आईओई इन्जिनियरिङ प्रवेश (त्रिवि) M.Sc. इन्जिनियरिङ प्रवेश तयारी
आईओई इन्जिनियरिङ प्रवेश (त्रिवि) – M.Sc. इन्जिनियरिङ प्रवेश
IOE M.Sc. Engineering Entrance · IOE Entrance (TU)
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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Maximise Z = 5x + 4y subject to 6x + 4y ≤ 24, x + 2y ≤ 6, x ≥ 0, y ≥ 0. The maximum value of Z is:
सही उत्तर: ग) 21
6x + 4y = 24 and x + 2y = 6 intersect at (3, 1.5). Corner values: (4,0) → 20, (3,1.5) → 21, (0,3) → 12. Maximum = 21.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Maximise Z = x + y subject to 2x + y ≤ 10, x + 2y ≤ 8, x ≥ 0, y ≥ 0. The maximum value of Z is:
सही उत्तर: ग) 6
The lines 2x + y = 10 and x + 2y = 8 meet at (4, 2). Corner values: (0,0) → 0, (5,0) → 5, (4,2) → 6, (0,4) → 4. Maximum = 6.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Minimise Z = 2x + 5y subject to x + y ≥ 4, x ≥ 1, y ≥ 0. The minimum value of Z is:
सही उत्तर: घ) 8
The (unbounded) region has corner points (4, 0) and (1, 3), where Z = 8 and 17. Since both coefficients are positive, Z only grows further out, so the minimum is 8 at (4, 0).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In a linear programming problem with a bounded feasible region, the optimal value of the objective function is attained:
सही उत्तर: क) at a corner (vertex) point of the feasible region
By the fundamental theorem of linear programming, a linear objective attains its maximum and minimum on a bounded convex polygon at its vertices.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Maximise Z = 3x + 2y subject to x + y ≤ 4, x ≤ 3, x ≥ 0, y ≥ 0. The maximum value of Z is:
सही उत्तर: ग) 11
The corner points are (0,0), (3,0), (3,1) and (0,4), giving Z = 0, 9, 11 and 8. The maximum is 11 at (3, 1).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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27 identical charged water drops, each at potential V, coalesce into one big drop. The potential of the big drop is:
सही उत्तर: ख) 9V
R = 3r and Q = 27q, so V′ = kQ/R = 27kq/(3r) = 9V.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The electric potential at the centre of a ring of radius R carrying charge Q distributed in any manner is:
सही उत्तर: ग) Q/(4πε₀R)
Every element of charge is at the same distance R from the centre, and potential is a scalar: V = kQ/R.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The electric field at the centre of a uniformly charged semicircular ring of radius R carrying total charge Q is:
सही उत्तर: घ) Q/(2π²ε₀R²)
With λ = Q/(πR), the field is 2kλ/R = 2kQ/(πR²) = Q/(2π²ε₀R²).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Rain falls vertically at 4 m/s and a man walks horizontally at 3 m/s. To protect himself he should hold his umbrella tilted forward at an angle to the vertical of:
सही उत्तर: क) tan⁻¹(3/4) ≈ 37°
The rain's velocity relative to the man has components 4 m/s down and 3 m/s backwards, so tan θ = 3/4 from the vertical.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A stone thrown vertically upward is at the same height at t = 2 s and t = 6 s. Its speed of projection is (g = 10 m/s²):
सही उत्तर: क) 40 m/s
It reaches the top midway at t = 4 s, so u = g × 4 = 40 m/s.
💬 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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