\(यदि (Y={x:x\in \mathbb{N},,x\) 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
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
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
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
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
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
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
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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