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 501-510 of 600 questions.
If \(^{n}C_{3}=4,^{n}C_{2}\), what is the value of (n)?
B. (14)
अनुपात \(\frac{^{n}C_{3}}{^{n}C_{2}}=\frac{n-2}{3}\) होगा, इसलिए (n=14)। परीक्षा में पहले अनुपात लिखें। / The ratio is \(\frac{^{n}C_{3}}{^{n}C_{2}}=\frac{n-2}{3}\), so (n=14). In exams write the ratio first.
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If \(^{n}C_{4}=^{n}C_{6}\), what is the value of (n)?
C. (10)
समान (n) के लिए \(^{n}C_{r}=^{n}C_{s}\) होने पर (r=s) या (r+s=n)। यहां (n=10) है। / For same (n), \(^{n}C_{r}=^{n}C_{s}\) implies (r=s) or (r+s=n). Here (n=10).
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If \(^{12}C_{r}=^{12}C_{r+4}\), what is the value of (r)?
B. (4)
समानता में (r+(r+4)=12) होगा। इससे (r=4) मिलता है। / In the equality, (r+(r+4)=12). Hence (r=4).
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If \(^{n}C_{2}=66\), what is the value of \(^{n}C_{4}\)?
A. (495)
\(^{n}C_{2}=66\) से (n=12) मिलता है। इसलिए \(^{12}C_{4}=495\)। / From \(^{n}C_{2}=66\), (n=12). Therefore \(^{12}C_{4}=495\).
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If \(^{n}C_{5}:^{n}C_{4}=7:2\), what is the value of (n)?
D. (21)
\(\frac{^{n}C_{5}}{^{n}C_{4}}=\frac{n-4}{5}=\frac{7}{2}\) से (n=21.5) नहीं आता, इसलिए सही अनुपात जांचना जरूरी है। यहां कोई पूर्णांक (n) संभव नहीं है। / \(\frac{^{n}C_{5}}{^{n}C_{4}}=\frac{n-4}{5}=\frac{7}{2}\) gives no integer (n). Always check validity of the ratio.
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C. (372)
दोनों विशेष चुने जाएं तो \(^{10}C_{3}\), और दोनों न चुने जाएं तो \(^{10}C_{5}\)। कुल (120+252=372)। / If both special students are selected, count \(^{10}C_{3}\); if both are not selected, count \(^{10}C_{5}\). Total (120+252=372).
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C. (560)
मामले (3W2M), (4W1M), (5W0M) हैं। मान \(^{6}C_{3}{}^{8}C_{2}+^{6}C_{4}{}^{8}C_{1}+^{6}C_{5}=560\)। / Cases are (3W2M), (4W1M), and (5W0M). The value is \(^{6}C_{3}{}^{8}C_{2}+^{6}C_{4}{}^{8}C_{1}+^{6}C_{5}=560\).
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C. (182)
कुल \(^{10}C_{4}=210\) हैं। दोनों विशेष साथ होने वाले \(^{8}C_{2}=28\) हटाएं, उत्तर (182)। / Total selections are \(^{10}C_{4}=210\). Remove \(^{8}C_{2}=28\) selections containing both special players, giving (182).
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B. (25)
कुल \(^{7}C_{4}=35\) हैं। दोनों निर्धारित पुस्तकें साथ होने पर \(^{5}C_{2}=10\) चयन हटेंगे। / Total selections are \(^{7}C_{4}=35\). If both specified books are together, \(^{5}C_{2}=10\) selections are removed.
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There are (9) points with no (3) collinear. How many triangles can be formed?
C. (84)
त्रिभुज के लिए (3) बिंदु चाहिए। इसलिए संख्या \(^{9}C_{3}=84\) है। / A triangle needs (3) points. Hence the number is \(^{9}C_{3}=84\).
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