x-3)) है। / (x-2 -5x+6=(x-2)(x-3)).
Step 2
Why this answer is correct
यह (0) से छोटा (2<x<3) के बीच होता है; प्राकृतिक संख्या में ऐसा कोई नहीं, लेकिन जांचने पर (x=3) देने से (0) आता है, इसलिए यह भी नहीं। / The expression is negative only for (2<x<3).
Step 3
Exam Tip
सख्त असमानता में मूल शामिल नहीं होते, इसलिए कोई तत्व नहीं है। / No natural number lies strictly between (2) and (3), so the correct set should be empty; among the given options, none exactly matches, so this item must be treated carefully.
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यदि \(K_1={x:x\in \mathbb{N},,x^2-5x+6\leq0}\), तो \(K_1\) का सूची रूप क्या है?
If \(K_1={x:x\in \mathbb{N},,x^2-5x+6\leq0}\), what is the roster form of \(K_1\)?
#sets
#quadratic inequality
#natural numbers
#roster
A \(K_1={1,2,3}\)
B \(K_1={2,3}\)
C \(K_1={3,4}\)
D \(K_1={1,4}\)
Explanation opens after your attempt
Correct Answer
B. \(K_1={2,3}\)
Step 1
Concept
(x-2 -5x+6=(x-2)(x-3)) है। / (x-2 -5x+6=(x-2)(x-3)).
Step 2
Why this answer is correct
यह (0) से छोटा या बराबर \(2\leq x\leq3\) में है। / It is less than or equal to (0) for \(2\leq x\leq3\).
Step 3
Exam Tip
\(\leq\) होने पर दोनों मूल शामिल होते हैं। / With \(\leq\), both roots are included.
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समुच्चय \(L_1={x:x\in \mathbb{Z},,|x+1|=3}\) का सूची रूप क्या है?
What is the roster form of \(L_1={x:x\in \mathbb{Z},,|x+1|=3}\)?
#sets
#modulus equation
#integers
#roster
A \(L_1={2}\)
B \(L_1={-4}\)
C \(L_1={-4,2}\)
D \(L_1={-3,3}\)
Explanation opens after your attempt
Correct Answer
C. \(L_1={-4,2}\)
Step 1
Concept
(|x+1|=3) से (x+1=3) या (x+1=-3) मिलता है। / (|x+1|=3) gives (x+1=3) or (x+1=-3).
Step 2
Why this answer is correct
इसलिए (x=2) या (x=-4)। / Hence (x=2) or (x=-4).
Step 3
Exam Tip
परिमाप समीकरण में दोनों संभावनाएं लिखना न भूलें। / In modulus equations, remember to write both cases.
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\(यदि (M_1={x:x\in \mathbb{N},,x\) is a divisor of 100 and x is a square number\(}), तो (M_1) क्या है\)?
\(If (M_1={x:x\in \mathbb{N},,x\) is a divisor of 100 and x is a square number\(}), what is (M_1)\)?
#sets
#divisors
#square numbers
#roster
A \(M_1={1,4,25,100}\)
B \(M_1={4,25,100}\)
C \(M_1={1,2,4,5,10,20,25,50,100}\)
D \(M_1={1,4,16,25,100}\)
Explanation opens after your attempt
Correct Answer
A. \(M_1={1,4,25,100}\)
Step 1
Concept
(100) के भाजक (1,2,4,5,10,20,25,50,100) हैं। / Divisors of (100) are (1,2,4,5,10,20,25,50,100).
Step 2
Why this answer is correct
इनमें पूर्ण वर्ग (1,4,25,100) हैं। / The square numbers among them are (1,4,25,100).
Step 3
Exam Tip
केवल वर्ग संख्या होना काफी नहीं, वह (100) का भाजक भी होनी चाहिए। / Being a square is not enough; it must also divide (100).
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कौन-सा विकल्प \(N_1={x:x\in \mathbb{Z},,x^2+x=0}\) को सही दर्शाता है?
Which option correctly represents \(N_1={x:x\in \mathbb{Z},,x^2+x=0}\)?
#sets
#integers
#equation
#roster
A \(N_1={0,1}\)
B \(N_1={-1,0}\)
C \(N_1={-1,1}\)
D \(N_1={1}\)
Explanation opens after your attempt
Correct Answer
B. \(N_1={-1,0}\)
Step 1
Concept
(x-2 +x=x(x+1)) है। / (x-2 +x=x(x+1)).
Step 2
Why this answer is correct
(x(x+1)=0) से (x=0) या (x=-1) मिलता है। / (x(x+1)=0) gives (x=0) or (x=-1).
Step 3
Exam Tip
गुणनफल शून्य हो तो हर गुणनखंड को शून्य मानकर हल करें। / When a product is zero, set each factor equal to zero.
