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 matrix [k 2; 3 6] is singular when k equals:
सही उत्तर: ख) 1
Singular means the determinant is zero: 6k − 6 = 0, so k = 1. The rows (1, 2) and (3, 6) are then proportional.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The equation of the circle with centre (1, −2) and radius 3 is:
सही उत्तर: ख) x² + y² − 2x + 4y − 4 = 0
Expand (x − 1)² + (y + 2)² = 9: x² + y² − 2x + 4y + 5 − 9 = 0, which gives the constant term −4. Using −9 forgets the 1 + 4 that comes from the squared terms.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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For f(x) = x² − 4x on [0, 4], the value of c given by Rolle's theorem is:
सही उत्तर: ख) 2
f(0) = f(4) = 0 and f'(c) = 2c − 4 = 0 gives c = 2. c must lie strictly inside (0, 4), so 4 cannot be the answer.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The roots of x² + kx + 9 = 0 are equal when k equals:
सही उत्तर: क) ±6
Equal roots need discriminant k² − 36 = 0, so k = ±6. ±3 comes from forgetting the factor 4 in 4ac.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The inverse of the matrix [2 1; 5 3] is:
सही उत्तर: ख) [3 −1; −5 2]
The determinant is 6 − 5 = 1, and A⁻¹ = adj A/|A| = [3 −1; −5 2] (swap the diagonal and negate the off-diagonal). [2 −1; −5 3] forgets to swap the diagonal entries.
💬 टिप्पणी / गल्ती रिपोर्ट (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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