List of top Questions asked in UP Board XII- 2024

Solve: \( \frac{dy}{dx} = \frac{x^2 + y^2}{2xy} \).
Prove that the radius of the right circular cylinder of maximum curved surface inscribed in a cone is half of the radius of the cone.
Prove: \[ \int_0^{\frac{\pi}{4}} \log_e (1 + \tan x) \, dx = \frac{\pi}{8} \log_e 2. \]
Evaluate: \[ \int \frac{x^2 + x + 1}{(x + 2)(x^2 + 1)} \, dx. \]
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One important river of North America.
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Country in Europe with the highest Human Development Index (2019).
Write the name of the country with the largest population (in 2023).
Write the name of the capital city of Japan.
Write the name of an important sea port of South-East Asia.
Write the name of an important river of North America.
Write the name of the country in Europe with the highest Human Development Index (2019).
Write the name of the State with the second largest population in India.
Write the name of an important sea port of Gujarat.
Write the name of an oil refinery of this State (Gujarat).
Write the name of the capital city of Arunachal Pradesh.
Write the name of an important coal mine of Madhya Pradesh.
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Country with the largest population (in 2023).
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Capital city of Japan.
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An important sea port of South-East Asia.
Discuss the importance of air transport.
Describe the characteristics of rail transport in India.
Describe the production and distribution of iron ore in India.
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The State with the second largest population in India.
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An important sea port of Gujarat.
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An oil refinery of this State.