ECAT Pre Engineering MCQ Test With Answer for Chapter 19 Mathematics

The approximate percentage increase in the volume of a cube if the length of its each edge changes from 5 to 5.02 is

• 1.2% A
• 1.5% B
• 0.16% C
• 100.16% D

• Y = -x log x -x + c A
• Y = x log x + x B
• Y = x log x - x + c C
• None of these D

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
• a f(x) + c B
• f(x) + a C
• 
  D

An integral of 1/x dx is:

• 1/x² A
• 1/-x² B
• 1/lnx C
• lnx D

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

If the lower limit of an integral is a constant and the upper limit is a variable, then the integral is a

• Constant function A
• Variable value B
• Function of upper limit C
• All D

• 
  A
• x^-2+ c B
• 
  C
• not possible D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

Which of the following integrals can be evaluated

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

The differential equation of all st. lines which are at a constant distance to form the origin is

• 
  A
• 
  B
• 
  C
• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D