If the cube roots of unity are 1, ω, ω² then the roots of the equation (x – 1)³ + 8 = 0, are

• -1 , - 1 + 2ω, - 1 - 2ω²

• -1 , -1, - 1

• -1 , 1 - 2ω, 1 - 2ω²

• -1 , 1 - 2ω, 1 - 2ω²

Area of the greatest rectangle that can be inscribed in the ellipse 

• 2ab

• ab

• 
• 

• 
• 

• tan 1

• tan 1

If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

• 22.0

• 20.5

• 25.5

• 25.5

5.

Let P be the point (1, 0) and Q a point on the locus y² = 8x. The locus of mid point of PQ is

• y² – 4x + 2 = 0

• y² + 4x + 2 = 0

• x² + 4y + 2 =

• x² + 4y + 2 =

If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the binomial expansion of (1 + y)^m are in A.P., then m and r satisfy the equation

• m² – m(4r – 1) + 4r² – 2 = 0

• m² – m(4r+1) + 4r² + 2 = 0

• m² – m(4r + 1) + 4r² – 2 = 0

• m² – m(4r + 1) + 4r² – 2 = 0

In a triangle PQR, ∠R =π/2. If (P/2) and tan (Q/2) are the roots of ax² +bx+ c = 0, a ≠ 0 then 

• a = b + c

• c = a + b

• b = c

• b = c

The system of equations 
αx + y + z = α - 1, 
x + αy + z = α - 1, 
x + y + αz = α - 1 

has no solution, if α is

• -2

• either-2 or 1

• not -2

• not -2

The value of α for which the sum of the squares of the roots of the equation x² – (a – 2)x – a – 1 = 0 assume the least value is

• 1

• 0

• 3

• 3

If roots of the equation x² – bx + c = 0 be two consectutive integers, then b² – 4c equals

• – 2

• 3

• 2

• 2