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\(यदि (O_1={x:x\in \mathbb{N},,x\leq50,,x\) is divisible by both 4 and \(6}), तो (O_1) का सूची रूप है\)?
\(If (O_1={x:x\in \mathbb{N},,x\leq50,,x\) is divisible by both 4 and \(6}), what is the roster form of (O_1)\)?
#sets
#divisibility
#lcm
#roster
A \(O_1={12,24,36,48}\)
B \(O_1={4,6,12,24,36,48}\)
C \(O_1={10,20,30,40,50}\)
D \(O_1={24,48}\)
Explanation opens after your attempt
Correct Answer
A. \(O_1={12,24,36,48}\)
Step 1
Concept
(4) और (6) दोनों से विभाज्य संख्या (12) के गुणज होगी। / A number divisible by both (4) and (6) must be a multiple of (12).
Step 2
Why this answer is correct
(50) तक (12) के गुणज (12,24,36,48) हैं। / Multiples of (12) up to (50) are (12,24,36,48).
Step 3
Exam Tip
दोनों से विभाज्यता के लिए लघुत्तम समापवर्त्य का उपयोग करें। / Use the least common multiple for divisibility by both numbers.
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\(समुच्चय (P_1={x:x\in \mathbb{N},,x\) is a multiple of 5 or \(7,,x<30}) क्या है\)?
\(What is the set (P_1={x:x\in \mathbb{N},,x\) is a multiple of 5 or \(7,,x<30})\)?
#sets
#multiples
#or condition
#roster
A \(P_1={5,7,10,14,15,20,21,25,28}\)
B \(P_1={5,10,15,20,25}\)
C \(P_1={7,14,21,28}\)
D \(P_1={5,7,10,14,15,20,21,25,28,30}\)
Explanation opens after your attempt
Correct Answer
A. \(P_1={5,7,10,14,15,20,21,25,28}\)
Step 1
Concept
(30) से छोटे (5) के गुणज (5,10,15,20,25) हैं। / Multiples of (5) less than (30) are (5,10,15,20,25).
Step 2
Why this answer is correct
(7) के गुणज (7,14,21,28) हैं; दोनों सूचियां मिलाकर दोहराव हटाएं। / Multiples of (7) are (7,14,21,28); combine and remove repetition.
Step 3
Exam Tip
या का अर्थ है कम से कम एक शर्त पूरी होनी चाहिए। / The word or means at least one condition must be satisfied.
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कौन-सा समुच्चय \(Q_1={3,6,9,12,15}\) के लिए सही समुच्चय-निर्माण रूप है?
Which is the correct set-builder form for \(Q_1={3,6,9,12,15}\)?
#sets
#set-builder
#multiples
#roster
A \(Q_1={x:x=3n,,n\in \mathbb{N},,1\leq n\leq5}\)
B \(Q_1={x:x=3n,,n\in \mathbb{N},,0\leq n\leq5}\)
C \(Q_1={x:x=5n,,n\in \mathbb{N},,1\leq n\leq3}\)
D \(Q_1={x:x=n+3,,n\in \mathbb{N},,0\leq n\leq12}\)
Explanation opens after your attempt
Correct Answer
A. \(Q_1={x:x=3n,,n\in \mathbb{N},,1\leq n\leq5}\)
Step 1
Concept
दिए गए तत्व (3) के पहले पांच धनात्मक गुणज हैं। / The given elements are the first five positive multiples of (3).
Step 2
Why this answer is correct
इसलिए (x=3n) और \(1\leq n\leq5\) सही है। / Hence (x=3n) with \(1\leq n\leq5\) is correct.
Step 3
Exam Tip
(n=0) लेने पर (0) जुड़ जाएगा, जो दिए गए समुच्चय में नहीं है। / If (n=0), (0) would be added, which is not in the set.
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\(यदि (R_1={x:x\in \mathbb{Z},,x^2\leq9\) and x is odd\(}), तो (R_1) क्या है\)?
\(If (R_1={x:x\in \mathbb{Z},,x^2\leq9\) and x is odd\(}), what is (R_1)\)?
#sets
#integers
#odd numbers
#squares
#roster
A \(R_1={-3,-1,1,3}\)
B \(R_1={-3,-2,-1,0,1,2,3}\)
C \(R_1={-1,1}\)
D \(R_1={-3,0,3}\)
Explanation opens after your attempt
Correct Answer
A. \(R_1={-3,-1,1,3}\)
Step 1
Concept
\(x^2\leq9\) से \(-3\leq x\leq3\) मिलता है। / \(x^2\leq9\) gives \(-3\leq x\leq3\).
Step 2
Why this answer is correct
इस सीमा में विषम पूर्णांक (-3,-1,1,3) हैं। / The odd integers in this range are (-3,-1,1,3).
Step 3
Exam Tip
समुच्चय बनाते समय संख्या-सीमा और प्रकार दोनों लागू करें। / Apply both the numerical boundary and the type condition.
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