ECAT Pre Engineering Entry Test

The square root of every incomplete square is an

• Rational numbers A
• Even numbers B
• odd numbers C
• Irrational numbers D

x = secθ,y = tanθ are the parametric equations of

• Circle A
• Hyperbola B
• Ellipse C
• parabola D

If n is not natural number, then the expansion (1 + x)ⁿis valid for

• 
  A
• 
  B
• 
  C
• 
  D

sin -1(sin2π/3) =

• π/2 A
• 2π/3 B
• -3π/2 C
• π/3 D

The number of 5-digit number that can be formed from the digits 1,2,4,6,8, when 2 and 8 are never together is

• 72 A
• 48 B
• 144 C
• 20 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

∀x∈(a,b),f(x) is increasing if

• f′(x) >0 A
• f′(x) <0 B
• f′′(x) >0 C
• f′′(x) =0 D

• quadrant I A
• quadrant II B
• quadrant III C
• quadrant IV D

f(x) = 2^x+ 3 . 2^2x+ 5 is

• trigonometric function A
• algebraic function B
• exponential function C
• logarithmic function D

• 
  A
• 
  B
• 
  C
• 
  D
• 
  E

• 
  A
• 
  B
• 
  C
• 
  D

If distance of (a,b) from y-axis is 2 then

• a = 2 A
• b = 2 B
• a = b C
• a = 4 D

• 
  A
• 
  B
• 
  C
• none of these D

3, 6, 12,.... is

• A.P A
• G.P. B
• H.P. C
• None of these D

• 0 A
• -1 B
• 1 C
• 2 D

y=-a is the equation of the directrix of

• y2 =4ax A
• x2=-4ay B
• x2=4ay C
• y2=-4ax D

• 
  A
• 
  B
• 
  C
• 
  D

ᵨ is a

• variable A
• Positive constant B
• Positive variable C
• Directrix D

A vector of magnitude zero is called

• Position vector A
• Null vector B
• Free vector C
• None of these D

If 3x4 +4x3+x5is divided by x+1 , which of the following is the remainder

• 7 A
• -2 B
• 6 C
• 1 D

• 
  A
• 
  B
• 
  C
• 
  D

The function whose range consists of just one element is called

• One-One Function A
• Identity Function B
• Onto Function C
• Constant Function D

The period of cot 8x is

• π/10 A
• 9π/7 B
• π/9 C
• π/8 D

In how many ways can 5 persons be seated at a round table

• 5! A
• 4! B
• 3! C
• 120 D

• 
  A
• 
  B
• 
  C
• 
  D

• quadrant I A
• quadrant II B
• quadrant III C
• quadrant IV D

• (x, y) A
• (kx, y) B
• (x, ky) C
• (kx, ky) D

How many arrangements of the letters of the word MATHEMATICS can be made

• 
  A
• 
  B
• 
  C
• 
  D

Every identity matrix is

• Row-vector A
• Scalar B
• Column-vector C
• All D

Every prime number is also

• Rational number A
• Even number B
• Irrational number C
• Multiple of two numbers D