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 281-290 of 606 questions.
A. (360)
हजार स्थान पर (7,8,9) में से (3) विकल्प हैं और बाकी \(6\cdot5\cdot4\) तरीके हैं। कुल (360) है। / The thousands place has (3) choices from (7,8,9), and the remaining places have \(6\cdot5\cdot4\) ways. The total is (360).
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In how many ways can (7) distinct prizes be distributed one each among (5) students?
A. (2520)
(5) विद्यार्थियों को (7) पुरस्कारों में से क्रमित रूप से एक-एक मिलेगा, इसलिए \(^{7}P_5=2520\)। परीक्षा में recipients अलग हों तो permutation लें। / The (5) students receive one prize each from (7) prizes in an ordered way, so \(^{7}P_5=2520\). In exams, distinct recipients imply permutation.
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In how many ways can (4) books be selected from (9) distinct books and arranged on a shelf?
A. (3024)
पुस्तकें चुनी भी जा रही हैं और क्रम में रखी भी जा रही हैं, इसलिए \(^{9}P_4=3024\)। परीक्षा में shelf arrangement में क्रम गिनें। / The books are selected and arranged in order, so \(^{9}P_4=3024\). In exams, count order in shelf arrangements.
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In how many ways can (3) students be called in speaking order from (8) students?
A. (336)
भाषण का क्रम महत्वपूर्ण है, इसलिए \(^{8}P_3=336\)। परीक्षा में order of performance को permutation मानें। / The speaking order is important, so \(^{8}P_3=336\). In exams, treat order of performance as permutation.
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How many (4)-digit numbers divisible by (5) can be formed from (0,1,2,3,4,5,6) without repetition?
B. (180)
अंतिम अंक (0) या (5) होगा। cases जोड़ने पर (120+100=220) संख्याएं मिलती हैं। / The last digit is (0) or (5). Adding the cases gives (120+100=220) numbers.
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A. (120)
तीसरा स्थान निश्चित है, इसलिए शेष (5) अंक (5!) तरीकों से रखे जाएंगे। उत्तर (120) है। / The third position is fixed, so the remaining (5) digits are arranged in (5!) ways. The answer is (120).
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B. (40320)
अंतिम स्थान निश्चित है, इसलिए शेष (8) वस्तुएं (8!) तरीकों से रखें। उत्तर (40320) है। / The last position is fixed, so the remaining (8) objects are arranged in (8!) ways. The answer is (40320).
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A. (38880)
कुल (8!) में से दोनों विशेष सिक्कों के सिरों पर आने वाली \(2!\cdot6!\) व्यवस्थाएं घटाएं। उत्तर (40320-1440=38880) है। / Subtract the cases where the two particular coins occupy the two ends, which are \(2!\cdot6!\), from total (8!). The answer is (40320-1440=38880).
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In how many ways can (7) distinct students be seated one each on (7) distinct benches?
A. (5040)
(7) विद्यार्थियों को (7) अलग स्थानों पर बैठाने की संख्या (7!=5040) है। परीक्षा में positions अलग हों तो factorial लगाएं। / The number of seating (7) students in (7) distinct positions is (7!=5040). In exams, use factorial when positions are distinct.
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In how many ways can (2) letters be selected in order from (15) letters?
A. (210)
क्रमित चयन \(^{15}P_2=15\cdot14=210\) है। परीक्षा में in order लिखा हो तो permutation लगाएं। / Ordered selection is \(^{15}P_2=15\cdot14=210\). In exams, use permutation when in order is given.
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