If the mean deviation of the numbers 1, 1 + d, 1+ 2d, ... , 1 + 100d from their mean is 255, then the d is equal to 

• 10.0

• 20.0

• 10.1

• 10.1

If the roots of the equation bx²+ cx + a = 0 be imaginary, then for all real values of x, the expression 3b²x² + 6bcx + 2c² is

• greater than 4ab

• less than 4ab

• greater than -4ab

• greater than -4ab

Let A and B denote the statements
A: cos α + cosβ + cosγ = 0
B : sinα + sinβ + sinγ = 0
If cos(β – γ) + cos(γ – α) + cos(α – β) = – 3/2, then

•  A is true and B is false

• A is false and B is true

• both A and B are true

• both A and B are true

If A, B and C are three sets such that A ∩ B = A∩ C and A ∪ B = A ∪ C, then

• A = B

• A = C

• B = C

• B = C

The projections of a vector on the three coordinate axis are 6, - 3, 2 respectively. The direction cosines of the vector are

•  6, –3, 2 

• 6/5, -3/5, 2/5

• 6/7, -3/7, 2/7

• 6/7, -3/7, 2/7

Three distinct points A, B and C are given in the 2 – dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point ( - 1, 0) is equal to 1/3 . Then the circumcentre of the triangle ABC is at the point

• (0,0)

• (5/4, 0)

• (5/2, 0)

• (5/2, 0)

The remainder left out when 8²ⁿ –(62)²ⁿ⁺¹ is divided by 9 is 

• 0

• 2

• 7

• 7

The ellipse x²+ 4y²= 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

• x²+ 16y²= 16 

• x²+ 12y²= 16 

• 4x²+ 48y²= 48 

• 4x²+ 48y²= 48 

The sum to infinity of the series 

• 2

• 3

• 4

• 4

10.

The differential equation which represents the family of curves y=c₁e^c₂xe, where c₁ and c₂ are arbitrary constants, is

• y' =y²

•  y″ = y′ y

• yy″ = y′

• yy″ = y′