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 21-30 of 600 questions.
How many ways are there to select (3) chairs from (7) chairs?
B. (35)
चयन में व्यवस्था नहीं करनी है इसलिए \(\binom{7}{3}=35\) है। कुर्सियां चुनना संयोजन है। / No arrangement is required, so \(\binom{7}{3}=35\). Choosing chairs is a combination.
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B. (78)
समिति के लिए केवल चयन है इसलिए \(\binom{13}{2}=78\) होगा। पद अलग न हों तो क्रम नहीं गिना जाता। / It is only selection for a committee, so \(\binom{13}{2}=78\). If posts are not different, order is not counted.
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How many ways are there to choose (4) subjects from (6) subjects?
C. (15)
\(\binom{6}{4}=\binom{6}{2}=15\) होता है। \(\binom{n}{r}=\binom{n}{n-r}\) याद रखें। / \(\binom{6}{4}=\binom{6}{2}=15\). Remember \(\binom{n}{r}=\binom{n}{n-r}\).
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What is the value of \(\binom{8}{2}\)?
C. (28)
\(\binom{8}{2}=\frac{8\cdot7}{2}=28\) है। दो वस्तुओं के चयन का सूत्र तेज होता है। / \(\binom{8}{2}=\frac{8\cdot7}{2}=28\). The formula for choosing two objects is quick.
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Find the value of \(\binom{10}{3}\).
C. (120)
\(\binom{10}{3}=\frac{10\cdot9\cdot8}{3\cdot2\cdot1}=120\) है। छोटे (r) के लिए सीधे गुणा करें। / \(\binom{10}{3}=\frac{10\cdot9\cdot8}{3\cdot2\cdot1}=120\). For small (r), multiply directly.
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What will be the value of \(\binom{9}{0}\)?
B. (1)
किसी भी (n) के लिए \(\binom{n}{0}=1\) होता है। यह संयोजन की मूल पहचान है। / For any (n), \(\binom{n}{0}=1\). This is a basic identity of combinations.
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What is the value of \(\binom{7}{7}\)?
B. (1)
सभी (7) वस्तुओं को चुनने का केवल एक तरीका है। अतः \(\binom{7}{7}=1\) है। / There is only one way to choose all (7) objects. Therefore \(\binom{7}{7}=1\).
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What is the value of \(\binom{12}{1}\)?
C. (12)
\(\binom{n}{1}=n\) होता है। इसलिए \(\binom{12}{1}=12\) सही है। / \(\binom{n}{1}=n\). Hence \(\binom{12}{1}=12\) is correct.
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Find the value of \(\binom{9}{2}\).
B. (36)
\(\binom{9}{2}=\frac{9\cdot8}{2}=36\) है। दो वस्तुओं के चयन में (2!) से भाग देना न भूलें। / \(\binom{9}{2}=\frac{9\cdot8}{2}=36\). Do not forget to divide by (2!) when choosing two objects.
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What is the value of \(\binom{11}{1}+\binom{11}{0}\)?
C. (12)
मान \(\binom{11}{1}=11\) और \(\binom{11}{0}=1\) हैं। कुल (12) होगा। / The values are \(\binom{11}{1}=11\) and \(\binom{11}{0}=1\). The total is (12).
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