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
-
If f(x) + 2f(1/x) = 3x for all x ≠ 0, then f(2) equals:
सही उत्तर: ख) −1
Put x = 2: f(2) + 2f(1/2) = 6; put x = 1/2: f(1/2) + 2f(2) = 3/2. Solving gives −3f(2) = 3, so f(2) = −1.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
The number of binary operations that can be defined on a set with 2 elements is:
सही उत्तर: ख) 16
A binary operation is a function from A × A (4 ordered pairs) to A (2 elements), so there are 2⁴ = 16 of them.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
A and B toss a fair coin alternately, A starting; whoever gets the first head wins. The probability that A wins is:
सही उत्तर: घ) 2/3
P(A) = 1/2 + (1/2)²(1/2) + … = (1/2)/(1 − 1/4) = 2/3.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
A marksman hits a target with probability 1/3 per shot. In 4 independent shots, the probability of hitting the target at least once is:
सही उत्तर: ग) 65/81
P(at least one hit) = 1 − (2/3)⁴ = 1 − 16/81 = 65/81.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
A family has two children. Given that at least one of them is a boy, the probability that both are boys is (boys and girls equally likely):
सही उत्तर: ख) 1/3
Sample space {BB, BG, GB, GG}; given at least one boy leaves {BB, BG, GB}, so P = 1/3.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
Three fair dice are thrown. The probability that the sum of the numbers shown is 4 is:
सही उत्तर: क) 1/72
Only the arrangements of (1, 1, 2) give a sum of 4: 3 outcomes out of 216, i.e. 3/216 = 1/72.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
The two regression lines of a bivariate data are 3x + 2y = 26 and 6x + y = 31. The mean values (x̄, ȳ) are:
सही उत्तर: ग) (4, 7)
Both regression lines pass through (x̄, ȳ); solving 3x + 2y = 26 and 6x + y = 31 gives x = 4, y = 7.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
For a moderately skewed distribution with mean 20 and mode 14, the empirical relation gives the median as:
सही उत्तर: घ) 18
Mode ≈ 3 Median − 2 Mean ⇒ 14 = 3M − 40 ⇒ M = 18.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
The (population) standard deviation of the observations 2, 4, 4, 4, 5, 5, 7, 9 is:
सही उत्तर: क) 2
Mean = 40/8 = 5; squared deviations 9, 1, 1, 1, 0, 0, 4, 16 sum to 32; variance = 32/8 = 4, so σ = 2.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
-
The order and degree of the differential equation (d³y/dx³)² + (d²y/dx²)⁵ + y = sin x are respectively:
सही उत्तर: ख) 3 and 2
The highest derivative is d³y/dx³ (order 3), and its power is 2 (degree 2) since the equation is polynomial in the derivatives.
💬 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।