ECAT Mathematics Chapter 18 MCQ Test With Answer for Mathematics chapter 18 (Basic Concepts & Definition)

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

If y = xⁿthen dy/dx equals:

• nx A
• x^n-1 B
• nx^n-1 C
• n D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

d / dx (cot x) =

• Sec x tan x A
• -csc² x B
• Sec² x C
• 1/cot² x D

• -2x A
• x^-3 B
• 
  C
• -2x³ D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If∱(x) = x^-100the value of∱¹ (1) is:

• 100 A
• -100 B
• 0 C
• -101 D

The derivative of√x at x =a is:

• 1/2a A
• 2 / √a B
• 2√x C
• 1 / 2√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

• 
  A
• 
  B
• 
  C
• 
  D

If∱(x) = c then∱^{1 (x0 equals:}

• 1 A
• 0 B
• cx C
• c D

If f(x) = c then∱¹(x) equals:

• 1 A
• 0 B
• cx C
• c D

• 
  A
• 
  B
• 
  C
• 
  D

d/dx (cos x²) =

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

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

• 2 A
• 3 B
• -2 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

if y=x² then dy/dx equals:

• 2x A
• x/2 B
• 2x³ C
• x³/2 D

If y = 1/x² then dy/dx equals:

• -2x A
• x^-3 B
• -2/x³ C
• -2x³ 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

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

If∱(x) = x⁵ + x³ + x the value of∱¹(1) is:

• 0 A
• 8 B
• 5 C
• 9 D

• 
  A
• 
  B
• 
  C
• 
  D

• 2x A
• x/2 B
• 2x³ C
• x³/2 D

• 8 A
• 1/8 B
• 1/3 C
• 2/3 D

If x² + y² = 1, then dy/dx

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

If x = at² and y = 2at then dy/dx =

• 2a/y A
• y/2a B
• -a/2y C
• -2y/a D