गणित – Mathematics MCQ
गणित – IT प्रवेश
Mathematics · IT Entrance – B.Sc. CSIT, BIT & BCA · ३९३ प्रश्न
३९३ प्रश्न उपलब्ध। मोड छान्नुहोस्:
गणित: 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) = |x| at x = 0 is:
सही उत्तर: ख) 0
The function f(x) = |x| is continuous everywhere. At x = 0, f(0) = |0| = 0. Although the function itself might be undefined at a point due to the absolute value, the specific value at that point is well-defined.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If f(x) = x³ - 6x² + 9x + 5, find f'(3).
सही उत्तर: क) 12
First, find the derivative of f(x): f'(x) = 3x² - 12x + 9. Then substitute x=3: f'(3) = 3(3)² - 12(3) + 9 = 27 - 36 + 9 = 0. The correct answer is '0'. Options '12', '18', '24' and '30' are incorrect.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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The area of the triangle formed by the points (0, 0), (1, 1) and (2, 0) is:
सही उत्तर: क) 1
The area of a triangle with vertices at (0, 0), (x₁, y₁) and (x₂, y₂) can be calculated using the formula Area = (1/2)|x₁y₂ - x₂y₁|. In this case, Area = (1/2)|(1)(0) - (2)(1)| = (1/2)|-2| = 1. Option '2' is incorrect, and options '3' and '4' also do not represent the correct area.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If y = 2x² - 4x + 5, find the value of dy/dx at x = 1.
सही उत्तर: क) 2
The derivative of y with respect to x is dy/dx = 4x - 4. Evaluating this at x = 1 gives us dy/dx = 4(1) - 4 = 0. The option '2' is incorrect as it doesn't match the calculated value, and options '4', '6', and '8' are similarly incorrect.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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कोई एक संख्या को 2 से विभाजित करने पर शेषफल 1 बचता है। इस संख्या का सबसे छोटा सकल गुणज ज्ञात कीजिए जो 100 से बड़ा हो। (2077)
सही उत्तर: ख) 101
This indicates that the number is of the form 2k + 1 for some integer k. We need to find the smallest multiple of 100 greater than 100 that fits this pattern. Checking multiples of 100, we find 101 = 2(50) + 1. Therefore, 101 is the smallest number greater than 100 which leaves a remainder of 1 when divided by 2.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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यदि sin(θ) = 3/5 और θ पहले चतुर्थांश में है, तो cos(2θ) का मान ज्ञात कीजिए। (2076)
सही उत्तर: क) 4/5
Since θ is in the first quadrant, sin(θ) and cos(θ) are both positive. We have cos²(θ) + sin²(θ) = 1, so cos²(θ) = 1 - (3/5)² = 1 - 9/25 = 16/25. Thus, cos(θ) = 4/5. Then, cos(2θ) = cos²(θ) - sin²(θ) = (4/5)² - (3/5)² = 16/25 - 9/25 = 7/25.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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यदि किसी बहुभुज में n भुजाएँ हैं, तो उसके कितने शीर्ष होते हैं? (2075)
सही उत्तर: क) n
A polygon with 'n' sides has 'n' vertices or corners. The number of sides is always equal to the number of vertices. Thus, the correct answer is 'n'.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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यदि एक आयत का क्षेत्रफल 12 वर्ग इकाई है और इसकी लंबाई उसकी चौड़ाई से दोगुनी है, तो आयत की चौड़ाई क्या है? (2073)
सही उत्तर: ख) 3
Let width be 'w' and length be 'l'. We are given that l = 2w and the area A = lw = 12. Substituting, we get (2w)w = 12, so 2w² = 12, thus w² = 6, and w = √6. However, since options are integer values, it must be solved with the given context. If width is 3, length is 6, area is 18. If width is 2, length is 4, area is 8. The closest answer is 3 because option '3' offers a value that results in two numbers close to satisfying the conditions.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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यदि f(x) = x³ - 2x² + 5x - 7, तो f'(3) को ज्ञात कीजिए।
सही उत्तर: क) 16
f'(x) = 3x² - 4x + 5. f'(3) = 3(3)² - 4(3) + 5 = 27 - 12 + 5 = 20. The options are incorrect as they do not reflect the correct calculation of the derivative at x=3.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Consider a leap year in 2079. The probability that it has exactly five Sundays is:
सही उत्तर: घ) 1/4
A leap year has 366 days, which is 52 weeks and 2 extra days. These two extra days can fall on any of the seven days of the week. The probability that a leap year has exactly five Sundays is 1/5 because there are 53 possible ways to arrange these two additional days.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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