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 581-590 of 600 questions.
B. (450)
(3) के (5) गुणज और (10) गैर-गुणज हैं। चयन \(^{5}C_{2}\times{}^{10}C_{2}=450\) होगा। / There are (5) multiples of (3) and (10) non-multiples. The selection count is \(^{5}C_{2}\times{}^{10}C_{2}=450\).
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How many rectangles are there in a grid of small squares with (5) rows and (6) columns?
C. (315)
आयत के लिए (6) क्षैतिज रेखाओं में से (2) और (7) ऊर्ध्व रेखाओं में से (2) चुनें। संख्या \(^{6}C_{2}\times{}^{7}C_{2}=315\)। / For a rectangle, choose (2) horizontal lines from (6) and (2) vertical lines from (7). The count is \(^{6}C_{2}\times{}^{7}C_{2}=315\).
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(10) students are to be divided into two unnamed groups of (5) and (5). How many ways are possible?
A. (126)
पहले (5) विद्यार्थी \(^{10}C_{5}\) तरीकों से चुने जाते हैं। दो समूह अनाम हैं, इसलिए (2) से भाग दें और उत्तर (126) है। / First choose (5) students in \(^{10}C_{5}\) ways. Since the two groups are unnamed, divide by (2) to get (126).
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D. (210)
पहले (4) लोगों को \(^{8}C_{4}\) तरीकों से चुनें और उन्हें (3) तरीकों से दो जोड़ों में बांटें। कुल \(70\times3=210\)। / First choose (4) people in \(^{8}C_{4}\) ways and split them into two pairs in (3) ways. Total \(70\times3=210\).
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B. (240)
पहले (6) जोड़ों में से (4) जोड़े चुनें और हर चुने जोड़े से (1) व्यक्ति चुनें। संख्या \(^{6}C_{4}\times2^{4}=240\)। / Choose (4) couples from (6) and then choose (1) person from each selected couple. The number is \(^{6}C_{4}\times2^{4}=240\).
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A. (163)
एक जैसी टॉफियों की संख्या (0) से (4) तक हो सकती है। योग \(^{8}C_{4}+^{8}C_{3}+^{8}C_{2}+^{8}C_{1}+1=163\)। / The number of identical candies can be from (0) to (4). Sum \(^{8}C_{4}+^{8}C_{3}+^{8}C_{2}+^{8}C_{1}+1=163\).
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C. (246)
पत्रिकाएं (2), (3), या (4) ली जा सकती हैं। इसलिए संख्या \(^{9}C_{4}+^{9}C_{3}+^{9}C_{2}=246\)। / The number of magazines can be (2), (3), or (4). Hence the count is \(^{9}C_{4}+^{9}C_{3}+^{9}C_{2}=246\).
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D. (20)
हर डिब्बे में पहले (1) गेंद रखें। बची (3) गेंदों का वितरण \(^{6}C_{3}=20\) तरीकों से होगा। / Place (1) ball in each box first. The remaining (3) balls can be distributed in \(^{6}C_{3}=20\) ways.
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B. (10)
कुल \(^{11}C_{2}=55\) वितरण हैं। किसी एक डिब्बे में कम से कम (5) गेंदें होने वाले \(3\times{}^{6}C_{2}=45\) घटाएं, उत्तर (10)। / Total distributions are \(^{11}C_{2}=55\). Subtract \(3\times{}^{6}C_{2}=45\) cases where one box has at least (5) balls, giving (10).
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How many subsets with exactly (5) elements does a set of (12) elements have?
A. (792)
ठीक (5) तत्वों वाला उपसमुच्चय चुनना (12) में से (5) तत्व चुनना है। संख्या \(^{12}C_{5}=792\) है। / Choosing a subset with exactly (5) elements means choosing (5) elements from (12). The number is \(^{12}C_{5}=792\).
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