Â·If the normals of the parabola y2=4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2(y+2)2=r2 , then the value of r2 is
The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?
For a>b>c>0, if the distance between (1,1) and the point of intersection of the line ax+by−c=0 is less than 22 then,
In a triangle PQR, P is the largest angle and cosP=31. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)
Let f:R→(0,∞) and g:R→R be twice differentiable functions such that f" and g" are continuous functions on R. suppose fprime(2)=g(2)=0,f(2)=0 and g′(2)=0, If x→2limf′(x)g′(x)f(x)g(x)=1 then
Let f[0,1]→R (the set of all real numbers be a function.Suppose the function f is twice differentiable, f(0)=f(1)=0,and satisfies f′(x)–2f′(x)+f(x)≤ex,x∈[0,1].Which of the following is true for 0<x<1?