यदि \(A={x:x\in \mathbb{N},,x^2-7x+10=0}\), तो (A) का सूची रूप क्या होगा?
If \(A={x:x\in \mathbb{N},,x^2-7x+10=0}\), what is the roster form of (A)?
#sets
#set-builder
#roster
#quadratic
#natural numbers
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A \(A=\{1,10\}\)
B \(A=\{2,5\}\)
C \(A=\{3,4\}\)
D \(A=\{5,7\}\)
Explanation opens after your attempt
Correct Answer
B. \(A=\{2,5\}\)
Step 1
Concept
दिए गए बहुपद को गुणनखंड करें: (x-2 -7x+10=(x-2)(x-5))। / Factor the quadratic: (x-2 -7x+10=(x-2)(x-5)).
Step 2
Why this answer is correct
इसलिए प्राकृतिक संख्याओं में (x=2) और (x=5) मिलते हैं। / The natural number solutions are (x=2) and (x=5).
Step 3
Exam Tip
परीक्षा में पहले प्रतिबंध \(x\in \mathbb{N}\) जरूर देखें, फिर सूची बनाएं। / In exams, always check the given domain before writing the roster form.
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यदि \(A={x:x=\frac{n}{n+1},,n\in \mathbb{N},,1\leq n\leq4}\), तो (A) का सूची रूप कौन-सा है?
If \(A={x:x=\frac{n}{n+1},,n\in \mathbb{N},,1\leq n\leq4}\), which is the roster form of (A)?
#sets
#set-builder
#roster form
#rational numbers
#exam oriented
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A \(A=\left{\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}\right}\)
B \(A=\left{\frac{2}{1},\frac{3}{2},\frac{4}{3},\frac{5}{4}\right}\)
C \(A=\left{\frac{1}{1},\frac{2}{2},\frac{3}{3},\frac{4}{4}\right}\)
D \(A=\left{\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5}\right}\)
Explanation opens after your attempt
Correct Answer
A. \(A=\left{\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}\right}\)
Step 1
Concept
दिए गए नियम में (n) के मान (1,2,3,4) रखने हैं। / Substitute the allowed values (n=1,2,3,4).
Step 2
Why this answer is correct
\(\frac{n}{n+1}\) से क्रमशः \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}\) मिलते हैं। / The expression \(\frac{n}{n+1}\) gives \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}\).
Step 3
Exam Tip
सूची रूप लिखते समय नियम को हर अनुमत मान पर अलग-अलग लागू करें। / In roster form questions, apply the rule separately to every permitted value.
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\(समुच्चय (B={x:x\) is a prime divisor of 84}) का सही सूची रूप कौन-सा है?
\(Which is the correct roster form of the set (B={x:x\) is a prime divisor of 84})?
#sets
#prime divisors
#roster
#representation
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A \(B=\{2,3,7\}\)
B \(B=\{2,3,4,7\}\)
C \(B=\{1,2,3,7\}\)
D \(B=\{2,6,7,14\}\)
Explanation opens after your attempt
Correct Answer
A. \(B=\{2,3,7\}\)
Step 1
Concept
(84) का अभाज्य गुणनखंडन \(84=2^2\cdot3\cdot7\) है। / Prime factorize (84): \(84=2^2\cdot3\cdot7\).
Step 2
Why this answer is correct
अभाज्य भाजक केवल (2,3,7) हैं। / The prime divisors are only (2,3,7).
Step 3
Exam Tip
सूची रूप में किसी तत्व को दोहराया नहीं जाता, इसलिए घातों को तत्व न मानें। / In roster form, repeated factors or powers are not listed as separate elements.
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यदि \(C={x:x\in \mathbb{Z},,-3<x\leq2}\), तो (C) में कितने तत्व हैं?
If \(C={x:x\in \mathbb{Z},,-3<x\leq2}\), how many elements are in (C)?
#sets
#integers
#inequality
#cardinality
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(x) पूर्णांक है और \(-3<x\leq2\) दिया है। / (x) is an integer and \(-3<x\leq2\).
Step 2
Why this answer is correct
संभव मान (-2,-1,0,1,2) हैं, इसलिए (5) तत्व हैं। / The possible values are (-2,-1,0,1,2), so there are (5) elements.
Step 3
Exam Tip
असमानता में खुली और बंद सीमा पर ध्यान देना बहुत जरूरी है। / Pay close attention to open and closed boundaries in inequalities.
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\(समुच्चय (D={x:x\in \mathbb{N},,x\) is a factor of 36 and x is odd}) का सूची रूप क्या है?
