इन्जिनियरिङ प्रवेश – Mathematics, Physics, Chemistry, English
इन्जिनियरिङ प्रवेश – Mathematics, Physics, Chemistry, English
Engineering Entrance – Mathematics, Physics, Chemistry & English · ३,८२१ प्रश्न
३,८२१ 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 angle between the lines 2x + 3y = 5 and 3x − 2y = 7 is:
सही उत्तर: ख) 90°
The slopes are −2/3 and 3/2, and their product is −1, so the lines are perpendicular. In general, a₁a₂ + b₁b₂ = 2·3 + 3·(−2) = 0 also confirms this.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The derivative of |x| at x = 0:
सही उत्तर: क) does not exist
The left-hand derivative is −1 and the right-hand derivative is +1. Since they differ, |x| is continuous at 0 but not differentiable there.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The eccentricity of a rectangular hyperbola is:
सही उत्तर: ख) √2
For a rectangular hyperbola a = b, so e = √(1 + b²/a²) = √2. e = 1 is the eccentricity of a parabola.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The area enclosed between the curves y = x² and y = x is:
सही उत्तर: घ) 1/6
The curves meet at x = 0 and x = 1, so the area is ∫₀¹(x − x²)dx = 1/2 − 1/3 = 1/6. 1/3 is only the area under y = x².
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If A is a 3 × 3 matrix with |A| = 5, then |adj A| equals:
सही उत्तर: घ) 25
|adj A| = |A|ⁿ⁻¹ = 5² = 25 for n = 3. 125 wrongly uses the power n instead of n − 1.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The principal argument of −1 + i√3 is:
सही उत्तर: क) 2π/3
The point lies in the second quadrant with tan⁻¹(√3/1) = π/3, so the argument is π − π/3 = 2π/3. π/3 ignores that the real part is negative.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The derivative of log(sec x + tan x) with respect to x is:
सही उत्तर: घ) sec x
The derivative is (sec x tan x + sec²x)/(sec x + tan x) = sec x(tan x + sec x)/(sec x + tan x) = sec x. This is why ∫sec x dx = log|sec x + tan x| + C.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The roots of x² + x + 1 = 0 are:
सही उत्तर: ग) imaginary (non-real)
The discriminant is 1 − 4 = −3 < 0, so the roots are non-real complex conjugates (they are ω and ω²). A negative discriminant rules out every real option.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The value of lim(x→0) (aˣ − 1)/x (a > 0) is:
सही उत्तर: ग) ln a
Since aˣ = e^(x ln a), (aˣ − 1)/x → ln a. With a = e this gives the familiar limit 1.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The domain of f(x) = √(4 − x²) is:
सही उत्तर: ख) [−2, 2]
We need 4 − x² ≥ 0, that is, |x| ≤ 2. The endpoints are included because √0 is defined, so the open interval (−2, 2) is too small.
💬 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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