\(यदि (T={x:x\in \mathbb{N},,x\) 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
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).
Login to save your score, XP, coins and progress. Login
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
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.
Login to save your score, XP, coins and progress. Login
\(यदि (V={x:x\in \mathbb{N},,x\) 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
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.
Login to save your score, XP, coins and progress. Login
कौन-सा समुच्चय अनंत समुच्चय है?
Which of the following is an infinite set?
#sets
#infinite set
#even numbers
#conceptual
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.
Login to save your score, XP, coins and progress. Login
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
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.
Login to save your score, XP, coins and progress. Login
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
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.
Login to save your score, XP, coins and progress. Login
\(यदि (Y={x:x\in \mathbb{N},,x\) 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.
Login to save your score, XP, coins and progress. Login
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).
Login to save your score, XP, coins and progress. Login
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.
Login to save your score, XP, coins and progress. Login
\(यदि (B_1={x:x\in \mathbb{N},,x\) 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.
Login to save your score, XP, coins and progress. Login
