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 length of the intercept made on the x-axis by the circle x² + y² − 6x − 8y = 0 is:
सही उत्तर: ख) 6
Putting y = 0 gives x² − 6x = 0, so x = 0 or 6; the intercept length is 6.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The sum of the slopes of the two lines represented by 3x² + 4xy − y² = 0 is:
सही उत्तर: ग) 4
Putting y = mx gives 3 + 4m − m² = 0, i.e. m² − 4m − 3 = 0, so m₁ + m₂ = 4.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The general second-degree equation ax² + 2hxy + by² + 2gx + 2fy + c = 0 represents a pair of straight lines if:
सही उत्तर: ख) abc + 2fgh − af² − bg² − ch² = 0
The condition is that the determinant |a h g; h b f; g f c| = abc + 2fgh − af² − bg² − ch² vanishes.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The line through the point of intersection of 2x + y = 5 and x + 3y = 8 and parallel to the x-axis is:
सही उत्तर: घ) 5y = 11
Solving, x = 7/5 and y = 11/5; the horizontal line through this point is y = 11/5, i.e. 5y = 11.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The circumcentre of the triangle with vertices (0, 0), (6, 0) and (0, 8) is:
सही उत्तर: ख) (3, 4)
The triangle is right-angled at the origin, so the circumcentre is the midpoint of the hypotenuse joining (6, 0) and (0, 8), i.e. (3, 4).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The orthocentre of the triangle with vertices (0, 0), (4, 0) and (0, 3) is:
सही उत्तर: ग) (0, 0)
The triangle is right-angled at the origin, and the orthocentre of a right triangle is the vertex of the right angle.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The area of the triangle formed by the line 3x + 4y = 12 and the coordinate axes is:
सही उत्तर: ख) 6 sq. units
The intercepts are 4 (x-axis) and 3 (y-axis), so the area is ½ × 4 × 3 = 6.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The angle of elevation of the top of a tower is 60° from a point A on level ground and 30° from a point B 20 m farther from the tower in line with A. The height of the tower is:
सही उत्तर: ख) 10√3 m
h cot 30° − h cot 60° = 20 gives h(√3 − 1/√3) = 20, i.e. h(2/√3) = 20, so h = 10√3 m.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The angles of elevation of the top of a tower from two points on the ground, at distances 4 m and 9 m from its base on the same straight line, are complementary. The height of the tower is:
सही उत्तर: ग) 6 m
tan θ = h/4 and cot θ = h/9 (complementary angles), so h² = 4 × 9 = 36 and h = 6 m.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In any triangle ABC, tan((B − C)/2) equals (Napier's analogy):
सही उत्तर: क) ((b − c)/(b + c)) cot(A/2)
Napier's analogy: tan((B − C)/2) = ((b − c)/(b + c)) cot(A/2).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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