Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 91-100 of 600 questions.
How many distinct words can be formed using all letters of (BIHAR)?
B. (120)
(BIHAR) में (5) अलग अक्षर हैं इसलिए (5!=120)। सभी अक्षर अलग हों तो denominator नहीं लगता। / The word (BIHAR) has (5) distinct letters, so (5!=120). No denominator is needed when all letters are distinct.
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In how many ways can (4) different subjects be arranged in (4) periods on Monday?
C. (24)
(4) अलग विषय (4) अलग पीरियड में (4!=24) तरीकों से लगते हैं। timetable में order महत्त्वपूर्ण होता है। / (4) different subjects can be arranged in (4) different periods in (4!=24) ways. Order matters in a timetable.
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How many (4)-digit numbers can be formed from digits (1,2,3,4,5) without repetition?
D. (120)
चार स्थानों के लिए \(5\times4\times3\times2=120\) तरीके हैं। बिना पुनरावृत्ति में विकल्प घटते जाते हैं। / For four places, there are \(5\times4\times3\times2=120\) ways. Without repetition, choices keep decreasing.
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In how many ways can first, second and third prizes be given to (3) painters from (8) painters?
A. (336)
पुरस्कार अलग हैं इसलिए \({}^{8}P_{3}=8\times7\times6=336\)। अलग पुरस्कारों में order गिना जाता है। / The prizes are distinct, so \({}^{8}P_{3}=8\times7\times6=336\). Order is counted for distinct prizes.
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How many distinct arrangements are there for the word (NOON)?
B. (6)
(N) दो बार और (O) दो बार हैं इसलिए \(\frac{4!}{2!2!}=6\)। दो repeated groups हों तो दोनों से भाग दें। / (N) occurs twice and (O) occurs twice, so \(\frac{4!}{2!2!}=6\). Divide by both repeated groups.
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What will be the value of \({}^{10}P_{0}+{}^{10}P_{1}\)?
C. (11)
\({}^{10}P_{0}=1\) और \({}^{10}P_{1}=10\), इसलिए योग (11) है। आसान योग में पहले values अलग निकालें। / \({}^{10}P_{0}=1\) and \({}^{10}P_{1}=10\), so the sum is (11). In simple sums, find the values separately first.
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In how many ways can (6) different posters be arranged on a wall from left to right?
D. (720)
बाएँ से दाएँ (6) अलग पोस्टरों की व्यवस्था (6!=720) है। linear arrangement में factorial लें। / The left-to-right arrangement of (6) distinct posters is (6!=720). Use factorial in linear arrangement.
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How many (2)-digit even numbers can be formed from digits (2,3,4,5,6) without repetition?
A. (12)
इकाई स्थान पर (2,4,6) में से (3) विकल्प हैं और दहाई पर (4) विकल्प, कुल (12)। even number में इकाई स्थान पहले देखें। / The units place has (3) choices from (2,4,6), and the tens place has (4) choices, total (12). For even numbers, check the units place first.
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How many ways are there to arrange (4) files from (9) different files in order?
B. (3024)
\({}^{9}P_{4}=9\times8\times7\times6=3024\) है। क्रम वाले चयन में \({}^{n}P_{r}\) लगाएं। / \({}^{9}P_{4}=9\times8\times7\times6=3024\). Use \({}^{n}P_{r}\) for ordered selection.
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C. (30)
व्यवस्थाएँ \(\frac{5!}{2!2!}=30\) होंगी। समान अक्षरों को अलग-अलग मानकर गिनती न करें। / The arrangements are \(\frac{5!}{2!2!}=30\). Do not count identical letters as different.
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