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?
Let P be the point on parabola y2=4x which is at the shortest distance from the center S of the circle x2+y2−4x−16y+64=0 let Q be the point on the circle dividing the line segment SP internally. Then
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
Let αandβ be nonzero real numbers such that 2(cosβ−cosα)+cosαcosβ=1 . Then which of the following is/are true? (a) 3tan(2α)+tan(2β)=0 (b) 3tan(2α)−tan(2β)=0 (c) tan(2α)+3tan(2β)=0 (d) tan(2α)−3tan(2β)=0
If a chord, which is not a tangent of the parabola y2=16xhas the equation 2x+y=p,and midpoint (h,k),then which of the following is(are) possible values (s) of p,handk?p=−1,h=1,k=−3 p=2,h=3,k=−4 p=−2,h=2,k=−4 p=5,h=4,k=−3
Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is