ECAT Mathematics Online Test

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• -1 B
• 5 C
• 2 D

• a²b²c² A
• 4a²b²c² B
• 4abc C
• None D

if one root of the equation ix2 - 2(i + 1) x +(2 - i)= 0 is 2 - i then the other root is

• -i A
• 2 + i B
• i C
• 2 - i D

• Only one real solution A
• Exactly three real solution B
• Exactly one rational solution C
• Non-real roots 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

The expansion (1 + x)^-3holds when

• |x| > 1 A
• |x| < 1 B
• x < 1 C
• x > 1 D

If y = 2x , then

• y1 -ln2y = 0 A
• y2-(ln2)2 y = 0 B
• y2-(ln2)y1 = 0 C
• All are correct D

The mid point of the line joining the points P(x₁, y₁) and Q(x₂, y₂) is

• 
  A
• 
  B
• 
  C
• 
  D

The middle term of (x-y)⁸is

• 25 x⁴y⁴ A
• 70 x⁴y⁴ B
• 120 x⁴y⁴ C
• 97x⁴y⁴ D

Which element is the additive inverse of (a, b) in Complex numbers?

• (a, 0) A
• (0, b) B
• (a, b) C
• (-a, -b) D

Two circle s1: x2+ y2 +2x- 2y- 7= 0: s2: x2+ y2- 6x+ 4y+ 9= 0

• Touch externally A
• Touch internally B
• Intersects each other C
• Do not intersects D

Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if

• c = 0 A
• c = 0,b≠ 0 B
• b = 0,c = 0 C
• b = 0,c≠ 0 D

If n is any positive integer ,t hen 2+4+6+......+2 n=

• 2ⁿ-1 A
• 2ⁿ+1 B
• n²+1 C
• n(n+1) D

An event having more than one sample point is called

• Certain event A
• Compound event B
• Simple event C
• None D

Cos (α+β) - cos (α-β) =

• -2 sinα sinβ A
• 2 sinαcosβ B
• -2 sinαcosα C
• 4 sinα cosβ D

The number of terms in the expansion of (a + b)⁹is

• 10 A
• 11 B
• 9 C
• 12 D

• 1.5 A
• 1.2 B
• 8 C
• None of these D

• 3, -3, 11 A
• 3, 3, 11 B
• -3, 3, -11 C
• -3, -3, 11 D

If cos 20°=K and cos x=2 k²-1, then the possible values of x between 0° and 360° are

• 140° A
• 50° and 140° B
• 50° and 130° C
• 40° and 320° D

The slope of y-axis is

• 0 A
• undefined B
• 1 C
• 
  D

A series consisting of an unlimited number of terms is termed as an

• Finite sequence A
• Infinite sequence B
• ^{Infinite series} C
• geometric sequence D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If order of A is m x n, then order of A^tis

• m x m A
• n x n B
• m x n C
• n x m D

Any point, where f is neither increasing nor decreasing and f(x) = 0 at that point, is called a

• Minimum A
• Maximum B
• Stationary point C
• Constant point D

The range of the principal sine function is

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

cos(a-β) = ______;

• sin a cosβ + cos a sinβ A
• sin a cos β - cos a sinβ B
• cos a cos β + sin a sinβ C
• cos a cosβ - sin a sinβ D

• At A
• -A B
• A C
• A-1 D