\(What is the roster form of (D={x:x\in \mathbb{N},,x\) is a factor of 36 and x is odd})?
#sets
#factors
#odd numbers
#roster
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A \(D=\{1,3,9\}\)
B \(D=\{3,9\}\)
C \(D=\{1,3,6,9\}\)
D \(D=\{1,3,9,12\}\)
Explanation opens after your attempt
Correct Answer
A. \(D=\{1,3,9\}\)
Step 1
Concept
(36) के भाजक (1,2,3,4,6,9,12,18,36) हैं। / The factors of (36) are (1,2,3,4,6,9,12,18,36).
Step 2
Why this answer is correct
इनमें विषम भाजक (1,3,9) हैं। / The odd factors among them are (1,3,9).
Step 3
Exam Tip
दो शर्तें हों तो दोनों को साथ-साथ लागू करें। / When two conditions are given, apply both before writing the set.
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यदि \(E={x:x\in \mathbb{Z},,x^2<10}\), तो (E) का सूची रूप क्या है?
If \(E={x:x\in \mathbb{Z},,x^2<10}\), what is the roster form of (E)?
#sets
#integers
#roster
#inequality
#squares
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A \(E=\{-4,-3,-2,-1,0,1,2,3,4\}\)
B \(E=\{-3,-2,-1,0,1,2,3\}\)
C \(E=\{-2,-1,0,1,2\}\)
D \(E=\{-3,-2,-1,1,2,3\}\)
Explanation opens after your attempt
Correct Answer
B. \(E=\{-3,-2,-1,0,1,2,3\}\)
Step 1
Concept
\(x^2<10\) का अर्थ है \(|x|<\sqrt{10}\)।
Step 2
Why this answer is correct
पूर्णांक मान (-3,-2,-1,0,1,2,3) मिलते हैं। / The integer values are (-3,-2,-1,0,1,2,3).
Step 3
Exam Tip
वर्ग वाली शर्तों में शून्य और ऋणात्मक मान भूलना आम गलती है। / In square-based conditions, do not forget zero and negative integers.
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समुच्चय \(F={x:x=2n+1,,n\in \mathbb{Z},,-2\leq n\leq2}\) का सूची रूप क्या होगा?
What is the roster form of \(F={x:x=2n+1,,n\in \mathbb{Z},,-2\leq n\leq2}\)?
#sets
#roster
#set-builder
#integers
#odd numbers
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A \(F=\{-3,-1,1,3,5\}\)
B \(F=\{-5,-3,-1,1,3\}\)
C \(F=\{-2,-1,0,1,2\}\)
D \(F=\{-3,0,1,3,5\}\)
Explanation opens after your attempt
Correct Answer
A. \(F=\{-3,-1,1,3,5\}\)
Step 1
Concept
(n=-2,-1,0,1,2) रखिए। / Put (n=-2,-1,0,1,2).
Step 2
Why this answer is correct
(x=2n+1) से मान (-3,-1,1,3,5) मिलते हैं। / Using (x=2n+1), we get (-3,-1,1,3,5).
Step 3
Exam Tip
ऐसे प्रश्नों में पहले छिपे हुए चर के सभी मान लिखें। / In such questions, first list all allowed values of the hidden variable.
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कौन-सा विवरण \(G=\{4,9,16,25\}\) को सही समुच्चय-निर्माण रूप में दर्शाता है?
Which description correctly represents \(G=\{4,9,16,25\}\) in set-builder form?
#sets
#set-builder
#squares
#roster
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A \(G={x:x=n^2,,n\in \mathbb{N},,2\leq n\leq5}\)
B \(G={x:x=n^2,,n\in \mathbb{N},,1\leq n\leq5}\)
C \(G={x:x=2n,,n\in \mathbb{N},,2\leq n\leq5}\)
D \(G={x:x=n+2,,n\in \mathbb{N},,2\leq n\leq5}\)
Explanation opens after your attempt
Correct Answer
A. \(G={x:x=n^2,,n\in \mathbb{N},,2\leq n\leq5}\)
Step 1
Concept
(4,9,16,25) क्रमशः \(2^2,3^2,4^2,5^2\) हैं। / (4,9,16,25) are \(2^2,3^2,4^2,5^2\).
Step 2
Why this answer is correct
इसलिए \(x=n^2\) और \(2\leq n\leq5\) सही है। / Hence \(x=n^2\) with \(2\leq n\leq5\) is correct.
Step 3
Exam Tip
केवल पैटर्न नहीं, आरंभ और अंत की सीमा भी जांचें। / Check both the pattern and the starting and ending limits.
