Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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If (2) books are to be selected from (5) books, how many selections are possible?
B. (10)
यह \(\binom{5}{2}=10\) का सरल प्रयोग है। परीक्षा में चयन का क्रम नहीं गिना जाता। / This is a direct use of \(\binom{5}{2}=10\). In exams, order is not counted in selection.
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In how many ways can a team of (3) students be selected from (6) students?
C. (20)
टीम चुनने में क्रम महत्वपूर्ण नहीं होता। इसलिए \(\binom{6}{3}=20\) सही है। / Order is not important while selecting a team. Hence \(\binom{6}{3}=20\) is correct.
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How many ways are there to choose (2) flowers from (7) different flowers?
B. (21)
यह \(\binom{7}{2}=\frac{7\cdot6}{2}=21\) है। ऐसे प्रश्नों में वस्तुओं की जोड़ी बनती है। / It is \(\binom{7}{2}=\frac{7\cdot6}{2}=21\). Such questions form pairs of objects.
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In how many ways can a group of (4) players be formed from (8) players?
C. (70)
समूह में क्रम नहीं होता इसलिए \(\binom{8}{4}=70\) होगा। परीक्षा में समूह शब्द दिखे तो संयोजन लगाएं। / A group has no order, so \(\binom{8}{4}=70\). In exams, the word group usually indicates combination.
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How many ways are there to select (1) question from (9) questions?
C. (9)
एक वस्तु चुनने पर \(\binom{9}{1}=9\) होता है। \(\binom{n}{1}=n\) याद रखें। / Selecting one object gives \(\binom{9}{1}=9\). Remember \(\binom{n}{1}=n\).
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Why is selecting (0) pens from (10) pens considered one way?
A. क्योंकि \(\binom{10}{0}=1\)Because \(\binom{10}{0}=1\)
कुछ भी न चुनना भी एक निश्चित चयन है। इसलिए \(\binom{n}{0}=1\) होता है। / Choosing nothing is also one definite selection. Therefore \(\binom{n}{0}=1\).
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How many ways are there to choose all (5) colors from (5) colors?
B. (1)
सभी वस्तुएं चुनने का केवल एक तरीका होता है। इसलिए \(\binom{5}{5}=1\) है। / There is only one way to choose all objects. Hence \(\binom{5}{5}=1\).
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In how many ways can a pair of friends be selected from (6) friends?
B. (15)
जोड़ी के लिए \(\binom{6}{2}=15\) होगा। जोड़ी में पहला और दूसरा अलग नहीं गिने जाते। / For a pair, \(\binom{6}{2}=15\). In a pair, first and second are not counted separately.
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From (4) boys and (3) girls, in how many ways can (1) boy and (1) girl be selected?
B. (12)
चयन \(\binom{4}{1}\binom{3}{1}=12\) है। अलग-अलग वर्गों से चयन में गुणा करते हैं। / The selection is \(\binom{4}{1}\binom{3}{1}=12\). Multiply choices when selecting from different groups.
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From (5) boys and (4) girls, how many ways are there to select (2) boys?
A. (10)
केवल लड़कों में से चयन है इसलिए \(\binom{5}{2}=10\) होगा। अनावश्यक सूचना से भ्रमित न हों। / Only boys are being selected, so \(\binom{5}{2}=10\). Do not get confused by extra information.
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