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

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

d/dx [tan² x]

• 2tan x sec² x A
• 2tan x sec x B
• 2 cot x tan x C
• 2sec² x cos² x D

If x² + y² = 1, then dy/dx

• y/x A
• -x/y B
• 1/x C
• None of these D

• 8 A
• 1/8 B
• 1/3 C
• 2/3 D

• mx A
• x/m B
• mx^m-1 C
• xm^m-1 D

• 
  A
• 
  B
• 
  C
• 
  D

If∱(x) = x^-100the value of∱¹ (1) is:

• 100 A
• -100 B
• 0 C
• -101 D

• 
  A
• 
  B
• 
  C
• 
  D

If∱(x) = c then∱^{1 (x0 equals:}

• 1 A
• 0 B
• cx C
• c D

• 100 A
• -100 B
• 0 C
• -101 D

• 
  A
• 
  B
• 
  C
• 
  D

if y=x² then dy/dx equals:

• 2x A
• x/2 B
• 2x³ C
• x³/2 D

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

∱(x) = ax²-3x -5, and∱¹ (2) = 9, a is equal to

• 2 A
• 3 B
• -2 C
• 4 D

The derivative of√x at x =a is:

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

If∱(x) = 1/x-2 then∱¹(0) equals:

• -1/4 A
• -3/2 B
• -1/2 C
• 1/5 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If y = xⁿthen dy/dx equals:

• nx A
• x^n-1 B
• nx^n-1 C
• n D

If x = at² and y = 2at then dy/dx =

• 2a/y A
• y/2a B
• -a/2y C
• -2y/a D

Let∫ be real valued function continuous in the interval (x,x₁)⊆ D∫ (the domain of∫),

then∱(x₁) -∱ (x)/x₁-x represents:

• Instantaneous rate A
• Average rate of change B
• Differential coefficient C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

If y = 1/x² then dy/dx equals:

• -2x A
• x^-3 B
• -2/x³ C
• -2x³ D

• 
  A
• 
  B
• 
  C
• 
  D

If 3x + 4y +7 = 0 , then dy / dx =

• -1/2
  A
• -4/3 B
• 7/2 C
• -3/4 D

If x =1 -t² and y =3t² - 2t³ then dy/dx =

• (1-t) A
• 3(1+t) B
• 3(t-1) C
• 3/1-t D

If f(x) = c then∱¹(x) equals:

• 1 A
• 0 B
• cx C
• c D

• 
  A
• 
  B
• 
  C
• 
  D

d/dx (cosec x)

• -sec x tan x A
• sin x cos x B
• -csc x cot x C
• 2sin x cos x D