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\(यदि (H={x:x\in \mathbb{N},,12<x<30,,x\) is divisible by 6}), तो (H) क्या है?
\(If (H={x:x\in \mathbb{N},,12<x<30,,x\) is divisible by 6}), what is (H)?
#sets
#multiples
#inequality
#roster
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A \(H=\{12,18,24,30\}\)
B \(H=\{18,24\}\)
C \(H=\{6,12,18,24\}\)
D \(H=\{18,24,30\}\)
Explanation opens after your attempt
Correct Answer
B. \(H=\{18,24\}\)
Step 1
Concept
(12) और (30) के बीच (6) से विभाज्य संख्याएं देखें। / Look for multiples of (6) between (12) and (30).
Step 2
Why this answer is correct
(18) और (24) ही खुली सीमा के अंदर आते हैं। / Only (18) and (24) lie strictly inside the open interval.
Step 3
Exam Tip
(<) वाली सीमा में किनारे के मान शामिल नहीं होते। / With (<), boundary values are not included.
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समुच्चय \(I={x:x\in \mathbb{R},,x^2+1=0}\) के बारे में सही कथन कौन-सा है?
Which statement is correct about the set \(I={x:x\in \mathbb{R},,x^2+1=0}\)?
#sets
#empty set
#real numbers
#equation
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A \(I=\{1\}\)
B \(I=\{-1\}\)
C \(I=\{-1,1\}\)
D \(I=\varnothing\)
Explanation opens after your attempt
Correct Answer
D. \(I=\varnothing\)
Step 1
Concept
वास्तविक संख्या के लिए \(x^2\geq0\) होता है। / For any real number, \(x^2\geq0\).
Step 2
Why this answer is correct
इसलिए \(x^2+1\) कभी (0) नहीं हो सकता। / Therefore \(x^2+1\) can never be (0) in real numbers.
Step 3
Exam Tip
संख्या-समूह वास्तविक है या सम्मिश्र, यह पहले देखना चाहिए। / Always check whether the domain is real or complex before solving.
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\(यदि (J={x:x\) is a letter in the word STATISTICS}), तो सूची रूप में सही समुच्चय कौन-सा है?
\(If (J={x:x\) is a letter in the word STATISTICS}), which is the correct roster form?
#sets
#roster
#letters
#repetition
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A \(J=\{S,T,A,I,C\}\)
B \(J=\{S,T,A,T,I,S,T,I,C,S\}\)
C \(J=\{S,T,A,T,I,C\}\)
D \(J=\{A,C,I,S,T,S\}\)
Explanation opens after your attempt
Correct Answer
A. \(J=\{S,T,A,I,C\}\)
Step 1
Concept
शब्द में आने वाले अलग-अलग अक्षर पहचानें। / Identify the distinct letters in the word.
Step 2
Why this answer is correct
समुच्चय में दोहराए गए अक्षर फिर से नहीं लिखे जाते, इसलिए (S,T,A,I,C) मिलते हैं। / Repeated letters are not written again in a set, so we get (S,T,A,I,C).
Step 3
Exam Tip
सूची रूप में क्रम और पुनरावृत्ति दोनों महत्वपूर्ण नहीं माने जाते। / In roster form, order and repetition do not matter.
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कौन-सा समुच्चय \(K=\{0,1,4,9,16\}\) के बराबर है?
Which set is equal to \(K=\{0,1,4,9,16\}\)?
#sets
#equal sets
#squares
#set-builder
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A \({x:x=n^2,,n\in \mathbb{Z},,-4\leq n\leq4}\)
B \({x:x=n^2,,n\in \mathbb{Z},,0\leq n\leq4}\)
C \({x:x=n,,n\in \mathbb{N},,0\leq n\leq16}\)
D \({x:x=2n,,n\in \mathbb{N},,0\leq n\leq8}\)
Explanation opens after your attempt
Correct Answer
B. \({x:x=n^2,,n\in \mathbb{Z},,0\leq n\leq4}\)
Step 1
Concept
(0,1,4,9,16) ये \(0^2,1^2,2^2,3^2,4^2\) हैं। / (0,1,4,9,16) are \(0^2,1^2,2^2,3^2,4^2\).
Step 2
Why this answer is correct
\(0\leq n\leq4\) रखने पर ठीक यही वर्ग मिलते हैं। / Taking \(0\leq n\leq4\) gives exactly these squares.
Step 3
Exam Tip
ऋणात्मक (n) लेने पर भी नए वर्ग नहीं मिलते, पर सरल सही रूप विकल्प B है। / Negative (n) may repeat values, but option B is the clean exact representation.
