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 order and degree of the differential equation (d²y/dx²)³ + (dy/dx)⁴ + y = 0 are respectively:
सही उत्तर: क) 2 and 3
The order is that of the highest derivative, d²y/dx², so it is 2. The degree is the power of that derivative, which is 3. The 4 belongs to the lower-order derivative dy/dx.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The sum of all the coefficients in the expansion of (2x − 1)⁵ is:
सही उत्तर: ख) 1
Put x = 1: (2 − 1)⁵ = 1. 32 = 2⁵ would be the sum for (1 + x)⁵.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The focus of the parabola y² = 8x is:
सही उत्तर: ग) (2, 0)
Compare with y² = 4ax: 4a = 8, so a = 2 and the focus is (a, 0) = (2, 0). (0, 2) would be the focus of x² = 8y.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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For f(x) = x³ on [0, 3], the value of c given by Lagrange's mean value theorem is:
सही उत्तर: ग) √3
(f(3) − f(0))/3 = 27/3 = 9 = 3c², so c = √3, which lies in (0, 3). 3/2 is just the midpoint, which works only for quadratics.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The solution set of |2x − 3| < 5 is:
सही उत्तर: क) −1 < x < 4
|2x − 3| < 5 means −5 < 2x − 3 < 5, so −2 < 2x < 8 and −1 < x < 4. 'x < −1 or x > 4' is the solution of the opposite inequality.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If the radius of a circle increases at 2 cm/s, the rate of increase of its area when r = 5 cm is:
सही उत्तर: ख) 20π cm²/s
dA/dt = 2πr·dr/dt = 2π·5·2 = 20π cm²/s. 10π forgets the dr/dt factor of 2.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The radius of the circle x² + y² − 4x + 6y − 3 = 0 is:
सही उत्तर: क) 4
The centre is (2, −3) and r = √(g² + f² − c) = √(4 + 9 + 3) = 4. 16 is r², not r.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The foci of the hyperbola x²/16 − y²/9 = 1 are:
सही उत्तर: ग) (±5, 0)
For a hyperbola, c² = a² + b² = 16 + 9 = 25, so the foci are (±5, 0). (±√7, 0) comes from the ellipse relation c² = a² − b².
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The area of a triangle with sides 13, 14 and 15 units is:
सही उत्तर: ग) 84 sq. units
s = 21, so by Heron's formula Area = √(21·8·7·6) = √7056 = 84. 42 is half of the correct area.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If ω is a non-real cube root of unity, then (1 + ω − ω²)(1 − ω + ω²) equals:
सही उत्तर: ख) 4
Using 1 + ω = −ω² and 1 + ω² = −ω, the factors become (−2ω²)(−2ω) = 4ω³ = 4. 0 is the tempting answer if you wrongly use 1 + ω + ω² = 0 inside each factor.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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