काठमाडौं विश्वविद्यालय KUUMAT / KU CBT तयारी
काठमाडौं विश्वविद्यालय – KUUMAT / KU CBT
KUUMAT / KU CBT · Kathmandu University (KUUMAT / KU CBT)
३,८४१ प्रश्न उपलब्ध। मोड छान्नुहोस्:
BE/B.Arch प्रवेश: प्रश्न र उत्तर
सही लागेको विकल्पमा थिच्नुहोस्। सही भए हरियो, गलत भए रातो देखिन्छ; ३ सेकेन्डपछि सही उत्तर र व्याख्या देखिन्छ।
सही: ० / ०
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How many 5-letter arrangements (meaningful or not, no letter repeated) can be formed using 2 vowels and 3 consonants chosen from 5 vowels and 7 consonants?
सही उत्तर: ख) 42000
Choose ⁵C₂ × ⁷C₃ = 10 × 35 = 350 sets of letters and arrange each in 5! = 120 ways: 350 × 120 = 42000.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In how many ways can 6 students be allotted to 3 different rooms so that each room gets exactly 2 students?
सही उत्तर: क) 90
6!/(2!·2!·2!) = 720/8 = 90 (the rooms are distinct, so we do not divide by 3!).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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From 5 mathematics books and 4 physics books, in how many ways can 2 mathematics books and 1 physics book be selected?
सही उत्तर: ग) 40
⁵C₂ × ⁴C₁ = 10 × 4 = 40.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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How many 4-digit numbers greater than 5000 can be formed from the digits 0, 1, 3, 5, 7 without repetition?
सही उत्तर: घ) 48
The first digit must be 5 or 7 (2 ways); the remaining 3 places are filled from the other 4 digits in ⁴P₃ = 24 ways: 2 × 24 = 48.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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There are 10 points in a plane, of which exactly 4 are collinear (no other three collinear). The number of distinct straight lines through pairs of these points is:
सही उत्तर: क) 40
C(10, 2) − C(4, 2) + 1 = 45 − 6 + 1 = 40, since the 4 collinear points give only one line.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In how many arrangements of the letters of the word EQUATION do all the vowels come together?
सही उत्तर: ख) 2880
Treat the 5 vowels (E, U, A, I, O) as one block with Q, T, N: 4! arrangements, times 5! inside the block = 24 × 120 = 2880.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The 4th term of the harmonic progression 1/2, 1/5, 1/8, ... is:
सही उत्तर: ख) 1/11
The reciprocals 2, 5, 8, ... form an AP with d = 3; its 4th term is 11, so the HP's 4th term is 1/11.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Three geometric means are inserted between 2 and 162. The middle one of them is:
सही उत्तर: क) 18
2r⁴ = 162 gives r = 3, so the means are 6, 18, 54 and the middle one is 18.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The sum to infinity of 1/(1·3) + 1/(2·4) + 1/(3·5) + 1/(4·6) + ... is:
सही उत्तर: घ) 3/4
1/(n(n + 2)) = ½(1/n − 1/(n + 2)); the sum telescopes to ½(1 + 1/2) = 3/4.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The sum of the infinite series 1/2 + 2/4 + 3/8 + 4/16 + ... is:
सही उत्तर: ग) 2
Σ n xⁿ = x/(1 − x)²; with x = 1/2 this gives (1/2)/(1/4) = 2.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
यी अभ्यास प्रश्न हुन्, आधिकारिक प्रश्न होइनन्। पाठ्यक्रम, विज्ञापन र नतिजाका लागि सम्बन्धित निकायको आधिकारिक वेबसाइट हेर्नुहोस्। उत्तरमा गल्ती भेटे प्रश्नमुनिको "टिप्पणी / गल्ती रिपोर्ट" मा लेख्नुहोस्।
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