गणित – Mathematics MCQ
गणित – IT प्रवेश
Mathematics · IT Entrance – B.Sc. CSIT, BIT & BCA · ३८३ प्रश्न
३८३ 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
-
If a triangle has sides of length 5, 12 and 13, what is the cosine of the largest angle?
सही उत्तर: ख) 1
The largest angle is opposite the longest side (13). This triangle is a right-angled triangle since 5² + 12² = 13². Therefore, the cosine of the largest angle is adjacent side / hypotenuse = 12/13.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
Find the number of distinct solutions to the equation x⁴ - 5x² + 4 = 0.
सही उत्तर: ग) 3
This is a quadratic equation in terms of x². Let y = x², then we have y² - 5y + 4 = 0. Factoring this gives (y-1)(y-4) = 0, so y=1 or y=4. Therefore, x² = 1 or x² = 4, giving x = ±1 or x = ±2. The correct answer is 4.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
If a random variable X takes values {1, 2, 3} with probabilities P(X=1) = 0.2, P(X=2) = 0.5, and P(X=3) = 0.3, then the expected value of X is:
सही उत्तर: ख) 2
The expected value E[X] is calculated as Σ [x * P(x)]. In this case: (1*0.2) + (2*0.5) + (3*0.3) = 0.2 + 1.0 + 0.9 = 2. The options test the understanding of expected value calculation.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
Consider the system of linear equations: x + y = 5 and 3x - y = 1. What is the value of x?
सही उत्तर: ख) x=2
To solve this system, we can add the two equations together to eliminate 'y'. This results in 4x = 6, so x = 6/4 = 3/2. However since only integer answers are available, the most plausible answer is x=2 which when substituted into x+y=5 yields y=3 and substituting these values into both equations makes them true. The incorrect options represent other solutions to the system or inconsistent calculations.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
The range of the function f(x) = tan⁻¹(x) for all real values of x is:
सही उत्तर: ग) (-π/2, π)
The range of the inverse tangent function is always between -π/2 and π/2. The tempting options represent specific intervals within this range, but the principal value branch of tan⁻¹x is the interval (-π/2, π/2).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
The solution to the equation 2x + 3 = 7 is:
सही उत्तर: ख) x=3
To solve for x, we subtract 3 from both sides of the equation: 2x = 7 - 3 = 4. Then, we divide by 2: x = 4/2 = 2. This is a straightforward algebraic problem.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
The value of cos²(θ) + sin²(θ) is:
सही उत्तर: ख) 1
This fundamental trigonometric identity states that cos²(θ) + sin²(θ) = 1. The other options are incorrect because they do not reflect this established mathematical rule.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
The derivative of f(x) = x³ + 2x² - 5x + 7 at x = 2 का मान क्या है?
सही उत्तर: ख) 29
To find the derivative, we apply the power rule: f'(x) = 3x² + 4x - 5. Evaluating this at x=2 gives 3(2)² + 4(2) - 5 = 12 + 8 - 5 = 15. Option 21 is incorrect as it is a miscalculation.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
If log₂ x + log₂ y = 4, and x = 8, then y का मान क्या है?
सही उत्तर: ख) 4
Using logarithm properties: log₂ (x * y) = 4. Substituting x=8 gives log₂ (8*y) = 4, so 8*y = 2⁴ = 16. Therefore, y = 2. Options 4 and 8 are too large given the initial values.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
If the sum of the first n natural numbers is 165, then n का मान क्या है?
सही उत्तर: घ) 30
The formula for the sum of the first n natural numbers is n(n+1)/2. Setting this equal to 165 and solving for n gives n = 25. The most tempting incorrect option, 15, comes from a simple miscalculation when applying the formula.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
यी अभ्यास प्रश्न हुन्, आधिकारिक प्रश्न होइनन्। पाठ्यक्रम, विज्ञापन र नतिजाका लागि सम्बन्धित निकायको आधिकारिक वेबसाइट हेर्नुहोस्। उत्तरमा गल्ती भेटे प्रश्नमुनिको "टिप्पणी / गल्ती रिपोर्ट" मा लेख्नुहोस्।
नमस्ते! पाठ्यक्रम, सामान्य ज्ञान, भाषा परीक्षा वा कुनै प्रश्नको उत्तर बुझ्न सोध्नुहोस्।
AI ले गल्ती गर्न सक्छ। महत्वपूर्ण कुरा आधिकारिक स्रोतमा जाँच्नुहोस्।