The intercept on the line y = x by the circle x2 +y2 -2x = 0 is AB. Equation of the circle on AB as a diameter is

• x² +y² -x-y =0

• x² -y² -x-y =0

• x² +y² +x-y =0

• x² +y² +x-y =0

If a ≠ 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y²+ 4ax = and  x²+ 4ay = , then

• d² + (2b+3c)² = 0

• d² +(3d+2c²) = 0

• d² + (2b-3c)² = 0

• d² + (2b-3c)² = 0

33.

The eccentricity of an ellipse, with its centre at the origin, is 1 /2 . If one of the directrices is x = 4, then the equation of the ellipse is

• 3x² +4y² = 1

• 3x²+ 4y² = 12

• 4x² +3y² = 12

• 4x² +3y² = 12

Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is independent of the change of origin and scale. Which of these is/are correct?

• only (a)

• only (b)

• only (a) and (b)

• only (a) and (b)

In a series of 2n observations, half of them equal a and remaining half equal –a. If the standard deviation of the observations is 2, then |a| equals 

• 1/n

• 

• 2

• 2

The probability that A speaks truth is 4/ 5 , while this probability for B is 3/ 4 . The probability that they contradict each other when asked to speak on a fact is

• 3/20

• 1/20

• 7/20

• 7/20

Suppose four distinct positive numbers a₁, a₂, a3, a₄ are in G.P. Let b₁ = a₁, b₂ = b₁ + a₂, b₃ = b₂ + a₃ and b₄ = b₃ + a₄.
Statement-I: The numbers b₁, b₂, b₃, b₄are neither in A.P. nor in G.P. Statement-II: The numbers b₁, b₂, b₃, b₄ are in H.P.

• Both statement-I and statement-II are true but statement-II is not the correct explanation of statement-I

• Both statement-I and statement-II are true, and statement-II is correct explanation of Statement-I

• Statement-I is true but statement-II is false.

• Statement-I is true but statement-II is false.

If x = ω – ω² – 2. Then the value of (x⁴ + 3x³ + 2x² – 11x – 6) is

• 0

• -1

• 1

• 1

Maximum sum of coefficient in the expansion of (1 – x sinθ + x² )ⁿ is

• 1

• 2ⁿ

• 3ⁿ

• 3ⁿ

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

• a function

• reflexive

• not symmetric

• not symmetric