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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On a two-element set, how many relations are antisymmetric?
सही उत्तर: ग) 12
The 2 diagonal pairs can each be in or out (2² = 4 ways); for the pair {(1,2), (2,1)} at most one may be included (3 ways). Total = 4 × 3 = 12.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Let A = {1, 2, 3} and B = {2, 3, 4}. How many ordered pairs belong to both A × B and B × A?
सही उत्तर: घ) 4
(A × B) ∩ (B × A) = (A ∩ B) × (A ∩ B), and A ∩ B = {2, 3} has 2 elements, so the set has 2 × 2 = 4 elements.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The real function f(x) = 1/√(|x| − x) is defined exactly for:
सही उत्तर: ख) x < 0
We need |x| − x > 0. For x ≥ 0, |x| − x = 0; for x < 0, |x| − x = −2x > 0. So the domain is x < 0.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The converse of the conditional statement p → q is:
सही उत्तर: घ) q → p
The converse interchanges hypothesis and conclusion; ~q → ~p is the contrapositive and ~p → ~q the inverse.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If n(A) = 3 and n(B) = 2, the number of subsets of A × B is:
सही उत्तर: घ) 64
A × B has 3 × 2 = 6 elements, so it has 2⁶ = 64 subsets.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The inverse of the function f(x) = eˣ⁺¹ is:
सही उत्तर: घ) f⁻¹(x) = ln x − 1
y = eˣ⁺¹ gives x + 1 = ln y, so x = ln y − 1; hence f⁻¹(x) = ln x − 1 for x > 0.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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For every natural number n, n³ − n is always divisible by:
सही उत्तर: ख) 6
n³ − n = (n − 1)n(n + 1) is a product of three consecutive integers, so it is divisible by 2 and by 3, hence by 6 (this can also be proved by induction).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If the correlation coefficient is 0.5, σₓ = 2 and σᵧ = 6, the regression coefficient of y on x (b_yx) is:
सही उत्तर: घ) 1.5
b_yx = r σᵧ/σₓ = 0.5 × 6/2 = 1.5.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A fair die is thrown repeatedly. The probability that the first six appears on the third throw is:
सही उत्तर: क) 25/216
Two non-sixes then a six: (5/6)(5/6)(1/6) = 25/216.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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For a normal distribution, the mean, median and mode are:
सही उत्तर: घ) all equal
The normal curve is symmetric and unimodal about its mean, so mean = median = mode.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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