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Question: Solve the first-order linear differential equation dy/dx + y/x = x.Options: y = x^2 + C/xy..
Question: What is the integrating factor for the equation dy/dx + 2y = 3x?Options: e^(2x)e^(-2x)e^(3..
Question: Find the solution of the differential equation y\'\' + 4y = 0.Options: y = C1 cos(2x) + C2..
Question: What is the particular solution of the equation dy/dx = 2y with the initial condition y(0)..
Question: Solve the differential equation dy/dx = x^2 + y^2.Options: y = x^3/3 + Cy = x^2 + Cy = x^2..
Question: What is the general solution of the differential equation dy/dx = 3y?Options: y = Ce^(3x)y..
Question: Which functional group is present in the compound CH3-CO-CH3?Options: KetoneAldehydeAlcoho..
Question: Which of the following is the correct IUPAC name for CH3-CH2-CH2-CHO?Options: ButanalPenta..
Question: What is the stereochemical configuration of 2-butene if the two methyl groups are on oppos..
Question: What is the correct IUPAC name for the compound with the structure CH3-CH(CH3)-CH2-COOH?Op..
Question: The function f(x) = x^2 - 2x + 1 is differentiable at all points?Options: TrueFalseOnly at..
Question: If f(x) = x^4 - 4x^3 + 6x^2, find f\'(2).Options: 0123Correct Answer: 0Solution: f\'(x) = ..
Question: The function f(x) = ln(x) is differentiable at x = 1?Options: YesNoOnly for x > 1Only for ..
Question: If f(x) = e^x, then f\'(0) is equal to?Options: 01ee^0Correct Answer: 1Solution: f\'(x) = ..
Question: The function f(x) = x^2 for x < 1 and f(x) = 2x - 1 for x ≥ 1 is differentiable at x = 1?O..
Question: The function f(x) = x^2 + 2x + 1 is differentiable everywhere?Options: TrueFalseOnly at x ..
Question: The function f(x) = |x| is differentiable at x = 0?Options: YesNoOnly from the rightOnly f..
Question: If f(x) = x^3 - 3x^2 + 4, then f\'(2) is equal to?Options: 0123Correct Answer: 1Solution: ..
Question: Which of the following is a characteristic of alkenes?Options: Single bonds onlyAt least o..
Question: If f(x) = 5x^2 + 3x, what is f\'(1)?Options: 8101315Correct Answer: 10Solution: f\'(x) = 1..
Question: What is the derivative of f(x) = x^4?Options: 4x^33x^42x^4x^3Correct Answer: 4x^3Solution:..
Question: Find the derivative of f(x) = tan(x) at x = 0.Options: 01undefined1/2Correct Answer: 1Solu..
Question: What is the derivative of f(x) = 3x^3 - 5x + 2?Options: 9x^2 - 53x^2 - 59x^2 + 53x^2 + 5Co..
Question: If f(x) = ln(x), what is f\'(x)?Options: 1/xxln(x)0Correct Answer: 1/xSolution: f\'(x) = 1..
Question: What is the derivative of f(x) = e^x?Options: e^xx*e^x10Correct Answer: e^xSolution: The d..
Question: Find the derivative of f(x) = sin(x) at x = π/2.Options: 01-1undefinedCorrect Answer: 1Sol..
Question: What is the derivative of f(x) = x^2 at x = 3?Options: 36912Correct Answer: 6Solution: f\'..
Question: Evaluate ∫_0^1 (x^3 + 2x^2) dx.Options: 1/41/31/21Correct Answer: 1/2Solution: ∫_0^1 (x^3 ..
Question: Calculate ∫_1^e (ln(x)) dx.Options: 1e - 1e0Correct Answer: e - 1Solution: ∫_1^e ln(x) dx ..
Question: Evaluate the integral ∫_0^π/2 cos^2(x) dx.Options: π/4π/210Correct Answer: π/4Solution: ∫_..
