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

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 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

• mx A
• x/m B
• mx^m-1 C
• xm^m-1 D

• 0 A
• 8 B
• 5 C
• 9 D

• 
  A
• 
  B
• 
  C
• 
  D

Differentiation of sin x w.r.t. cot x is:

• -sin² x sec x A
• -cos x sin² x B
• -cos² x tan x C
• -sin² x D

if y=x² then dy/dx equals:

• 2x A
• x/2 B
• 2x³ C
• x³/2 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

• 
  A
• 
  B
• 
  C
• 
  D

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

d/dx(x³ + 2x +3)=

• x² + 2 A
• 3x + 2 B
• 3x² + 5 C
• 3x2 + 2 D

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

• 8 A
• 1/8 B
• 1/3 C
• 2/3 D

• 8 A
• 1/8 B
• 1/3 C
• 2/3 D

• -2x A
• x^-3 B
• 
  C
• -2x³ D

If∱(x) = c then∱^{1 (x0 equals:}

• 1 A
• 0 B
• cx C
• c D

• x²+ 2 A
• 3x + 2 B
• 3x²+ 5 C
• 3x²+ 2 D

• 
  A
• 
  B
• 
  C
• 
  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

• 
  A
• 
  B
• 
  C
• 
  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 c is a constant, then d/dx (c) =

• 0 A
• c B
• cx C
• 1 D

If x² + y² = 1, then dy/dx

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

If∱(x) = 2x³ + 1 then∱¹(0) =

• 0 A
• 1 B
• 6 C
• None of these D

The derivative of√x at x =a is:

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

• 
  A
• 
  B
• 
  C
• 
  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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D