Multiple Choice QuestionsThe 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
A.
x2 +y2 -x-y =0
The equation of line is y = x ........... (i)
and equation of circle is x2 + y2 - 2x = 0 ........... (ii)
On solving equation (i) and equation (ii),
we get x2 + x2 - 2x = 0
2x2 - 2x = 0
= 2x(x - 1) = 0
x = 0, x = 1
when x = 0, y = 0
when x = 1, y = 1
Let coordinate of A is (0, 0) and co-ordinate of B is (1, 1)
∴ Equation of circle (AB as a diameter)
(x - x1 )(x - x2 ) + (y - y1 )(y - y2 ) = 0
(x - 0)(x - 1) + (y - 0)(y - 1) = 0
x(x - 1) + y(y - 1) = 0
x2 - x + y2 - 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
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.
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
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