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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For f(x) = (x² − 1)/(x − 1) when x ≠ 1 and f(1) = k, f is continuous at x = 1 if k equals:
सही उत्तर: घ) 2
For x ≠ 1, f(x) = x + 1, which tends to 2 as x → 1, so k must be 2. Putting k = 0 is wrong because the 0/0 form does not mean the limit is 0.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A line makes angles of 60° with both the x-axis and the y-axis. The acute angle it makes with the z-axis is:
सही उत्तर: क) 45°
cos²α + cos²β + cos²γ = 1 gives cos²γ = 1 − 1/4 − 1/4 = 1/2, so γ = 45°. 60° wrongly assumes the line is equally inclined to all three axes.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If a = i + j + k and b = 2i − j + k, then a × b equals:
सही उत्तर: ख) 2i + j − 3k
a × b = (1·1 − 1·(−1))i − (1·1 − 1·2)j + (1·(−1) − 1·2)k = 2i + j − 3k. −2i − j + 3k is b × a, since swapping the order reverses the sign.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The determinant of a skew-symmetric matrix of odd order is always:
सही उत्तर: ग) 0
|A| = |Aᵀ| = |−A| = (−1)ⁿ|A| = −|A| for odd n, so |A| = 0. Being a perfect square is the property of skew-symmetric matrices of even order.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The number of ways in which 5 persons can sit around a round table is:
सही उत्तर: क) 24
n people can sit in a circle in (n − 1)! ways, so the answer is 4! = 24. 120 = 5! counts linear arrangements.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The sum of the infinite GP 1 + 1/3 + 1/9 + … is:
सही उत्तर: ख) 3/2
S∞ = a/(1 − r) = 1/(1 − 1/3) = 3/2. 3 comes from wrongly using a/r.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The equation of the plane with intercepts 2, 3 and 6 on the x-, y- and z-axes is:
सही उत्तर: ग) 3x + 2y + z = 6
The intercept form is x/2 + y/3 + z/6 = 1, and multiplying by 6 gives 3x + 2y + z = 6. 2x + 3y + 6z = 6 puts the intercepts in as coefficients instead of as denominators.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The value of lim(x→0) (e^(2x) − 1)/x is:
सही उत्तर: ग) 2
Write it as 2·(e^(2x) − 1)/(2x); since (e^t − 1)/t → 1, the limit is 2. Answering 1 ignores the factor 2 in the exponent.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The value of (1 + i)/(1 − i) is:
सही उत्तर: घ) i
Multiply by (1 + i)/(1 + i): (1 + i)²/2 = 2i/2 = i. −i is the value of the reciprocal (1 − i)/(1 + i).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The coefficient of x³ in the expansion of (1 + x)⁷ is:
सही उत्तर: ग) 35
The coefficient of x^r is C(7, r) = C(7, 3) = 35. 21 is C(7, 2), the coefficient of x².
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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