`A B C D` is a square `A-=(1,2),B-=(3,-4)dot` If line `C D` passes through `(3,8),` then the midpoint of `C D` is (a) (2, 6) (b) `(6,2)` (c) `(2,5)` (d) `((28)/5,1/5)`

If a , b and c are in A P , then the straight line a x+b y+c=0 will always pass through a fixed point whose coordinates are (a) (1,2) (b) (1,-2) (c) (2,3) (d) (0,0)

The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at the point (a) (1/2 ,3/4) (b) (1,3) (c) (3,1) (d) (3/4 ,1/2)

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is (a) 2-sqrt(2) (b) sqrt(2)-1 (c) sqrt(2)-1/2 (d) 1/(sqrt(2))

The vertices of a parallelogram A B C D are A(3,1),B(13 ,6),C(13 ,21), and D(3,16)dot If a line passing through the origin divides the parallelogram into two congruent parts, then the slope of the line is (a) (11)/(12) (b) (11)/8 (c) (25)/8 (d) (13)/8

The area of triangle A B C is 20c m^2dot The coordinates of vertex A are (-5,0) and those of B are (3,0)dot The vertex C lies on the line x-y=2 . The coordinates of C are (a) (5,3) (b) (-3,-5) (-5,-7) (d) (7,5)

If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the minimum value of a+b+c is (a) 1 (b) 3 (c) 5 (d) 9

If (log)_4 5=aa n d(log)_5 6=b , then (log)_3 2 is equal to 1/(2a+1) (b) 1/(2b+1) (c) 2a b+1 (d) 1/(2a b-1)

If a , ba n dc are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

A circle passes through the points A(1,0) and B(5,0), and touches the y-axis at C(0,h)dot . If /_A C B is maximum, then (a) h=3sqrt(5) (b) h=2sqrt(5) (c) h=sqrt(5) (d) h=2sqrt(10)

In triangle A B C ,b^2sin2C+c^2sin2B=2bc where b=20 ,c=21 , then inradius= (a) 4 (b) 6 (c) 8 (d) 9