A point moves in such a way that the difference of its distance from two points (8, 0) and (- 8, 0) always remains 4. Then, the locus of the point is
a circle
a parabola
an ellipse
a hyperbola
The number of integer values of m, for which the x - coordinate of the point of intersection of the lines 3x + 4y= 9 and y =mx + 1 is also an integer, is
0
2
4
1
If a straight line passes through the point () and the portion of the line intercepted between the axes is divided equally at that point, then is
0
1
2
4
The coefficient of x10 in the expansion of 1 + (1 + x) + ... + (1 + x)20
C.
The given series is in GP. Hence, its sum
S =
Therefore, the required coefficient of x10 in the eXpansion of
= Coefficient of x11 in the expansion of (1 + x)21 - 1
=
Let p, q and r be the altitudes of a triangle with area S and perimeter 2 t. Then, the value of is
Let C1 and C2 denote the centres of the circles x2 + y2 = 4 and (x - 2)2 + y2 = 1 respectively and let P and Q be their points of intersection. Then, the areas of C2PQ and CPQ are in the ratio
3 : 1
5 : 1
7 : 1
9 : 1
A straight line through the point of intersection of the lines x + 2y = 4 and 2x + y = 4 meets the coordinate axes at A and B. The locus of the mid-point of AB is
3(x + y) = 2xy
2(x + y) = 3xy
2(x + y) = xy
x + y = 3xy
Let P and Q be the points on the parabola y2 = 4x so that the line segment PQ subtends right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is
1
2
4
6
The incentre of an equilateral triangle is (1, 1) and the equation of one side is 3x + 4y + 3 = 0. Then, the equation of the circumcircle of the triangle is
x2 + y2 - 2x - 2y - 2 = 0
x2 + y2 - 2x - 2y - 14 = 0
x2 + y2 - 2x - 2y + 2 = 0
x2 + y2 - 2x - 2y + 14 = 0