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 51-60 of 600 questions.
How many ways are there to select a pair of (2) students from (15) students?
A. (105)
जोड़ी चुनने के तरीके \(\binom{15}{2}=105\) हैं। जोड़ी में क्रम नहीं गिना जाता। / The number of ways is \(\binom{15}{2}=105\). Order is not counted in a pair.
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In how many ways can a team of (6) students be selected from (8) students?
B. (28)
\(\binom{8}{6}=\binom{8}{2}=28\) होता है। अधिक चुनना हो तो न चुने गए लोगों को गिनना आसान होता है। / \(\binom{8}{6}=\binom{8}{2}=28\). When many are selected, counting those not selected is easier.
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In how many ways can a set of (3) books be made from (9) books?
C. (84)
सेट बनाने में क्रम का महत्व नहीं होता। इसलिए \(\binom{9}{3}=84\) सही है। / Order is not important while making a set. Hence \(\binom{9}{3}=84\) is correct.
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In how many ways can a practice group of (4) players be selected from (11) players?
B. (165)
यह चयन है इसलिए \(\binom{11}{4}=330\) नहीं बल्कि सही मान \(\binom{11}{4}=330\) है। विकल्पों में सही उत्तर (330) है। / This is selection, so the value is \(\binom{11}{4}=330\). The correct option is (330).
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How many ways are there to choose (3) pens from (12) pens?
C. (220)
तीन पेन चुनने के तरीके \(\binom{12}{3}=220\) हैं। चयन में पेन का क्रम नहीं देखा जाता। / The number of ways is \(\binom{12}{3}=220\). The order of pens is not considered in selection.
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How many ways are there to select (7) questions from (10) questions?
A. (120)
\(\binom{10}{7}=\binom{10}{3}=120\) है। पूरक चयन से गणना जल्दी होती है। / \(\binom{10}{7}=\binom{10}{3}=120\). Complementary selection makes calculation faster.
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From (5) boys and (4) girls, in how many ways can (2) boys and (2) girls be selected?
C. (60)
तरीके \(\binom{5}{2}\binom{4}{2}=10\cdot6=60\) हैं। अलग वर्गों से चयन में गुणा करते हैं। / The ways are \(\binom{5}{2}\binom{4}{2}=10\cdot6=60\). Multiply selections from different groups.
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From (6) red and (5) blue balls, in how many ways can (2) red and (1) blue ball be selected?
D. (75)
तरीके \(\binom{6}{2}\binom{5}{1}=15\cdot5=75\) हैं। रंग अलग हों तो चयन अलग-अलग करें। / The ways are \(\binom{6}{2}\binom{5}{1}=15\cdot5=75\). Select separately when colors are different.
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From (7) men and (3) women, in how many ways can (1) man and (2) women be selected?
B. (21)
तरीके \(\binom{7}{1}\binom{3}{2}=7\cdot3=21\) हैं। प्रत्येक शर्त को अलग संयोजन से लिखें। / The ways are \(\binom{7}{1}\binom{3}{2}=7\cdot3=21\). Write each condition as a separate combination.
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C. (40)
तरीके \(\binom{4}{1}\binom{5}{2}=4\cdot10=40\) हैं। अलग विषयों के चयन में गुणा नियम लगता है। / The ways are \(\binom{4}{1}\binom{5}{2}=4\cdot10=40\). The multiplication rule applies to selections from different subjects.
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