ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 18 (Basic Concepts & Definition)

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If y = xⁿthen dy/dx equals:

• nx A
• x^n-1 B
• nx^n-1 C
• n D

If c is a constant, then d/dx (c) =

• 0 A
• c B
• cx C
• 1 D

• 1 A
• 0 B
• cx C
• c D

if y=x² then dy/dx equals:

• 2x A
• x/2 B
• 2x³ C
• x³/2 D

The derivative of 1/x^m is:

• x^m+1/ m A
• m(x)^m-1 B
• (m-1) x^-m C
• m/x^m+1 D

d/dx (cos x²) =

• -2x cos x A
• -2x sin x² B
• -2x tan x C
• -2x sec² x D

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• -2x A
• x^-3 B
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• -2x³ D

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• zero at x A
• differentiable at x B
• continuous at x C
• none of these D

• 2x A
• x/2 B
• 2x³ C
• x³/2 D

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d/dx (cos x sin x) =

• cos² x - sin² x A
• 2cos² x + sin² x B
• 2cos² x - sin² x C
• 1 - sin² x D

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The derivative of√x at x =a is:

• 1/2a A
• 2 / √a B
• 2√x C
• 1 / 2√x D

• mx A
• x/m B
• mx^m-1 C
• xm^m-1 D

If x = at² and y = 2at then dy/dx =

• 2a/y A
• y/2a B
• -a/2y C
• -2y/a D

If y = 3 x + 2cos x, then dy/dx =

• 3-2 sin x A
• 3-t sin x B
• 3x² - 2sin x C
• 3(1-4 sin x) D

• 8 A
• 1/8 B
• 1/3 C
• 2/3 D

If ∱(x) = x^2/3then∱¹(x) at x = 8 equals:

• 8 A
• 1/8 B
• 1/3 C
• 2/3 D

if x∈ D∱ and∱^{1(x) exists, then}∱ is said to be

• zero at x A
• Differentiable at x B
• Continuous at x C
• None of these D