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\(यदि (L={x:x\in \mathbb{N},,x\leq20,,x\) is not divisible by 2 but divisible by 3}), तो (L) का सूची रूप है?
\(If (L={x:x\in \mathbb{N},,x\leq20,,x\) is not divisible by 2 but divisible by 3}), what is the roster form of (L)?
#sets
#multiples
#divisibility
#roster
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A \(L=\{3,6,9,12,15,18\}\)
B \(L=\{3,9,15\}\)
C \(L=\{6,12,18\}\)
D \(L=\{3,9,15,21\}\)
Explanation opens after your attempt
Correct Answer
B. \(L=\{3,9,15\}\)
Step 1
Concept
(20) तक (3) के गुणज (3,6,9,12,15,18) हैं। / Multiples of (3) up to (20) are (3,6,9,12,15,18).
Step 2
Why this answer is correct
इनमें (2) से विभाज्य संख्याएं हटाने पर (3,9,15) बचते हैं। / Removing numbers divisible by (2), we get (3,9,15).
Step 3
Exam Tip
मिली-जुली शर्तों में पहले बड़ी सूची बनाकर छांटना आसान रहता है। / For combined conditions, first make a broad list and then filter it.
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समुच्चय \(M={x:x\in \mathbb{Z},,|x-2|\leq3}\) का सूची रूप क्या होगा?
What is the roster form of \(M={x:x\in \mathbb{Z},,|x-2|\leq3}\)?
#sets
#modulus
#integers
#roster
#inequality
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A \(M=\{-1,0,1,2,3,4,5\}\)
B \(M=\{0,1,2,3,4\}\)
C \(M=\{-1,0,1,2,3\}\)
D \(M=\{1,2,3,4,5\}\)
Explanation opens after your attempt
Correct Answer
A. \(M=\{-1,0,1,2,3,4,5\}\)
Step 1
Concept
\(|x-2|\leq3\) से \(-3\leq x-2\leq3\) मिलता है। / \(|x-2|\leq3\) gives \(-3\leq x-2\leq3\).
Step 2
Why this answer is correct
इसमें (2) जोड़ने पर \(-1\leq x\leq5\), इसलिए पूर्णांक (-1,0,1,2,3,4,5) हैं। / Adding (2), we get \(-1\leq x\leq5\), so the integers are (-1,0,1,2,3,4,5).
Step 3
Exam Tip
परिमाप वाली असमानता को दो तरफ की असमानता में बदलें। / Convert modulus inequalities into a two-sided inequality.
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कौन-सा समुच्चय \(N=\{2,4,8,16,32\}\) को सबसे सही ढंग से दर्शाता है?
Which set best represents \(N=\{2,4,8,16,32\}\)?
#sets
#powers
#set-builder
#roster
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A \(N={x:x=2n,,n\in \mathbb{N},,1\leq n\leq16}\)
B \(N={x:x=2^n,,n\in \mathbb{N},,1\leq n\leq5}\)
C \(N={x:x=n^2,,n\in \mathbb{N},,1\leq n\leq5}\)
D \(N={x:x=2^n,,n\in \mathbb{N},,0\leq n\leq4}\)
Explanation opens after your attempt
Correct Answer
B. \(N={x:x=2^n,,n\in \mathbb{N},,1\leq n\leq5}\)
Step 1
Concept
दिए गए तत्व \(2^1,2^2,2^3,2^4,2^5\) हैं। / The given elements are \(2^1,2^2,2^3,2^4,2^5\).
Step 2
Why this answer is correct
इसलिए \(x=2^n\) और \(1\leq n\leq5\) सही है। / Hence \(x=2^n\) with \(1\leq n\leq5\) is correct.
Step 3
Exam Tip
घात वाले पैटर्न में (n) की शुरुआती कीमत बहुत ध्यान से देखें। / For power patterns, check the starting value of (n) carefully.
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\(यदि (P={x:x\in \mathbb{N},,x\) divides 48 and \(x>12}), तो (P) क्या है\)?
\(If (P={x:x\in \mathbb{N},,x\) divides 48 and \(x>12}), what is (P)\)?
#sets
#factors
#roster
#inequality
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A \(P=\{16,24,48\}\)
B \(P=\{12,16,24,48\}\)
C \(P=\{24,48\}\)
D \(P=\{14,16,24,48\}\)
Explanation opens after your attempt
Correct Answer
A. \(P=\{16,24,48\}\)
Step 1
Concept
(48) के भाजक (1,2,3,4,6,8,12,16,24,48) हैं। / Factors of (48) are (1,2,3,4,6,8,12,16,24,48).
