ECAT Pre Engineering MCQ Test With Answer for Chapter 19 Mathematics

Te order of the differential equation of all conics whose axes coincide with the axes of co-ordinates is

• 2 A
• 3 B
• 4 C
• 1 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• x²+ 2x + c C
• (x²+ 2x -1)⁴+ c D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

An integral of 1/x dx is:

• 1/x² A
• 1/-x² B
• 1/lnx C
• lnx D

The function ø(x) is ananti derivativeof function f (x),x∈Df if

• ø′(x) =∫f(x)dx A
• ø(x) =∫f(x)dx B
• ø′(x) =f(x) C
• ø(x) =∫′(x)dx D

• 
  A
• 
  B
• 
  C
• 
  D

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

∫x/Sin² x dx is equal to:

• x cot x + ln|sin⁡x | A
• -x cot x - ln|sin⁡x | B
• x cot x - ln|sin⁡x | C
• x. tan x- ln|sec⁡x | D

• 5x^{4 + c} A
• 1/6 x⁶+ c B
• 5x²+ c C
• 1/5 x⁶+ c D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

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

• cos 2x + c A
• - cos 2x + c B
• tan 2x + c C
• cot 2x + c D

The area enclosed between the graph y = x² -4x and the x- axis is:

• 20/3 A
• 41/3 B
• 32/3 C
• 25/3 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
• tan 3x + c B
• cot 3x + c C
• - cot 3x + c D

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

• 
  A
• 
  B
• 
  C
• 
  D

The solution of differential equation:

• dy/dx+y/x = x² is : A
• 4xy = x⁴+ c B
• 4x = x⁴= c C
• 4 y = x⁴+ c D
• 4x=4x³ + c E

The arbitrary constants involving in the solution can be determined by the given conditions. Such conditions are called

• Boundaries A
• Variable separable B
• Initial values C
• None D

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

• 
  A
• 
  B
• 
  C
• 
  D