If `4x+3y=24` cut at two points `A` & `B`, origin is `(O)` then incentre of `/_\AOB` is (a) `(2,4)` (b) `(4,4)` (c) `(2,2)` (d) `(4,2)`

If A(4,-4) and B(9,6) lies on y^2=4x and a point C on arc AOB (O= origin) such that the area of triangleACB is maximum then point c is (1) (1/4,1) (2) (1,1/4) (3) (1,1/2) (4) (1/2,1)

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is (a) (3,3) (b) (2,2) (c) (6,6) (d) (4,4)

If the mean of the following distribution is 2.6, then the value of y is Variable (x) : 1 2 3 4 5 Frequency (y) : 4 5 y 1 2 (a) 3 (b) 8 (c) 13 (d) 24

the coordinates of the foot of the perpendicular drawn from the point (2,-3,4) on the y-axis is (a) (2,3,4) (b) (-2,-3,-4) (c) (0,-3,0) (d) (2,0,4)

If A & B are the points (-3,4)a n d(2,1) , then the co-ordinates of the point C on AB produced such that A C=2B C are: a. (2,4) b. (3,7) c. (7,-2) d. (1/2,5/2)

The point on the curve y^2=x where tangent makes 45^o angle with x-axis is (a) (1//2,\ 1//4) (b) (1//4,\ 1//2) (c) (4,\ 2) (d) (1,\ 1)

The tangent and the normal at the point A-= (4, 4) to the parabola y^2 = 4x , intersect the x-axis at the point B and C respectively. The equation to the circumcircle of DeltaABC is (A) x^2 + y^2 - 4x - 6y=0 (B) x^2 + y^2 - 4x + 6y = 0 (C) x^2 + y^2 + 4x - 6y = 0 (D) none of these

If a circle of radius r is touching the lines x^2-4x y+y^2=0 in the first quadrant at points Aa n dB , then the area of triangle O A B(O being the origin) is (a) 3sqrt(3)(r^2)/4 (b) (sqrt(3)r^2)/4 (c) (3r^2)/4 (d) r^2

If a = 3x - 5y, b = 6x + 3y and c = 2y - 4x . Find : (i) a + b - c , (ii) 2a - 3b + 4c .

If (x, y) is the incentre of the triangle formed by the points (3, 4), (4, 3) and (1, 2), then the value of x^(2) is