Step 2
Why this answer is correct
(12) से बड़े भाजक (16,24,48) हैं। / The factors greater than (12) are (16,24,48).
Step 3
Exam Tip
(x>12) में (12) शामिल नहीं होता। / In (x>12), the value (12) itself is not included.
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कौन-सा विकल्प सुव्यवस्थित समुच्चय का उदाहरण नहीं है?
Which option is not an example of a well-defined set?
#sets
#well-defined set
#conceptual
#representation
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A ({x:x is an even natural number less than 20})
B ({x:x is a beautiful number})
C \({x:x\in \mathbb{Z},,x^2=4}\)
D ({x:x is a vowel in English alphabet})
Explanation opens after your attempt
Correct Answer
B. ({x:x is a beautiful number})
Step 1
Concept
समुच्चय तभी सुव्यवस्थित होता है जब सदस्यता साफ तय हो सके। / A set is well-defined when membership can be clearly decided.
Step 2
Why this answer is correct
सुंदर संख्या अलग-अलग लोगों के लिए अलग हो सकती है, इसलिए यह स्पष्ट नहीं है। / A beautiful number may mean different things to different people, so it is not clear.
Step 3
Exam Tip
परीक्षा में मत-आधारित शब्दों से सावधान रहें। / In exams, be careful with opinion-based words.
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यदि \(Q={x:x\in \mathbb{Z},,x^2-4x+3=0}\), तो (Q) का सूची रूप क्या है?
If \(Q={x:x\in \mathbb{Z},,x^2-4x+3=0}\), what is the roster form of (Q)?
#sets
#quadratic
#integers
#roster
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A \(Q=\{1,3\}\)
B \(Q=\{-1,-3\}\)
C \(Q=\{0,3\}\)
D \(Q=\{1,4\}\)
Explanation opens after your attempt
Correct Answer
A. \(Q=\{1,3\}\)
Step 1
Concept
(x-2 -4x+3=(x-1)(x-3)) है। / (x-2 -4x+3=(x-1)(x-3)).
Step 2
Why this answer is correct
अतः (x=1) या (x=3), दोनों पूर्णांक हैं। / Thus (x=1) or (x=3), and both are integers.
Step 3
Exam Tip
समीकरण हल करने के बाद ही सूची रूप लिखें। / Solve the equation first, then write the roster form.
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समुच्चय \(R={x:x\in \mathbb{N},,\sqrt{x}\in \mathbb{N},,10<x<50}\) कौन-सा है?
Which is the set \(R={x:x\in \mathbb{N},,\sqrt{x}\in \mathbb{N},,10<x<50}\)?
#sets
#perfect squares
#roster
#natural numbers
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A \(R=\{16,25,36,49\}\)
B \(R=\{9,16,25,36,49\}\)
C \(R=\{16,25,36\}\)
D \(R=\{11,16,25,36,49\}\)
Explanation opens after your attempt
Correct Answer
A. \(R=\{16,25,36,49\}\)
Step 1
Concept
\(\sqrt{x}\in \mathbb{N}\) का अर्थ है (x) पूर्ण वर्ग है। / \(\sqrt{x}\in \mathbb{N}\) means (x) is a perfect square.
Step 2
Why this answer is correct
(10) और (50) के बीच पूर्ण वर्ग (16,25,36,49) हैं। / The perfect squares between (10) and (50) are (16,25,36,49).
Step 3
Exam Tip
जड़ वाली शर्त में पूर्ण वर्गों की पहचान करें। / For square-root conditions, identify perfect squares.
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कौन-सा समुच्चय \(S=\{-2,-1,0,1,2\}\) के बराबर है?
Which set is equal to \(S=\{-2,-1,0,1,2\}\)?
#sets
#equal sets
#integers
#inequality
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A \({x:x\in \mathbb{Z},,x^2\leq4}\)
B \({x:x\in \mathbb{N},,x^2\leq4}\)
C \({x:x\in \mathbb{Z},,x^2<4}\)
D \({x:x\in \mathbb{Z},,|x|<2}\)
Explanation opens after your attempt
Correct Answer
A. \({x:x\in \mathbb{Z},,x^2\leq4}\)
Step 1
Concept
\(x^2\leq4\) का अर्थ \(-2\leq x\leq2\) है। / \(x^2\leq4\) means \(-2\leq x\leq2\).
Step 2
Why this answer is correct
पूर्णांक मान (-2,-1,0,1,2) मिलते हैं। / The integer values are (-2,-1,0,1,2).
