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 arrangements are formed from the letters of the word (SUN)?
B. (6)
(SUN) में (3) अलग अक्षर हैं इसलिए (3!=6)। छोटे शब्दों में अक्षर गिनकर factorial लगाएं। / The word (SUN) has (3) distinct letters, so (3!=6). Count the letters and apply factorial for small words.
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What is the value of \({}^{10}P_{1}\)?
C. (10)
\({}^{n}P_{1}=n\) होता है इसलिए \({}^{10}P_{1}=10\)। एक पद की व्यवस्था में सीधे (n) लिखें। / Since \({}^{n}P_{1}=n\), \({}^{10}P_{1}=10\). For one position, write (n) directly.
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In how many ways can (2) pictures from (6) pictures be placed in first and second positions?
D. (30)
पहले स्थान के लिए (6) और दूसरे के लिए (5) विकल्प हैं इसलिए \(6\times5=30\)। स्थान अलग-अलग हों तो क्रम गिनें। / There are (6) choices for the first position and (5) for the second, so \(6\times5=30\). Count order when positions are distinct.
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If (n=5) and (r=2), what is the value of \({}^{n}P_{r}\)?
A. (20)
\({}^{5}P_{2}=5\times4=20\)। (n) से शुरू करके (r) तक घटते गुणनखंड लें। / \({}^{5}P_{2}=5\times4=20\). Start from (n) and take (r) decreasing factors.
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How many ways are there to arrange (3) cards selected from (5) different cards in order?
B. (60)
यह \({}^{5}P_{3}=5\times4\times3=60\) है। कार्डों का क्रम बदलने से व्यवस्था बदलती है। / This is \({}^{5}P_{3}=5\times4\times3=60\). Changing the order of cards changes the arrangement.
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The word (BOOK) has (4) letters and (O) occurs twice. How many distinct arrangements are possible?
C. (12)
दो समान (O) होने से व्यवस्थाएँ \(\frac{4!}{2!}=12\) होंगी। समान वस्तुओं के लिए factorial से भाग दें। / Because two (O)'s are identical, arrangements are \(\frac{4!}{2!}=12\). For identical objects, divide by their factorial.
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In how many ways can (3) people be made to stand in a row from (4) people?
D. (24)
यह \({}^{4}P_{3}=4\times3\times2=24\) है। पंक्ति में खड़ा करना ordered arrangement है। / This is \({}^{4}P_{3}=4\times3\times2=24\). Standing in a row is an ordered arrangement.
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How many ways are possible to place (6) different balls in a row?
A. (720)
(6) अलग गेंदों की व्यवस्था (6!=720) है। सभी वस्तुएँ अलग हों तो कुल व्यवस्था factorial होती है। / The arrangement of (6) distinct balls is (6!=720). If all objects are distinct, total arrangements are factorial.
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How many (2)-digit numbers can be formed from digits (0,1,2) without repetition?
B. (4)
दहाई स्थान पर (0) नहीं आ सकता इसलिए (2) विकल्प और इकाई पर (2) विकल्प हैं, कुल (4)। संख्या बनाते समय पहले स्थान पर (0) की जाँच करें। / Zero cannot be in the tens place, so there are (2) choices for tens and (2) for units, total (4). In number formation, check zero in the first place.
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What will be the value of \({}^{8}P_{0}\)?
C. (1)
\({}^{n}P_{0}=1\) इसलिए \({}^{8}P_{0}=1\)। शून्य वस्तुओं की arrangement एक मानी जाती है। / \({}^{n}P_{0}=1\), so \({}^{8}P_{0}=1\). The arrangement of zero objects is counted as one.
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