Mathematics ECAT Pre Engineering Online Test

• A A
• 0 B
• Unit vector C
• None D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

How many signals can be given by 5 flags of different colours, using 3 flags at a time

• 120 A
• 60 B
• 24 C
• 15 D

The projections of a line segment on x, y, z axes are 12, 4, 3. The length and the direction cosines of the line segment are

• 
  A
• 
  B
• 
  C
• 
  D

Order (or sense) of an inequality is changed by multiplying or dividing its each side by a:

• Zero A
• one B
• negative constant C
• Non negative constant D

Two positive integers whose sum is 30 and their product will be maximum are

• 12,18 A
• 10,20 B
• 15,15 C
• 14,16 D

• A,. B, C are coincident A
• A, B, C are collinear B
• Both A and B C
• None of these D

The ortho center of triangle whose vertices are (0,0)(3,0)(0,4) is

• (0,0) A
• (1,1) B
• (2,2) C
• (3,3) D

Domain of sec x is ______

• 
  A
• 
  B
• 
  C
• 
  D

i³=

• -1 A
• i B
• -i C
• 1 D

The roots of the equation will be irrational if b²- 4ac is

• Positive and perfect square A
• Positive but not a perfect square B
• Negative C
• Zero D

• 
  A
• 
  B
• 
  C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D

For all positive integral value of n,3ⁿ< n! , when

• n> 6 A
• n< 6 B
• n<11 C
• n>11 D

The cube roots of 8 are

• 
  A
• 
  B
• 
  C
• 
  D

• A rational number A
• A natural number B
• An irrational number C
• An integer D

• Associative law of addition A
• Commutative law of addition B
• Additive identity C
• Closure law of addition D

• c/a A
• -c/a B
• b/a C
• -b/a D

Range of tan x is ______

• [-1, -] A
• R B
• Negative real numbers C
• R - {x | - 1 < x < 1} D

Three consecutive terms of a progression are 30, 24, 20. The next terms of the progression is

• 
  A
• 
  B
• 
  C
• 
  D

The horizontal distance between the two towers is 60 m. the angular elevation of the top of the taller tower as seen from the top of the shorter one is 30°. If the height of the taller tower is 150 m, the height of the shorter one is

• 116 m A
• 200 m B
• 216 m C
• None of these D

• xa^x-1 A
• a^x B
• x in a C
• a^xIn a D

The domain of f(x) = log x is

• [0,∞] A
• (0,∞) B
• [0,∞[ C
• [∞,∞] D

Tan 3x tan 2x-tan x is equal to

• Tan x tan 2x tan 3x A
• -tan x tan 2x tan 3x B
• Tan x tan 2x - tan - tan x tan 3x - tan 2x tan 3x C
• None of these D

The sum of all even numbers less than 100 is

• 2450 A
• 2352 B
• 2272 C
• 2468 D

The general solution of tan 3x = 1 is

• 
  A
• 
  B
• 
  C
• 
  D

A dice is rolled. The probability that the dots on the top are greater than 4 is

• 1/6 A
• 1/3 B
• 1/2 C
• 1 D

• 
  A
• 
  B
• 
  C
• 
  D

Both the roots of the equation (x -b) (x - c ) + (x -c) (x-a) +(x-a) (x-b) = 0 are always

• Positive A
• Negative B
• Real C
• None of these D