ECAT Pre Engineering Entry Test

The number of solution of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is

• 0 A
• 1 B
• 2 C
• 3 D

The solution set of the equation 1 + Cos x = 0 is __________

• 
  A
• 
  B
• 
  C
• none of these D

• 
  A
• 
  B
• 
  C
• both a & c D

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

• 
  A
• 
  B
• 
  C
• 
  D

The5thand 13th terms of an A.P are 5 and-3 respectively The first term of the A.P is

• 1 A
• -15 B
• 9 C
• 2 D

If (0,4) and (0,2) are vertex and focus of the parabola respectively, the the equation of the parabola is:

• x² = 4y -32 A
• x² =8y -32 B
• y³ = 16 x C
• x2 + 8y =32 D

• 
  A
• 
  B
• 
  C
• 
  D

The line y = 2 x + c is a tangent to the parabola y²= 16 x if c equals

• -2 A
• -1 B
• 0 C
• 2 D

The term involving x⁴in the expansion of (3 - 2x)⁷is

• 120 A
• 1512 B
• 1250 C
• 15120 D

The solution set of trigonometric equation contains

• one element A
• two elements B
• three elements C
• Infinite elements D

For any equilateral r :R :η :r1 :r2 :r3 =

• 1:2:3:4:5 A
• 1:2:3:3:3 B
• 1:2:4:4:4 C
• 2:1 :2 :2 :2 D

• Square matrix A
• Row matrix B
• Symmetric matrix C
• Null matrix D

The unit vector along z-axis is

• 
  A
• 
  B
• 
  C
• none of these D

The roots of ax2 + bx + c = 0 are always unequal if

• b2 - 4ac = 0 A
• b2- 4ac ≠ 0 B
• b2- 4ac > 0 C
• b2- 4ac ≥ 0 D

What is range of the function g (x) =|x-3|?

• [0 ,∞ ) A
• (0 ,∞) B
• (-∞ ,3] C
• [0,∞) D

The set of months in a year beginning with S.

• {September, October, November} A
• Singleton set B
• Null set C
• Empty set D

• Closure law of addition A
• Closure law of multiplication B
• Commutative law of addition C
• Commutative law of multiplication D

Three numbers are chosen random without replacement from {1, 2, 3, ...., 10}. the probability that minimum of the chosen numbering is 3 or their maximum is 7

• 7 / 40 A
• 5 / 40 B
• 11 / 40 C
• None of these D

The curve f(x,y) = 0 has a central symmetry if

• f(-x,-y)=f(x,y) A
• f(x,-y)=f(x,y) B
• f(-x,y)=f(x,y) C
• f(-x,-y)≠f(x,y) D

A line segment whose end points lie on a circle is called

• the secant of the circle A
• the arc of the circle B
• the chord of the circle C
• the circumference of the circle D

The number of different ways of describing a set is

• One A
• Two B
• Three C
• Four D

Total number of subsets that can be formed out of the set {a,b,c} is

• 1 A
• 4 B
• 8 C
• 12 D

Roots of the equation x²- x = 2 are

• {2, -1} A
• {1, 0} B
• {2, 1} C
• {-2, 1} D

• 5 / 12 A
• 3 / 8 B
• 5 / 8 C
• 7 / 4 D

If A and B are two sets then intersection of A and B is denoted by

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

• an ellipse A
• a hyperbola B
• a circle C
• a parabola D

If f(x) = x²-x then f(0) is

• 0 A
• 1 B
• 2 C
• 3 D

• 
  A
• tan 3x + c B
• cot 3x + c C
• - cot 3x + c D