Step 3
Exam Tip
\(\leq\) होने पर सीमा के मान भी शामिल होते हैं। / When \(\leq\) is used, boundary values are included.
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\(यदि (T={x:x\in \mathbb{N},,x\) is a two-digit number and sum of digits is 9}), तो (T) का सूची रूप क्या है?
\(If (T={x:x\in \mathbb{N},,x\) is a two-digit number and sum of digits is 9}), what is the roster form of (T)?
#sets
#digits
#roster
#natural numbers
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A \(T=\{18,27,36,45,54,63,72,81,90\}\)
B \(T=\{9,18,27,36,45,54,63,72,81,90\}\)
C \(T=\{18,27,36,45,54,63,72,81\}\)
D \(T=\{19,28,37,46,55,64,73,82,91\}\)
Explanation opens after your attempt
Correct Answer
A. \(T=\{18,27,36,45,54,63,72,81,90\}\)
Step 1
Concept
दो अंकों की संख्या में दहाई अंक (1) से (9) तक हो सकता है। / In a two-digit number, the tens digit can be (1) to (9).
Step 2
Why this answer is correct
अंकों का योग (9) रखने पर (18,27,36,45,54,63,72,81,90) मिलते हैं। / Making the digit sum (9) gives (18,27,36,45,54,63,72,81,90).
Step 3
Exam Tip
(90) को न भूलें, क्योंकि (9+0=9) है। / Do not miss (90), because (9+0=9).
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समुच्चय \(U={x:x\in \mathbb{Z},,3x+2=11}\) के लिए सही विकल्प क्या है?
What is the correct option for \(U={x:x\in \mathbb{Z},,3x+2=11}\)?
#sets
#linear equation
#integers
#roster
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A \(U=\{2\}\)
B \(U=\{3\}\)
C \(U=\{9\}\)
D \(U=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(U=\{3\}\)
Step 1
Concept
(3x+2=11) से (3x=9) मिलता है। / From (3x+2=11), we get (3x=9).
Step 2
Why this answer is correct
(x=3) है और यह पूर्णांक है, इसलिए \(U=\{3\}\)। / (x=3), which is an integer, so \(U=\{3\}\).
Step 3
Exam Tip
हल मिलने के बाद जांचें कि वह दिए गए संख्या-समूह में आता है या नहीं। / After solving, check whether the solution belongs to the given domain.
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\(यदि (V={x:x\in \mathbb{N},,x\) is a multiple of 4 and \(x<25}), तो सूची रूप क्या है\)?
\(If (V={x:x\in \mathbb{N},,x\) is a multiple of 4 and \(x<25}), what is the roster form\)?
#sets
#multiples
#natural numbers
#roster
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A \(V=\{4,8,12,16,20,24\}\)
B \(V=\{0,4,8,12,16,20,24\}\)
C \(V=\{4,8,12,16,20,24,28\}\)
D \(V=\{8,12,16,20,24\}\)
Explanation opens after your attempt
Correct Answer
A. \(V=\{4,8,12,16,20,24\}\)
Step 1
Concept
(25) से छोटी (4) की धनात्मक गुणज संख्याएं लिखें। / Write positive multiples of (4) less than (25).
Step 2
Why this answer is correct
वे (4,8,12,16,20,24) हैं। / They are (4,8,12,16,20,24).
Step 3
Exam Tip
प्राकृतिक संख्या की परिभाषा में (0) शामिल है या नहीं, प्रश्न के पाठ्यक्रम के अनुसार सावधानी रखें; यहां धनात्मक गुणज लिए गए हैं। / Be careful about whether (0) is included in natural numbers; here the intended positive multiples are listed.
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कौन-सा समुच्चय अनंत समुच्चय है?
Which of the following is an infinite set?
#sets
#infinite set
#even numbers
#conceptual
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A \({x:x\in \mathbb{N},,x<100}\)
B \({x:x\in \mathbb{Z},,-5\leq x\leq5}\)
C \(({x:x\in \mathbb{N},,x\) is even})
D ({x:x is a month of a year})
Explanation opens after your attempt
Correct Answer
C. \(({x:x\in \mathbb{N},,x\) is even})
Step 1
Concept
अनंत समुच्चय में तत्वों की संख्या समाप्त नहीं होती। / An infinite set has no last element.
Step 2
Why this answer is correct
सम प्राकृतिक संख्याएं \(2,4,6,\ldots\) बिना अंत के चलती हैं। / Even natural numbers \(2,4,6,\ldots\) continue without end.
Step 3
Exam Tip
सीमा लगी हो तो अक्सर समुच्चय परिमित होता है। / If a bound is given, the set is often finite.
