1
WB JEE 2020
+1
-0.25
The equation $$r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2$$ represents
A
a circle
B
a parabola
C
an ellipse
D
a straight line
2
WB JEE 2020
+1
-0.25
Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by
A
$$x - y = 0,\,x - 3y = 0$$
B
$$x + 3y = 0,\,3x + y = 0$$
C
$$3x + y = 0,\,3x - y = 0$$
D
$$(3x - 2y) = 0,\,x + y = 0$$
3
WB JEE 2020
+1
-0.25
A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. The point O divides the segment PQ in the ratio
A
1 : 2
B
3 : 4
C
2 : 1
D
4 : 3
4
WB JEE 2020
+2
-0.5
A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$-$$5). A variable line PQ is drawn perpendicular to AB cutting the X-axis at P(a, 0) and the Y-axis at Q(0, b). If AQ and BP intersect at R, the locus of R is
A
$${x^2} + {y^2} + 7x + 5y = 0$$
B
$${x^2} + {y^2} + 7x - 5y = 0$$
C
$${x^2} + {y^2} - 7x + 5y = 0$$
D
$${x^2} + {y^2} - 7x - 5y = 0$$
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