\(यदि (M_1={x:x\in \mathbb{N},,x\) 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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\(समुच्चय (S_1={x:x\in \mathbb{N},,x\) is a factor of 45 and x+2 is prime}) का सूची रूप क्या है?
\(What is the roster form of (S_1={x:x\in \mathbb{N},,x\) is a factor of 45 and x+2 is prime})?
#sets
#factors
#prime condition
#roster
A \(S_1={1,3,5,9,15,45}\)
B \(S_1={1,3,9,15}\)
C \(S_1={1,3}\)
D \(S_1={3,5,15}\)
Explanation opens after your attempt
Correct Answer
C. \(S_1={1,3}\)
Step 1
Concept
(45) के भाजक (1,3,5,9,15,45) हैं। / Factors of (45) are (1,3,5,9,15,45).
Step 2
Why this answer is correct
(x+2) जांचें: (3,5,7,11,17,47) मिलते हैं, और ये सभी अभाज्य हैं। / Adding (2) gives (3,5,7,11,17,47), all of which are prime.
Step 3
Exam Tip
इसलिए सभी भाजक लेने चाहिए, न कि केवल छोटे मान। / Therefore all listed factors satisfy the condition, so the full set of factors is needed.
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यदि \(T_1={x:x\in \mathbb{Z},,x^2-2x-8=0}\), तो \(T_1\) का सही सूची रूप कौन-सा है?
If \(T_1={x:x\in \mathbb{Z},,x^2-2x-8=0}\), which is the correct roster form of \(T_1\)?
#sets
#quadratic
#integers
#roster
A \(T_1={-2,4}\)
B \(T_1={2,-4}\)
C \(T_1={-4,2}\)
D \(T_1={4}\)
Explanation opens after your attempt
Correct Answer
A. \(T_1={-2,4}\)
Step 1
Concept
(x-2 -2x-8=(x-4)(x+2)) है। / (x-2 -2x-8=(x-4)(x+2)).
Step 2
Why this answer is correct
इसलिए (x=4) या (x=-2), दोनों पूर्णांक हैं। / Thus (x=4) or (x=-2), and both are integers.
Step 3
Exam Tip
सूची रूप में क्रम जरूरी नहीं, पर दोनों मूल लिखना जरूरी है। / Order does not matter in roster form, but both roots must be listed.
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\(कौन-सा विकल्प (U_1={x:x\in \mathbb{N},,10\leq x\leq40,,x\) has digit 3}) का सूची रूप है?
\(Which option is the roster form of (U_1={x:x\in \mathbb{N},,10\leq x\leq40,,x\) has digit 3})?
#sets
#digits
#roster
#natural numbers
A \(U_1={13,23,30,31,32,33,34,35,36,37,38,39}\)
B \(U_1={3,13,23,33}\)
C \(U_1={13,23,33,43}\)
D \(U_1={30,31,32,33,34,35,36,37,38,39,40}\)
Explanation opens after your attempt
Correct Answer
A. \(U_1={13,23,30,31,32,33,34,35,36,37,38,39}\)
Step 1
Concept
(10) से (40) तक वे संख्याएं लें जिनमें अंक (3) आता है। / Consider numbers from (10) to (40) that contain the digit (3).
Step 2
Why this answer is correct
इकाई स्थान पर (3) वाली (13,23) और दहाई स्थान पर (3) वाली (30) से (39) तक की संख्याएं मिलती हैं। / We get (13,23) from the units digit and (30) to (39) from the tens digit.
Step 3
Exam Tip
अंक-आधारित प्रश्नों में दहाई और इकाई दोनों स्थान देखें। / In digit-based questions, check both tens and units positions.
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\(यदि (V_1={x:x\in \mathbb{N},,x<100,,x\) is a square and a cube\(}), तो (V_1) क्या है\)?
\(If (V_1={x:x\in \mathbb{N},,x<100,,x\) is a square and a cube\(}), what is (V_1)\)?
#sets
#squares
#cubes
#sixth powers
#roster
A \(V_1={1,64}\)
B \(V_1={1,8,27,64}\)
C \(V_1={4,9,16,25,36,49,64,81}\)
D \(V_1={64}\)
Explanation opens after your attempt
Correct Answer
A. \(V_1={1,64}\)
Step 1
Concept
जो संख्या वर्ग और घन दोनों हो, वह छठी घात होती है। / A number that is both a square and a cube is a sixth power.
Step 2
Why this answer is correct
(100) से छोटी छठी घातें \(1^6=1\) और \(2^6=64\) हैं। / Sixth powers less than (100) are \(1^6=1\) and \(2^6=64\).
Step 3
Exam Tip
दोनों शर्तों को अलग-अलग नहीं, साथ में पूरा करना होता है। / Both conditions must be satisfied together, not separately.
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