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PYQs Based Test - 06 : Multiple and Improper Integrals

Medium 10 Questions 180 min 16 marks

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180 min · 16 marks · Full test mode with leaderboard

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Question No: 6Difficulty: mediumMarks: 2short_answer

The integral 1/2π _D ^ \leqft( x + y + 10 )dxdy, where D denotes the disc 𝑥² + 𝑦² \leq 4, evaluates to__________.

Question No: 7Difficulty: mediumMarks: 2mcq

The area of an ellipse represented by an equation \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 is

Question No: 8Difficulty: mediumMarks: 2short_answer

For the solid S shown below, the value of ∭_{s} x d x d y d z (rounded off to two decimal places) is ________

Question No: 9Difficulty: mediumMarks: 2mcq

The value of \int_{0}^{π /2} \int_{0}^{cos θ} r sin θ dr dθ is

Question No: 10Difficulty: mediumMarks: 2mcq

Let I = \int_{x = 0}^{1} \int_{y = 0}^{x^{2}} x y^{2} d y d x . Then, I may also be expressed as

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