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 201-210 of 608 questions.
A. (3600)
विशेष व्यक्ति के लिए (5) अंदरूनी स्थान हैं और बाकी (6!) तरीकों से बैठेंगे। कुल \(5\cdot6!=3600\) है। / The particular person has (5) inner positions and the others sit in (6!) ways. The total is \(5\cdot6!=3600\).
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How many distinct arrangements can be made from the letters of SAMBHAVNA?
A. (181440)
(9) अक्षरों में (2) अक्षर दो-दो बार आते हैं, इसलिए \(\frac{9!}{2!2!}=90720\); सही गणना में repeated letters को ठीक गिनना जरूरी है। / There are (9) letters with two different letters repeated twice, so \(\frac{9!}{2!2!}=90720\). In exams, accurate repeated-letter counting is essential.
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In how many ways can (4) students be called in speaking order from (8) distinct students?
A. (1680)
भाषण का क्रम महत्वपूर्ण है, इसलिए \(^{8}P_4=1680\)। परीक्षा में order of performance को permutation मानें। / The speaking order is important, so \(^{8}P_4=1680\). In exams, order of performance means permutation.
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How many (4)-digit odd numbers can be formed from (0,1,3,5,7,9) without repetition?
A. (500)
इकाई स्थान पर (5) विषम विकल्प हैं, लेकिन शेष में शुरुआत (0) न हो इसका ध्यान चाहिए। कुल \(5\cdot4\cdot4\cdot3=240\) है। / There are (5) odd choices for the unit place, but the first digit must not be (0). The total is \(5\cdot4\cdot4\cdot3=240\).
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In how many ways can (9) distinct pens be arranged in a row?
C. (362880)
अलग-अलग (9) वस्तुओं की व्यवस्था (9!) होती है। परीक्षा में सभी वस्तुएं अलग हों तो सीधे factorial लगाएं। / The arrangement of (9) distinct objects is (9!). In exams, use factorial directly when all objects are distinct.
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In how many ways can (4) different posts be filled from (8) students?
B. (1680)
अलग पदों में क्रम महत्वपूर्ण है, इसलिए \(^{8}P_4=1680\)। परीक्षा में पद अलग हों तो combination नहीं लगाएं। / Order matters for different posts, so \(^{8}P_4=1680\). In exams, do not use combination when posts are different.
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How many (3)-digit numbers can be formed from (0,1,2,3,4,5,6) without repetition?
D. (180)
सैकड़े के स्थान पर (0) नहीं आएगा, इसलिए \(6\cdot6\cdot5=180\)। परीक्षा में पहले अंक की शून्य-शर्त हमेशा जांचें। / The hundreds place cannot be (0), so \(6\cdot6\cdot5=180\). In exams, always check the zero restriction on the first digit.
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How many (5)-digit numbers can be formed from (1,2,3,4,5,6,7) without repetition and ending in (5)?
A. (360)
अंतिम अंक (5) निश्चित है और बाकी (4) स्थान \(^{6}P_4\) तरीकों से भरेंगे। इसलिए उत्तर (360) है। / The last digit is fixed as (5), and the remaining (4) places are filled in \(^{6}P_4\) ways. So the answer is (360).
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B. (20160)
एक अक्षर (2) बार समान है, इसलिए संख्या \(\frac{8!}{2!}=20160\) होगी। परीक्षा में समान अक्षरों से भाग दें। / One letter is repeated (2) times, so the number is \(\frac{8!}{2!}=20160\). In exams, divide by factorials of repeated letters.
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In how many ways can (7) girls and (3) boys be seated in a row so that all three boys sit together?
C. (241920)
तीनों लड़कों को एक ब्लॉक मानें, तब कुल (8) इकाइयां हैं। व्यवस्था \(8!\cdot3!=241920\) होगी। / Treat the three boys as one block, then there are (8) units. The arrangement is \(8!\cdot3!=241920\).
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