इन्जिनियरिङ प्रवेश – Mathematics, Physics, Chemistry, English
इन्जिनियरिङ प्रवेश – Mathematics, Physics, Chemistry, English
Engineering Entrance – Mathematics, Physics, Chemistry & English · ३,८४१ प्रश्न
३,८४१ प्रश्न उपलब्ध। मोड छान्नुहोस्:
इन्जिनियरिङ 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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The coefficient of x⁸ in the expansion of (1 + x²)⁶ is:
सही उत्तर: क) 15
x⁸ = (x²)⁴, so the coefficient is ⁶C₄ = 15.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In how many ways can 10 people be divided into two groups of 5 each (groups not labelled)?
सही उत्तर: ख) 126
¹⁰C₅ = 252 counts each division twice (group and its complement), so the answer is 252/2 = 126.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Eight straight lines are drawn in a plane so that no two are parallel and no three are concurrent. The number of their points of intersection is:
सही उत्तर: ग) 28
Each pair of lines meets in exactly one point: ⁸C₂ = 28.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In how many ways can 3 identical red balls and 2 identical blue balls be arranged in a row?
सही उत्तर: घ) 10
5!/(3! 2!) = 10.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In how many ways can 7 people stand in a row so that a particular person A is somewhere to the left of another particular person B?
सही उत्तर: ख) 2520
By symmetry, A is to the left of B in exactly half of the 7! = 5040 arrangements, i.e. 2520.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The number of solutions of x + y + z = 10 in positive integers is:
सही उत्तर: घ) 36
The number of positive integer solutions of x₁ + ... + x_k = n is ⁿ⁻¹C_{k−1} = ⁹C₂ = 36.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The number of 5-card hands from a pack of 52 cards that contain exactly 2 aces is:
सही उत्तर: क) 103776
Choose 2 of the 4 aces and 3 of the 48 non-aces: ⁴C₂ × ⁴⁸C₃ = 6 × 17296 = 103776.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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How many four-digit natural numbers have all their digits different?
सही उत्तर: ग) 4536
The first digit has 9 choices (not 0), then 9, 8 and 7 choices: 9 × 9 × 8 × 7 = 4536.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The number of triangles that can be formed by joining the vertices of an octagon is:
सही उत्तर: घ) 56
Any 3 of the 8 vertices form a triangle (no three are collinear): ⁸C₃ = 56.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In how many ways can 5 different books be arranged on a shelf so that two particular books are never side by side?
सही उत्तर: ग) 72
Total 5! = 120; arrangements with the two together = 4! × 2 = 48; so 120 − 48 = 72.
💬 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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