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यदि \(W={x:x\in \mathbb{Z},,x^2=9}\), तो (W) का सूची रूप है?
If \(W={x:x\in \mathbb{Z},,x^2=9}\), what is the roster form of (W)?
#sets
#squares
#integers
#roster
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A \(W=\{3\}\)
B \(W=\{-3\}\)
C \(W=\{-3,3\}\)
D \(W=\{9\}\)
Explanation opens after your attempt
Correct Answer
C. \(W=\{-3,3\}\)
Step 1
Concept
\(x^2=9\) से \(x=\pm3\) मिलता है। / From \(x^2=9\), we get \(x=\pm3\).
Step 2
Why this answer is correct
दोनों (-3) और (3) पूर्णांक हैं। / Both (-3) and (3) are integers.
Step 3
Exam Tip
वर्ग समीकरण में धनात्मक और ऋणात्मक दोनों मूल जांचें। / For square equations, check both positive and negative roots.
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समुच्चय \(X={x:x=3n-1,,n\in \mathbb{N},,1\leq n\leq5}\) का सूची रूप कौन-सा है?
Which is the roster form of \(X={x:x=3n-1,,n\in \mathbb{N},,1\leq n\leq5}\)?
#sets
#set-builder
#sequence
#roster
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A \(X=\{2,5,8,11,14\}\)
B \(X=\{1,4,7,10,13\}\)
C \(X=\{3,6,9,12,15\}\)
D \(X=\{-1,2,5,8,11\}\)
Explanation opens after your attempt
Correct Answer
A. \(X=\{2,5,8,11,14\}\)
Step 1
Concept
(n=1,2,3,4,5) रखें। / Put (n=1,2,3,4,5).
Step 2
Why this answer is correct
(3n-1) से (2,5,8,11,14) मिलते हैं। / (3n-1) gives (2,5,8,11,14).
Step 3
Exam Tip
सूत्र में (n) की हर कीमत अलग से रखकर सूची बनाएं। / Substitute each allowed value of (n) carefully to form the roster.
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\(यदि (Y={x:x\in \mathbb{N},,x\) is prime and x+2 is also prime\(,,x<20}), तो (Y) क्या है\)?
\(If (Y={x:x\in \mathbb{N},,x\) is prime and x+2 is also prime\(,,x<20}), what is (Y)\)?
#sets
#prime numbers
#conditions
#roster
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A \(Y=\{3,5,11,17\}\)
B \(Y=\{2,3,5,11,17\}\)
C \(Y=\{3,5,7,11,13,17\}\)
D \(Y=\{5,11,17,19\}\)
Explanation opens after your attempt
Correct Answer
A. \(Y=\{3,5,11,17\}\)
Step 1
Concept
(20) से छोटे अभाज्य (2,3,5,7,11,13,17,19) हैं। / Primes less than (20) are (2,3,5,7,11,13,17,19).
Step 2
Why this answer is correct
जिनके साथ (x+2) भी अभाज्य है, वे (3,5,11,17) हैं। / Values for which (x+2) is also prime are (3,5,11,17).
Step 3
Exam Tip
प्रत्येक मान पर दूसरी शर्त अलग से जांचें। / Check the second condition separately for every candidate.
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कौन-सा सूची रूप \(Z={x:x\in \mathbb{Z},,-2\leq x<4}\) के लिए सही है?
Which roster form is correct for \(Z={x:x\in \mathbb{Z},,-2\leq x<4}\)?
#sets
#integers
#inequality
#roster
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A \(Z=\{-2,-1,0,1,2,3,4\}\)
B \(Z=\{-1,0,1,2,3\}\)
C \(Z=\{-2,-1,0,1,2,3\}\)
D \(Z=\{-2,-1,1,2,3\}\)
Explanation opens after your attempt
Correct Answer
C. \(Z=\{-2,-1,0,1,2,3\}\)
Step 1
Concept
बायीं सीमा \(-2\leq x\) होने से (-2) शामिल है। / Since \(-2\leq x\), (-2) is included.
Step 2
Why this answer is correct
दायीं सीमा (x<4) होने से (4) शामिल नहीं है। / Since (x<4), (4) is not included.
Step 3
Exam Tip
पूर्णांक सूची बनाते समय (0) को न छोड़ें। / While listing integers, do not skip (0).
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समुच्चय \(A_1={x:x\in \mathbb{N},,x^2-1=0}\) का सही रूप क्या है?
What is the correct form of \(A_1={x:x\in \mathbb{N},,x^2-1=0}\)?
