If a,b,c are `p^(th) , q^(th) and r^(th)` term of an AP and GP both, then the product of the roots of equation `a^b b^c c^a x^2 - abcx + a^c b^c c^a = 0` is equal to :

If p^(t h),\ q^(t h),\ a n d\ r^(t h) terms of an A.P. and G.P. are both a ,\ b\ a n d\ c respectively show that a^(b-c)b^(c-a)c^(a-b)=1.

If the 4^(th),7^(th) and 10^(th) terms of a G.P. are a, b and c respectively, prove that : b^(2)=ac

If a ,\ b ,\ c are pth, qth and rth terms of a GP, the |loga p1logb q1logc r1| is equal to- log\ a b c b. 1 c. 0 d. p q r

If a,b,c are the p^("th") , q^("th") and r^("th") terms of G.P then the angle between the vector vecu = (log a) hati + (log b)hatj + (log c) hatk and vecv -( q -r) hati + ( r -p) hati + ( r-p) hatj + ( p-q) hatk , is

Let a,b,c are 7^(th) , 11^(th) and 13^(th) terms of constant A.P if a,b,c are also is G.P then find (a)/(c ) (a) 1 (b) 2 (c) 3 (d) 4

If a,b,c, be the pth, qth and rth terms respectivley of a G.P., then the equation a^q b^r c^p x^2 +pqrx+a^r b^-p c^q=0 has (A) both roots zero (B) at least one root zero (C) no root zero (D) both roots unilty

If a,b,c are in A.P. then the roots of the equation (a+b-c)x^2 + (b-a) x-a=0 are :

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, then show that (a-b)r+(b-c)p+(c-a)q=0