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ECE Correlations 1 2024 2025 2nd sem

ECE Correlations 1 2024 2025 2nd sem

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Integrate the square root of (1 − cos x) dx.

-2√3 (cos x/2) + C

2√3 (cos x/2) + C

2√2 (cos x/2) + C

-2√2 (cos x/2) + C

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Determine the area of the region bounded by and .

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Solve the differential equation (x² - xy + y²)dx - xydy = 0.

(y - x) e^y/x = c

(x - y) e^y/x = c

(x - y) e^x/y = c

(y - x) e^x/y = c

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Solve the differential equation e^-y (dy/dx + 1) = xe^x.

e^-(x-y) + x² = c

e^-(x+y) + x²/2 = c

e^x+y + x² = c

e^-(x+y) + x = c

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Determine the order of the differential equation d³y/dx³ + 5 d²y/dx² + 2y = e^3x.

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A body is launched straight upwards with an initial velocity of 1400 ft/s. What is its velocity at 30,000 ft going up?

166.74 ft/s

143.56 ft/s

121.33 ft/s

128.44 ft/s

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A hazardous material was found to decay at a rate proportional to the amount present. Initially, there were 50 mg of this radioactive material that was present. After two hours, it has lost 10% of its original amount. Find the mass of the material after four hours.

38.5 mg

40.5 mg

32.5 mg

43.5 mg

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Solve x in the equation 2x + A = B, If ;