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 31-40 of 600 questions.
If \(\binom{n}{1}=14\), what is the value of (n)?
C. (14)
\(\binom{n}{1}=n\) होता है। इसलिए (n=14) मिलेगा। / \(\binom{n}{1}=n\). Therefore (n=14).
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If \(\binom{n}{0}=1\), for which (n) is it true?
C. हर \(n\geq0\)Every \(n\geq0\)
शून्य वस्तु चुनने का एक तरीका हर \(n\geq0\) के लिए होता है। यह मूल नियम है। / There is one way to choose zero objects for every \(n\geq0\). This is a basic rule.
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What is the relation between \(\binom{6}{2}\) and \(\binom{6}{4}\)?
A. दोनों बराबर हैंThey are equal
क्योंकि \(\binom{n}{r}=\binom{n}{n-r}\) होता है। यहां (r=2) और (n-r=4) हैं। / Because \(\binom{n}{r}=\binom{n}{n-r}\). Here (r=2) and (n-r=4).
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What is the value of \(\binom{5}{2}+\binom{5}{3}\)?
C. (20)
\(\binom{5}{2}=10\) और \(\binom{5}{3}=10\) हैं। इसलिए कुल (20) है। / \(\binom{5}{2}=10\) and \(\binom{5}{3}=10\). Therefore the total is (20).
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B. (12)
चयन \(\binom{3}{1}\binom{4}{1}=12\) है। अलग प्रकारों में चयन की संख्याएं गुणा होती हैं। / The selection is \(\binom{3}{1}\binom{4}{1}=12\). Choices from different types are multiplied.
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From (5) pens and (6) pencils, in how many ways can (2) pens and (1) pencil be selected?
C. (60)
तरीके \(\binom{5}{2}\binom{6}{1}=10\cdot6=60\) हैं। प्रत्येक समूह से चयन अलग-अलग करें। / The ways are \(\binom{5}{2}\binom{6}{1}=10\cdot6=60\). Select from each group separately.
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From (4) white and (5) black balls, in how many ways can (2) black balls be selected?
A. (10)
केवल काली गेंदों में से चयन है इसलिए \(\binom{5}{2}=10\) होगा। बाकी सूचना केवल संदर्भ है। / Only black balls are selected, so \(\binom{5}{2}=10\). The remaining information is only context.
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B. (28)
यह \(\binom{8}{2}=28\) है। कार्य समान हो तो चयन में क्रम नहीं गिना जाता। / This is \(\binom{8}{2}=28\). If the work is same, order is not counted in selection.
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How many ways are there to select (5) students from (6) students for a competition?
B. (6)
\(\binom{6}{5}=\binom{6}{1}=6\) है। कभी-कभी न चुने गए व्यक्ति को गिनना आसान होता है। / \(\binom{6}{5}=\binom{6}{1}=6\). Sometimes counting the person not selected is easier.
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In how many ways can a set of (3) questions be made from (10) different questions?
C. (120)
प्रश्नों का सेट बनाना चयन है। इसलिए \(\binom{10}{3}=120\) सही है। / Making a set of questions is selection. Hence \(\binom{10}{3}=120\) is correct.
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