गणित (Mathematics) – Mathematics MCQ
गणित (Mathematics) – इन्जिनियरिङ प्रवेश
Mathematics · Engineering Entrance – Mathematics, Physics, Chemistry & English · १,३०८ प्रश्न
१,३०८ प्रश्न उपलब्ध। मोड छान्नुहोस्:
गणित (Mathematics): 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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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)
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How many terms of the geometric progression 3, 6, 12, ... must be added to give a sum of 381?
सही उत्तर: ग) 7
3(2ⁿ − 1) = 381 ⇒ 2ⁿ = 128 ⇒ n = 7.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The sum of the first n terms of a sequence is Sₙ = 2n² + 3n. Its 10th term is:
सही उत्तर: क) 41
t₁₀ = S₁₀ − S₉ = 230 − 189 = 41.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If α, β, γ are the roots of 2x³ − 3x² + 5x − 1 = 0, then αβ + βγ + γα equals:
सही उत्तर: घ) 5/2
For ax³ + bx² + cx + d = 0, the sum of products of roots two at a time is c/a = 5/2.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The polynomial x³ + ax² + bx + 6 has (x − 1) as a factor and leaves remainder 4 when divided by (x − 2). Then (a, b) equals:
सही उत्तर: ख) (2, −9)
p(1) = 0 gives a + b = −7; p(2) = 4 gives 4a + 2b = −10, i.e. 2a + b = −5; solving, a = 2 and b = −9.
💬 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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