If `a ,b ,c ,d` are positive real umbers such that `a=b+c+d=2,t h e nM=(a+b)(c+d)` satisfies the relation `0lt=Mlt=1` `1lt=Mlt=2` `2lt=Mlt=3` `3lt=Mlt=4`

If a ,b ,c ,d are positive real umbers such that a+b+c+d=2 ,then M=(a+b)(c+d) satisfies the relation (a) 0lt=Mlt=1 (b) 1lt=Mlt=2 (c) 2lt=Mlt=3 (d) 3lt=Mlt=4

If a, b, c, d in R such that a lt b lt c lt d, then roots of the equation (x-a)(x-c)+2(x-b)(x-d) = 0

If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0, then prove that a ,b ,c , d are in G.P.

If in triangle ABC, a, c and angle A are given and c sin A lt a lt c , then ( b_(1) and b_(2) are values of b)

If c lt a lt b lt d , then roots of the equation bx^(2)+(1-b(c+d)x+bcd-a=0

If c lt 0 and ax^2 + bx + c = 0 does not have any real roots then prove that: (i) a-b + c lt 0 , (ii) 9a +3b +c lt 0

If a, b, c, d and p are different real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0 , then show that a, b, c and d are in G.P.

If a ,b ,c are non zero complex numbers of equal modlus and satisfy a z^2+b z+c=0, hen prove that (sqrt(5)-1)//2lt=|z|lt=(sqrt(5)+1)//2.

Q. If a, b,c and d are distinct positive no. in AP. then (A) ad lt bc (B) a+c lt b+d (c) a+d=2(b+c) (D) a+d=3(b+c)

If a , b, c, d are non-zero integers such that a lt b lt c lt d and mean and median of a, b, c and d are both equal to zero, then which one of the following is correct?