#sets
#natural numbers
#equation
#roster
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A \(A_1={-1,1}\)
B \(A_1={1}\)
C \(A_1={-1}\)
D \(A_1=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(A_1={1}\)
Step 1
Concept
\(x^2-1=0\) से \(x=\pm1\) मिलता है। / From \(x^2-1=0\), we get \(x=\pm1\).
Step 2
Why this answer is correct
प्राकृतिक संख्या में केवल (1) स्वीकार होगा, (-1) नहीं। / In natural numbers, only (1) is accepted, not (-1).
Step 3
Exam Tip
समीकरण के मूलों को दिए गए संख्या-समूह से जरूर मिलाएं। / Always match the roots with the given domain.
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\(यदि (B_1={x:x\in \mathbb{N},,x\) is a factor of 72 and x is a multiple of \(6}), तो (B_1) क्या है\)?
\(If (B_1={x:x\in \mathbb{N},,x\) is a factor of 72 and x is a multiple of \(6}), what is (B_1)\)?
#sets
#factors
#multiples
#roster
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A \(B_1={6,12,18,24,36,72}\)
B \(B_1={6,12,24,36,72}\)
C \(B_1={6,18,36,54,72}\)
D \(B_1={12,24,36,72}\)
Explanation opens after your attempt
Correct Answer
B. \(B_1={6,12,24,36,72}\)
Step 1
Concept
(72) के भाजक (1,2,3,4,6,8,9,12,18,24,36,72) हैं। / Factors of (72) are (1,2,3,4,6,8,9,12,18,24,36,72).
Step 2
Why this answer is correct
इनमें (6) के गुणज (6,12,24,36,72) हैं। / Among them, multiples of (6) are (6,12,24,36,72).
Step 3
Exam Tip
हर गुणज जरूरी नहीं कि भाजक भी हो, इसलिए दोनों शर्तें जांचें। / Every multiple is not necessarily a factor, so verify both conditions.
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कौन-सा समुच्चय \(C_1={1,8,27,64}\) को सही दर्शाता है?
Which set correctly represents \(C_1={1,8,27,64}\)?
#sets
#cubes
#set-builder
#roster
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A \(C_1={x:x=n^2,,n\in \mathbb{N},,1\leq n\leq4}\)
B \(C_1={x:x=n^3,,n\in \mathbb{N},,1\leq n\leq4}\)
C \(C_1={x:x=2^n,,n\in \mathbb{N},,0\leq n\leq3}\)
D \(C_1={x:x=3n-2,,n\in \mathbb{N},,1\leq n\leq4}\)
Explanation opens after your attempt
Correct Answer
B. \(C_1={x:x=n^3,,n\in \mathbb{N},,1\leq n\leq4}\)
Step 1
Concept
(1,8,27,64) क्रमशः \(1^3,2^3,3^3,4^3\) हैं। / (1,8,27,64) are \(1^3,2^3,3^3,4^3\).
Step 2
Why this answer is correct
इसलिए \(x=n^3\) और \(1\leq n\leq4\) सही है। / Hence \(x=n^3\) with \(1\leq n\leq4\) is correct.
Step 3
Exam Tip
वर्ग और घन में अंतर पहचानना जरूरी है। / Distinguish squares and cubes carefully.
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यदि \(D_1={x:x\in \mathbb{Z},,2<x^2\leq16}\), तो \(D_1\) का सूची रूप क्या होगा?
If \(D_1={x:x\in \mathbb{Z},,2<x^2\leq16}\), what is the roster form of \(D_1\)?
#sets
#integers
#compound inequality
#squares
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A \(D_1={-4,-3,-2,2,3,4}\)
B \(D_1={-4,-3,-2,-1,1,2,3,4}\)
C \(D_1={-3,-2,2,3}\)
D \(D_1={-4,-3,-2,-1,0,1,2,3,4}\)
Explanation opens after your attempt
Correct Answer
A. \(D_1={-4,-3,-2,2,3,4}\)
Step 1
Concept
\(x^2\leq16\) से \(-4\leq x\leq4\) मिलता है। / \(x^2\leq16\) gives \(-4\leq x\leq4\).
Step 2
Why this answer is correct
\(2<x^2\) होने से \(x^2\) के मान (4,9,16) ही चलेंगे, इसलिए \(x=\pm2,\pm3,\pm4\)। / Since \(2<x^2\), only square values (4,9,16) work, so \(x=\pm2,\pm3,\pm4\).
Step 3
Exam Tip
संयुक्त असमानता में दोनों भागों को साथ लागू करें। / Apply both parts of a compound inequality together.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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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