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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If f(x) = 2x + 3, then f⁻¹(x) is:
सही उत्तर: ग) (x − 3)/2
Put y = 2x + 3, so x = (y − 3)/2; hence f⁻¹(x) = (x − 3)/2.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The number of subsets of a set containing 5 elements is:
सही उत्तर: घ) 32
A set with n elements has 2^n subsets, so 2^5 = 32.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If A = {1, 2, 3} and B = {2, 3, 4}, the number of elements in A × B is:
सही उत्तर: ख) 9
n(A × B) = n(A) × n(B) = 3 × 3 = 9.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The value of the determinant |1 1 1; a b c; a² b² c²| is:
सही उत्तर: घ) (a − b)(b − c)(c − a)
This is the Vandermonde determinant. It vanishes whenever two of a, b, c are equal, and it equals (a − b)(b − c)(c − a). abc is wrong because the determinant need not be zero when one of the variables is zero.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The value of log₃ 5 · log₅ 27 is:
सही उत्तर: ग) 3
By change of base, log₃ 5 · log₅ 27 = log₃ 27 = 3. 1 would be the answer only for log₃ 5 · log₅ 3.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The system 2x + 3y = 5, 4x + 6y = 10 has:
सही उत्तर: ग) infinitely many solutions
The second equation is just twice the first, so both describe the same line, and every point on it is a solution. If the constants were not in the same ratio, for example 4x + 6y = 11, the system would have no solution.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The sum of the squares of the first 10 natural numbers is:
सही उत्तर: क) 385
Σn² = n(n + 1)(2n + 1)/6 = 10·11·21/6 = 385. 3025 is (Σn)² = 55², which is the sum of the cubes.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The point that divides the join of (2, 3) and (8, 9) internally in the ratio 1 : 2 is:
सही उत्तर: घ) (4, 5)
By the section formula, the point is ((1·8 + 2·2)/3, (1·9 + 2·3)/3) = (4, 5). (6, 7) divides the segment in the ratio 2 : 1.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Three numbers in AP have sum 15 and product 105. The largest of them is:
सही उत्तर: घ) 7
Take the numbers as a − d, a, a + d. Then 3a = 15 gives a = 5, and 5(25 − d²) = 105 gives d = ±2, so the numbers are 3, 5, 7. 5 is the middle term, not the largest.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If A is a 3 × 3 matrix with |A| = 4, then |2A| equals:
सही उत्तर: क) 32
For an n × n matrix, |kA| = kⁿ|A|, so |2A| = 2³·4 = 32. 8 multiplies the determinant by 2 only once.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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