Sequences and Series
If α,β are the roots of ax2+2bx+c=0 and γ,δ are the rootes of px2+2qx+r=0. If α,β,γ,δ are in A.P., then q2−prb2−ac=
If A1,A2,.....A31 are arithmetic means inserted between the numbers a and b, then find the value of (b−A51b+A51 )−(A1−aA1+a )
If a1,a2,....an are positive real numbers whose product is a fixed number c, then the minimum value of a1+a2+....+an−1+2an is
A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then
Assertion :STATEMENT -1 : If x,y,z are the sides of a triangle such that x+y+z=1, then [32x−1+2y−1+2z−1]≥((2x−1)(2y−1)(2z−1))1/3
Reason :STATEMENT-2 : For positive numbers their A.M., G.M. and H.M. satisfy the relation A.M.>G.M.>H.M.