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 101-110 of 606 questions.
How many ways are there to arrange (4) files from (9) different files in order?
B. (3024)
\({}^{9}P_{4}=9\times8\times7\times6=3024\) है। क्रम वाले चयन में \({}^{n}P_{r}\) लगाएं। / \({}^{9}P_{4}=9\times8\times7\times6=3024\). Use \({}^{n}P_{r}\) for ordered selection.
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C. (30)
व्यवस्थाएँ \(\frac{5!}{2!2!}=30\) होंगी। समान अक्षरों को अलग-अलग मानकर गिनती न करें। / The arrangements are \(\frac{5!}{2!2!}=30\). Do not count identical letters as different.
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In how many ways can (8) different trophies be arranged in a straight row in a showcase?
A. (40320)
(8) अलग वस्तुओं की व्यवस्था (8!=40320) होती है। सभी अलग वस्तुओं के लिए factorial लगाएं। / The arrangement of (8) distinct objects is (8!=40320). Use factorial for all distinct objects.
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B. (132)
दो पद अलग हैं इसलिए \({}^{12}P_{2}=12\times11=132\)। अलग पदों में क्रम महत्त्वपूर्ण होता है। / The two posts are distinct, so \({}^{12}P_{2}=12\times11=132\). Order matters for different posts.
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How many distinct words can be formed using all letters of the word (TRAIN)?
C. (120)
(TRAIN) में (5) अलग अक्षर हैं इसलिए (5!=120)। सभी अक्षर अलग हों तो denominator नहीं लगता। / The word (TRAIN) has (5) distinct letters, so (5!=120). No denominator is needed when all letters are distinct.
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How many (3)-digit numbers can be formed from digits (2,3,5,7) without repetition?
D. (24)
तीन स्थानों के लिए \(4\times3\times2=24\) तरीके हैं। बिना पुनरावृत्ति में हर अगला विकल्प घटता है। / For three places, there are \(4\times3\times2=24\) ways. Without repetition, each next choice decreases.
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What is the value of \({}^{11}P_{2}\)?
A. (110)
\({}^{11}P_{2}=11\times10=110\) होता है। (r=2) होने पर दो घटते गुणनखंड लें। / \({}^{11}P_{2}=11\times10=110\). When (r=2), take two decreasing factors.
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B. (210)
बजाने का क्रम महत्त्वपूर्ण है इसलिए \({}^{7}P_{3}=7\times6\times5=210\)। क्रम बदलने से सूची बदल जाती है। / Playing order matters, so \({}^{7}P_{3}=7\times6\times5=210\). Changing the order changes the list.
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The word (PAPER) has (P) twice. How many distinct letter arrangements are possible?
C. (60)
(P) दो बार समान है इसलिए व्यवस्थाएँ \(\frac{5!}{2!}=60\) होंगी। समान अक्षर के factorial से भाग दें। / Since (P) occurs twice, arrangements are \(\frac{5!}{2!}=60\). Divide by the factorial of the repeated letter.
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In how many ways can (2) students be seated at (6) different desks?
D. (30)
मेजें अलग हैं इसलिए \({}^{6}P_{2}=6\times5=30\)। अलग स्थानों पर बैठाने में क्रम गिना जाता है। / The desks are distinct, so \({}^{6}P_{2}=6\times5=30\). Order is counted when seating at distinct places.
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