The tangent to the curve `y=e^x` drawn at the point `(c,e^c)` intersects the line joining `(c-1,e^(c-1)) and (c+1,e^(c+1))` (a) on the left of `n=c` (b) on the right of `n=c` (c) at no points (d) at all points

If the line joining the points (0,3)a n d(5,-2) is a tangent to the curve y=C/(x+1) , then the value of c is 1 (b) -2 (c) 4 (d) none of these

If the line joining the points (0,3) and (5,-2) is a tangent to the curve y=C/(x+1) , then the value of C is (a) 1 (b) -2 (c) 4 (d) none of these

Let C be a curve defined by y=e^(a+b x^2)dot The curve C passes through the point P(1,1) and the slope of the tangent at P is (-2)dot Then the value of 2a-3b is_____.

Locus of the point of intersection of tangents at the end points of a focal chord is (A) x=- a/e , if agtb (B) x=a/e , if agtb (C) y=-b/e , if altb (D) y=b/e , if altb

Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0 . Then, a. C1 and C2 touch each other at one point b. C1 and C2 touch each other exactly at two point c. C1 and C2 intersect(but do not touch) at exactly two point d. C1 and C2 neither intersect nor touch each other

If the line y=x touches the curve y=x^2+b x+c at a point (1,\ 1) then (a) b=1,\ c=2 (b) b=-1,\ c=1 (c) b=2,\ c=1 (d) b=-2,\ c=1

D , E ,a n dF are the middle points of the sides of the triangle A B C , then (a) centroid of the triangle D E F is the same as that of A B C (b) orthocenter of the tirangle D E F is the circumcentre of A B C

From an external point P , tangents P A and P B drawn to a circle with centre O . If C D is the tangent to the circle at a point E and P A=14 c m , find the perimeter of P C D .

In Figure, A B=C D . Prove that B E=D E\ a n d\ A E=C E , where E is the point of intersecting of A D\ a n d\ B C .

Prove the following identity: (s e c A\ s e c B+t a n AtanB)^2-(s e c A\ t a n B+t a n A s e c B)^2=1