TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)
TG EAMCET Mathematics MCQs (Serials 241 to 250)
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241. The definite integral ∫ab f(x) dx represents:
- A) The area under the curve f(x) from x = a to x = b
- B) The slope of the curve between a and b
- C) The average value of f(x) over the interval [a, b]
- D) The sum of the function values at a and b
Answer: A) The area under the curve f(x) from x = a to x = b
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242. The fundamental theorem of Integral Calculus states that:
- A) The derivative of an integral is zero
- B) The integral of a derivative is zero
- C) The derivative of the integral of a function is the function itself
- D) The definite integral of a function is always positive
Answer: C) The derivative of the integral of a function is the function itself
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243. The reduction formula for ∫ xn dx, where n ≠ -1, is:
- A) xn+1 / (n+1) + C
- B) xn / n + C
- C) xn+2 / (n+2) + C
- D) xn+1 / (n-1) + C
Answer: A) xn+1 / (n+1) + C
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244. The application of definite integrals can be used to find:
- A) The slope of a function
- B) The area between a curve and the x-axis
- C) The value of a function at a point
- D) The value of the second derivative of a function
Answer: B) The area between a curve and the x-axis
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245. In the formation of a differential equation, the order of the differential equation is defined as:
- A) The highest power of the derivative in the equation
- B) The highest power of the derivatives after removing fractions
- C) The number of terms in the equation
- D) The highest power of the dependent variable
Answer: A) The highest power of the derivative in the equation
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246. The degree of the differential equation is:
- A) The highest power of the dependent variable
- B) The highest power of the derivatives after removing fractions
- C) The sum of all the powers in the equation
- D) The highest order of the derivative
Answer: B) The highest power of the derivatives after removing fractions
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247. The solution to a differential equation of the form &frac{dy}{dx} = f(x)g(y) is found using:
- A) Homogeneous method
- B) Variables separable method
- C) Non-homogeneous method
- D) Linear differential equation method
Answer: B) Variables separable method
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248. A linear differential equation is of the form:
- A) &frac{dy}{dx} = f(x)g(y)
- B) &frac{dy}{dx} + p(x)y = q(x)
- C) &frac{d^2y}{dx^2} + p(x) &frac{dy}{dx} = q(x)
- D) &frac{d^2y}{dx^2} = 0
Answer: B) &frac{dy}{dx} + p(x)y = q(x)
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249. In the method of homogeneous differential equations, the equation is of the form:
- A) &frac{dy}{dx} = f(x, y)
- B) &frac{dy}{dx} = &frac{f(x)}{y}
- C) &frac{dy}{dx} = &frac{g(x, y)}{x}
- D) &frac{dy}{dx} = f(x) + g(y)
Answer: B) &frac{dy}{dx} = &frac{f(x)}{y}
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250. The non-homogeneous differential equation is of the form:
- A) &frac{dy}{dx} = 0
- B) &frac{dy}{dx} + p(x)y = q(x), where q(x) ≠ 0
- C) &frac{dy}{dx} = &frac{f(x)}{y}
- D) &frac{dy}{dx} = y2 + x2
Answer: B) &frac{dy}{dx} + p(x)y = q(x), where q(x) ≠ 0
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