ECAT Pre Engineering MCQ Test With Answer for Chapter 19 Mathematics

The area under the curve y = 1/x² between x = 1 and x =4 is:

• -25 A
• 0.75 B
• -0.35 C
• -10 D

• 
  A
• 
  B
• 
  C
• 
  D

An equation in which at least one term contains dy/dx, d² y /dx²etc, is called.

• Differential equation A
• Initial condition B
• General solution C
• Singular equation D

• 6x - 2 + c A
• x³- x²+ x + c B
• 6x - x²+ c C
• 6x³- x²+ c D

The integral of 3x⁵dx is:

• 15 x⁴ A
• x⁶ /2 B
• 1/6x⁵ C
• x⁵ /ln3 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• sin 2x + c B
• -sin 2x + c C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• sec 3x + c A
• - cosec 3x + c B
• 
  C
• 
  D

• 
  A
• In(x²- x + 1) + c B
• 
  C
• In(2x - 1) + c D

The general solution of the differential equation x dy / dx = 1 + y is:

• 2 A
• 1 B
• 3 C
• None D

• 
  A
• 
  B
• 
  C
• 
  D

The differential equations of all conis whose axes coincide with the co-ordinate axis is

• 
  A
• 
  B
• 
  C
• 
  D

Which of the following integrals can be evaluated

• 
  A
• 
  B
• 
  C
• 
  D

• a cot(ax + b) + c A
• - a cot(ax + b) + c B
• 
  C
• 
  D

• 1 A
• 2 B
• 3 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• In(x²- x + 1)⁴+ c B
• 
  C
• 
  D

• 
  A
• 
  B
• In f(x) + c C
• f(x) - c D

• 
  A
• 
  B
• 
  C
• 
  D

The area between the x-axis the curve y =4x-x2 is :

• 32/2 A
• 15 B
• 18 C
• 21 D

• 
  A
• 
  B
• 
  C
• 
  D

• 4(x³- 3x²)³+ c A
• 3x²- 6x + c B
• 
  C
• 
  D

∫sin(ax+b) dx is equal to:

• 1/2a cos (ax + b) A
• -1/a cos (ax +b) B
• 1/a cos (ax +b) C
• 1/a ln (ax + b) D

• 
  A
• 
  B
• 
  C
• 
  D

• cosec x + c A
• -cosec x + c B
• -sec x + c C
• sec x + c D

• sec 5x + c A
• - sec 5x + c B
• 
  C
• 
  D

∫x sin xdx is equal to:

• sin x/x + cos x A
• sin x - cos x/x B
• x cos x + sin x C
• - x cos x + sin x D

• 
  A
• 
  B
• 
  C
• 
  D

• e^x+ c A
• e^-x+ c B
• x e^x+ c C
• not possible D