Multiple Choice QuestionsIf in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in
G.P.
A.P.
Arithmetic − Geometric Progression
Arithmetic − Geometric Progression
The locus of a point P (α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola 
an ellipse
a circle
a parabola
a parabola
If non-zero numbers a, b, c are in H.P., then the straight line 
always passes through a fixed point. That point is
(-1, 2)
(-1, -2)
(1, -2)
(1, -2)
If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for
exactly one value of a
no value of a
infinitely many values of a
infinitely many values of a
B.
no value of a
S1 = x2 + y2 + 2ax + cy + a = 0 S2 = x2 + y2 – 3ax + dy – 1 = 0 Equation of radical axis of S1 and S2 S1 – S2 = 0 ⇒ 5ax + (c – d)y + a + 1 = 0 Given that 5x + by – a = 0 passes through P and Q
No real value to a
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is
an ellipse
a circle
a hyperbola
a hyperbola
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = p2 orthogonally, then the equation of the locus of its centre is
x2 + y2 – 3ax – 4by + (a2 + b2 – p2 ) = 0
2ax + 2by – (a2 – b2 + p2 ) = 0
x2 + y2 – 2ax – 3by + (a2 – b2 – p2 ) = 0
x2 + y2 – 2ax – 3by + (a2 – b2 – p2 ) = 0
An ellipse has OB as semi-minor axis, F and F′ its focii and the angle FBF′ is a right angle. Then the eccentricity of the ellipse is
1/2
1/4
1/4
Let A and B be two events such that 
where 
stands for complement of event A. Then events A and B are
equally likely and mutually exclusive
equally likely but not independent
independent but not equally likely
independent but not equally likely
A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s2 and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then the lizard will catch the insect after
20 s
1 s
21 s
21 s
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