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 251-260 of 606 questions.
A. (576)
चार मोबाइल को एक ब्लॉक मानें, तब (4) इकाइयां हैं। व्यवस्था \(4!\cdot4!=576\) होगी। / Treat the four mobiles as one block, then there are (4) units. The arrangement is \(4!\cdot4!=576\).
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In how many ways can (4) students be called to the prize stage in order from (9) students?
A. (3024)
मंच पर बुलाने का क्रम महत्वपूर्ण है, इसलिए \(^{9}P_4=3024\)। परीक्षा में क्रम बताया हो तो permutation लगाएं। / The calling order to the stage is important, so \(^{9}P_4=3024\). In exams, use permutation when order is specified.
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In how many ways can (10) distinct cards be arranged in a row?
B. (3628800)
(10) अलग वस्तुओं की पंक्ति व्यवस्था (10!) होती है। परीक्षा में सभी वस्तुएं अलग हों तो सीधे factorial लगाएं। / The row arrangement of (10) distinct objects is (10!). In exams, use factorial directly when all objects are distinct.
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In how many ways can a president, secretary and treasurer be chosen from (12) students?
C. (1320)
तीनों पद अलग हैं, इसलिए \(^{12}P_3=1320\)। परीक्षा में अलग पदों के लिए क्रम महत्वपूर्ण होता है। / The three posts are different, so \(^{12}P_3=1320\). In exams, order matters for different posts.
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How many (4)-digit numbers can be formed from (0,1,2,3,4,5,6,7) without repetition?
A. (1470)
पहला अंक (0) नहीं हो सकता, इसलिए \(7\cdot7\cdot6\cdot5=1470\)। परीक्षा में leading zero की शर्त पहले लगाएं। / The first digit cannot be (0), so \(7\cdot7\cdot6\cdot5=1470\). In exams, apply the leading-zero condition first.
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How many (5)-digit even numbers can be formed from (1,2,3,4,5,6,7,8) without repetition?
D. (3360)
अंतिम स्थान पर (4) सम विकल्प हैं और बाकी (4) स्थान \(^{7}P_4\) तरीकों से भरेंगे। कुल \(4\cdot840=3360\) है। / There are (4) even choices for the last place and the remaining (4) places are filled in \(^{7}P_4\) ways. The total is \(4\cdot840=3360\).
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How many distinct arrangements are possible using the letters of (ALGEBRA)?
C. (2520)
(7) अक्षरों में (A) दो बार है, इसलिए \(\frac{7!}{2!}=2520\)। परीक्षा में repeated letters से भाग देना जरूरी है। / There are (7) letters with (A) repeated twice, so \(\frac{7!}{2!}=2520\). In exams, divide by repeated letters.
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In how many ways can (6) boys and (4) girls be seated in a row so that all girls sit together?
B. (120960)
चार लड़कियों को एक ब्लॉक मानें, तब (7) इकाइयां हैं। कुल व्यवस्था \(7!\cdot4!=120960\) है। / Treat the four girls as one block, then there are (7) units. The total arrangement is \(7!\cdot4!=120960\).
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In how many ways can (9) people be seated around a circular table?
A. (40320)
गोल मेज पर घुमाव समान माने जाते हैं, इसलिए संख्या ((9-1)!=40320) है। परीक्षा में circular seating में एक स्थान स्थिर मानें। / Rotations are considered the same around a circular table, so the number is ((9-1)!=40320). In exams, fix one position in circular seating.
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A. (2520)
माला में घुमाव और पलटना दोनों समान हैं, इसलिए (\frac{(8-1)!}{2}=2520)। परीक्षा में necklace में reflection भी घटाएं। / In a necklace, both rotation and reflection are the same, so (\frac{(8-1)!}{2}=2520). In exams, reduce reflections for necklaces.
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