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TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

TG EAMCET - Mathematics - Calculus

221. The limit of lim_x→0 (sin x / x) is:
A) 0
B) 1
C) ∞
D) Does not exist

Answer: B) 1

222. Which of the following functions is continuous at x = 1?
A) f(x) = 1 / (x-1)
B) f(x) = √x
C) f(x) = (x² - 1) / (x-1)
D) f(x) = 1 / x

Answer: C) f(x) = (x² - 1) / (x-1)

223. The derivative of sin x with respect to x is:
A) cos x
B) -cos x
C) sin x
D) -sin x

Answer: A) cos x

224. What is the second derivative of f(x) = x³ - 5x² + 4x - 7?
A) 6x - 10
B) 6x² - 10x + 4
C) 6x² - 10
D) 3x² - 10

Answer: C) 6x² - 10

225. The equation of the tangent to the curve y = x² at the point (1,1) is:
A) y = 2x - 1
B) y = x + 1
C) y = 2x - 1
D) y = 1

Answer: A) y = 2x - 1

226. If f(x) = x², then the approximate value of f(1.01) using the linear approximation is:
A) 1.0201
B) 1.02
C) 1.0101
D) 1.0205

Answer: B) 1.02

227. The derivative of tan x with respect to x is:
A) sec² x
B) cos x
C) sec x
D) sin x

Answer: A) sec² x

228. According to Rolle's Theorem, if f(a) = f(b) = 0, then there exists at least one c in (a, b) such that:
A) f'(c) = 0
B) f(c) = 0
C) f'(c) = 1
D) f(c) = 1

Answer: A) f'(c) = 0

229. If a function f(x) is increasing in the interval (a, b), then its derivative f'(x) is:
A) Positive
B) Zero
C) Negative
D) Undefined

Answer: A) Positive

230. The maximum value of the function f(x) = -x² + 4x - 3 is:
A) -3
B) 1
C) 5
D) 3

Answer: C) 5

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TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

TG EAMCET - Mathematics - Calculus

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