समुच्चय \(E_1={x:x\in \mathbb{N},,x=\frac{30}{n},,n\in \mathbb{N}}\) किससे बराबर है?
The set \(E_1={x:x\in \mathbb{N},,x=\frac{30}{n},,n\in \mathbb{N}}\) is equal to which set?
#sets
#divisors
#set-builder
#roster
A ({1,2,3,5,6,10,15,30})
B ({2,3,5,30})
C ({1,2,3,4,5,6,10,15,30})
D \({n:n\in \mathbb{N},,n<30}\)
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,5,6,10,15,30})
Step 1
Concept
\(\frac{30}{n}\) प्राकृतिक संख्या तभी होगा जब (n), (30) का भाजक हो। / \(\frac{30}{n}\) is natural only when (n) is a divisor of (30).
Step 2
Why this answer is correct
तब मिलने वाले (x) भी (30) के सभी धनात्मक भाजक होंगे। / The possible (x) values are all positive divisors of (30).
Step 3
Exam Tip
भाग वाली शर्तों में पूर्ण भागफल की शर्त पहचानें। / For division-based conditions, identify when the quotient remains an integer.
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\(यदि (F_1={x:x\in \mathbb{N},,x\) has exactly two distinct positive factors and \(x<15}), तो (F_1) क्या है\)?
\(If (F_1={x:x\in \mathbb{N},,x\) has exactly two distinct positive factors and \(x<15}), what is (F_1)\)?
#sets
#prime numbers
#factors
#roster
A \(F_1={1,2,3,5,7,11,13}\)
B \(F_1={2,3,5,7,11,13}\)
C \(F_1={2,4,6,8,10,12,14}\)
D \(F_1={3,5,7,9,11,13}\)
Explanation opens after your attempt
Correct Answer
B. \(F_1={2,3,5,7,11,13}\)
Step 1
Concept
ठीक दो धनात्मक भाजक वाली संख्याएं अभाज्य संख्याएं होती हैं। / Numbers with exactly two positive factors are prime numbers.
Step 2
Why this answer is correct
(15) से छोटी अभाज्य संख्याएं (2,3,5,7,11,13) हैं। / Primes less than (15) are (2,3,5,7,11,13).
Step 3
Exam Tip
(1) अभाज्य नहीं है, क्योंकि उसके दो अलग भाजक नहीं होते। / (1) is not prime because it does not have two distinct positive factors.
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कौन-सा विकल्प \(G_1={x:x\in \mathbb{Z},,x^3=x}\) का सही सूची रूप है?
Which option is the correct roster form of \(G_1={x:x\in \mathbb{Z},,x^3=x}\)?
#sets
#integers
#cubic equation
#roster
A \(G_1={-1,0,1}\)
B \(G_1={0,1}\)
C \(G_1={-1,1}\)
D \(G_1={1}\)
Explanation opens after your attempt
Correct Answer
A. \(G_1={-1,0,1}\)
Step 1
Concept
\(x^3=x\) से \(x^3-x=0\) मिलता है। / \(x^3=x\) gives \(x^3-x=0\).
Step 2
Why this answer is correct
(x(x-1)(x+1)=0), इसलिए (x=-1,0,1)। / (x(x-1)(x+1)=0), so (x=-1,0,1).
Step 3
Exam Tip
गुणनखंडन से मिले हर मूल को दिए गए समूह में जांचें। / Check every factor-based solution in the given domain.
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\(समुच्चय (H_1={x:x\in \mathbb{N},,5\leq x\leq15,,x\) is composite}) का सूची रूप क्या है?
\(What is the roster form of (H_1={x:x\in \mathbb{N},,5\leq x\leq15,,x\) is composite})?
#sets
#composite numbers
#roster
#natural numbers
A \(H_1={6,8,9,10,12,14,15}\)
B \(H_1={5,6,8,9,10,12,14,15}\)
C \(H_1={6,8,9,10,11,12,14,15}\)
D \(H_1={4,6,8,9,10,12,14,15}\)
Explanation opens after your attempt
Correct Answer
A. \(H_1={6,8,9,10,12,14,15}\)
Step 1
Concept
(5) से (15) तक संख्याएं देखें। / Check numbers from (5) to (15).
Step 2
Why this answer is correct
संयुक्त संख्याएं (6,8,9,10,12,14,15) हैं; (5,7,11,13) अभाज्य हैं। / Composite numbers are (6,8,9,10,12,14,15); (5,7,11,13) are prime.
Step 3
Exam Tip
सीमा के अंदर हर संख्या की प्रकृति जांचें। / Test the nature of each number within the boundary.
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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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