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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The number of triangles that can be formed from 12 points in a plane, of which exactly 5 are collinear, is:
सही उत्तर: ख) 210
¹²C₃ − ⁵C₃ = 220 − 10 = 210, since three collinear points do not form a triangle.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A student must answer 4 out of 10 questions, and 2 particular questions are compulsory. The number of choices is:
सही उत्तर: घ) 28
After the 2 compulsory questions, 2 more are chosen from the remaining 8: ⁸C₂ = 28.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Bag I contains 3 red and 2 black balls, and Bag II contains 2 red and 3 black balls. A bag is chosen at random and a ball drawn from it is red. The probability that it came from Bag I is:
सही उत्तर: ग) 3/5
By Bayes' theorem: (½ × 3/5)/(½ × 3/5 + ½ × 2/5) = 3/5.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In how many ways can 6 boys be arranged in a row so that two particular boys are always together?
सही उत्तर: घ) 240
Treat the two as one unit: 5! arrangements, and the two can interchange in 2! ways, giving 5! × 2 = 240.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The value of 1³ + 2³ + 3³ + ... + 10³ is:
सही उत्तर: ख) 3025
Sum of cubes = [n(n + 1)/2]² = (10 × 11/2)² = 55² = 3025.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Three numbers in arithmetic progression have sum 15 and product 80. The numbers are:
सही उत्तर: ग) 2, 5, 8
Let them be 5 − d, 5, 5 + d: 5(25 − d²) = 80 gives d² = 9, d = 3, so the numbers are 2, 5, 8.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The number of terms in the arithmetic progression 7, 11, 15, ..., 139 is:
सही उत्तर: ख) 34
139 = 7 + (n − 1) × 4 gives n − 1 = 33, so n = 34.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If the 3rd term of a geometric progression is 4, the product of its first five terms is:
सही उत्तर: ग) 1024
The five terms are a/r², a/r, a, ar, ar² with a = 4 as the middle term, so the product = a⁵ = 4⁵ = 1024.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If α and β are the roots of x² − 3x + 1 = 0, the equation whose roots are α² and β² is:
सही उत्तर: घ) x² − 7x + 1 = 0
α² + β² = (α + β)² − 2αβ = 9 − 2 = 7 and α²β² = 1, so the equation is x² − 7x + 1 = 0.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The roots of ax² + bx + c = 0 (a, c ≠ 0) are reciprocals of each other if:
सही उत्तर: ख) a = c
If the roots are α and 1/α, their product is 1, so c/a = 1, i.e. a = c.
💬 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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