Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 61-70 of 608 questions.
How many distinct letter arrangements are possible for the word (APPLE)?
C. (60)
(P) दो बार है इसलिए व्यवस्थाएँ \(\frac{5!}{2!}=60\) होंगी। समान अक्षरों के factorial से भाग दें। / Since (P) occurs twice, arrangements are \(\frac{5!}{2!}=60\). Divide by the factorial of repeated letters.
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In how many ways can (3) people be seated on (5) different chairs?
D. (60)
कुर्सियाँ अलग हैं इसलिए \({}^{5}P_{3}=5\times4\times3=60\)। सीटों का क्रम बदलने से व्यवस्था बदलती है। / The chairs are distinct, so \({}^{5}P_{3}=5\times4\times3=60\). Changing seats changes the arrangement.
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What will be the value of \({}^{6}P_{6}\)?
A. 720
क्रमचय का सूत्र \,\({}^{n}P_r=\frac{n!}{(n-r)!}\) है। अतः \,\({}^{6}P_{6}=\frac{6!}{(6-6)!}=\frac{6!}{0!}=6!=720\), क्योंकि \,\(0!=1\)। विकल्प 120, \,\(5!\) का मान है, इसलिए यह सही नहीं है। परीक्षा टिप: जब \,\(r=n\) हो, तब सीधे \,\({}^{n}P_n=n!\) लिखें। / The permutation formula is \({}^{n}P_r=\frac{n!}{(n-r)!}\). Therefore, \({}^{6}P_{6}=\frac{6!}{(6-6)!}=\frac{6!}{0!}=6!=720\), since \(0!=1\). The option 120 is the value of \(5!\), so it is not correct. Exam tip: when \(r=n\), use \({}^{n}P_n=n!\) directly.
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How many (2)-digit numbers can be formed from digits (0,3,6,9) without repetition?
B. (9)
दहाई स्थान पर (0) नहीं आ सकता, इसलिए \(3\times3=9\) संख्याएँ बनेंगी। संख्या बनाते समय पहले स्थान की शर्त देखें। / Zero cannot be in the tens place, so \(3\times3=9\) numbers are possible. Check the first-place condition in number formation.
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In how many ways can (4) different flowers be placed one each in (4) vases?
C. (24)
(4) अलग फूल (4) अलग स्थानों पर (4!=24) तरीकों से रखे जा सकते हैं। एक-एक वस्तु रखने में व्यवस्था गिनी जाती है। / (4) distinct flowers can be placed in (4) distinct positions in (4!=24) ways. Placing one each counts arrangements.
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How many ways are there to place (3) colours from (7) colours in top, middle and bottom positions?
D. (210)
तीनों स्थान अलग हैं इसलिए \({}^{7}P_{3}=7\times6\times5=210\)। स्थानों के नाम अलग हों तो क्रमचय लें। / The three positions are distinct, so \({}^{7}P_{3}=7\times6\times5=210\). Use permutation when positions have different names.
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How many arrangements of the letters of (NOTE) are possible if the first letter is (N)?
A. (6)
पहला स्थान निश्चित है और शेष (3) अक्षर (3!=6) तरीकों से लगेंगे। fixed position को पहले अलग करें। / The first position is fixed and the remaining (3) letters can be arranged in (3!=6) ways. Separate fixed positions first.
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In how many ways can a captain, vice-captain and wicketkeeper be chosen from (10) players?
B. (720)
तीन पद अलग हैं इसलिए \({}^{10}P_{3}=10\times9\times8=720\)। अलग पदों में order महत्त्वपूर्ण होता है। / The three posts are distinct, so \({}^{10}P_{3}=10\times9\times8=720\). Order matters for different posts.
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How many (2)-digit numbers can be formed from digits (2,5,8) if repetition is allowed?
C. (9)
दोनों स्थानों पर (3) विकल्प हैं इसलिए \(3\times3=9\)। पुनरावृत्ति हो तो विकल्प कम नहीं होते। / There are (3) choices for each place, so \(3\times3=9\). With repetition, choices do not decrease.
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D. (24)
पहला स्थान निश्चित है और शेष (4) बैग (4!=24) तरीकों से लगेंगे। fixed item के बाद बचे items की व्यवस्था करें। / The first position is fixed and the remaining (4) bags can be arranged in (4!=24) ways. Arrange the remaining items after fixing the item.
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