The graph of function f contains the point P(1, 2) and Q(s, r). The equation of the secant line through P and Q is `y = ((s^(2)+2s-3)/(s-1))x - 1 - s`. The value of f'(1), is

Consider two regions: R_1: Point P is nearer to (1,0) then to x=-1. R_2: Point P is nearer to (0,0) then to (8,0). Then which of the following statements are true: Statement 1 : The area of the region common to R_1 and R_2 is (128)/3s q dotu n i t s . Statement 2 : The area bounded by x=4sqrt(y) and y=4 is (32)/3s qdotu n i t s .

Point P lie on hyperbola 2xy=1 . A triangle is contructed by P, S and S' (where S and S' are foci). The locus of ex-centre opposite S (S and P lie in first quandrant) is (x+py)^(2)=(sqrt(2)-1)^(2)(x-y)^(2)+q , then the value of p+q is

If p,q are roots of the quadratic equation x^(2)-10rx -11s =0 and r,s are roots of x^(2)-10px -11q=0 then find the value of p+q +r+s.

P,Q,R,S are the points (1,2,-2), (8,10,11), (1,2,3) and (3,5,7) respectively. If s denotes the projection of PQ on RS then 29s^(2) + 29 is equal to :

If P is a point on the ellipse (x^(2))/(36)+(y^(2))/(9)=1 , S and S ’ are the foci of the ellipse then find SP + S^1P

The base B C of a A B C is bisected at the point (p ,q) & the equation to the side A B&A C are p x+q y=1 & q x+p y=1 . The equation of the median through A is: (p-2q)x+(q-2p)y+1=0 (p+q)(x+y)-2=0 (2p q-1)(p x+q y-1)=(p^2+q^2-1)(q x+p y-1) none of these

Let S = {1, 2, 3, 4). The number of functions f: S->S. Such that f(i) le 2i for all i in S is

In P Q R , S is any point on the side Q R . Show that P Q+Q R+R P >2P S

Let A=[(1, 2),(3, 4)] and B=[(p,q),(r,s)] are two matrices such that AB = BA and r ne 0 , then the value of (3p-3s)/(5q-4r) is equal to

Let T be the line passing through the points P(-2,\ 7) and Q(2,\ -5) . Let F_1 be the set of all pairs of circles (S_1,\ S_2) such that T is tangent to S_1 at P and tangent to S_2 at Q , and also such that S_1 and S_2 touch each other at a point, say, M . Let E_1 be the set representing the locus of M as the pair (S_1,\ S_2) varies in F_1 . Let the set of all straight lines segments joining a pair of distinct points of E_1 and passing through the point R(1,\ 1) be F_2 . Let E_2 be the set of the mid-points of the line segments in the set F_2 . Then, which of the following statement(s) is (are) TRUE? The point (-2,\ 7) lies in E_1 (b) The point (4/5,7/5) does NOT lie in E_2 (c) The point (1/2,\ 1) lies in E_2 (d) The point (0,3/2) does NOT lie in E_1