Roots of the equation `|x m n1a x n1a b x1a b c1|=0` are independent of `m ,a n dn` independent of `a ,b ,a n dc` depend on `m ,n ,a n da ,b ,c` independent of `m , na n da ,b ,c`

Roots of the equations |{:(x,,m,,n,,1),(a,,x,,n,,1),(a,,b,,x,,1),(a,,b,,c,,1):}|=0 are

If aa n dc are odd prime numbers and a x 62+b x+c=0 has rational roots , where b in I , prove that one root of the equation will be independent of a ,b ,cdot

If a ,b ,a n dc be in G.P. and a+x ,b+x ,a n dc+x in H.P. then find the value of x ( a,b,c are distinct numbers) .

If A ,B ,C be three mutually independent events, then Aa n dBuuC are also independent events. Statement 2: Two events Aa n dB are independent if and only if P(AnnB)=P(A)P(B)dot

If 1/(b-a)+1/(b-c)=1/a+1/c , then A. a ,b ,a n dc are in H.P. B. a ,b ,a n dc are in A.P. C. b=a+c D. 3a=b+c

Events Aa n dC are independent. If the probabilities relating A ,B ,a n dC are P(A)=1//5, P(B)=1//6; P(AnnC)=1//20 ; P(BuuC)=3//8. Then (a)events Ba n dC are independent (b)events Ba n dC are mutually exclusive events.(c) Ba n dC are neither independent nor mutually exclusive (d)events Ba n dC are equiprobable

If one root of the equation ax^2 + bx + c = 0 is equal to the n^(th) power of the other, then (ac^n)^(1/(n+1)) + (a^n c)^(1/(n+1)) + b is equal to

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alphaa n dbetadot

A ,B ,Ca n dD have position vectors vec a , vec b , vec ca n d vec d , respectively, such that vec a- vec b=2( vec d- vec c)dot Then a. A Ba n dC D bisect each other b. B Da n dA C bisect each other c. A Ba n dC D trisect each other d. B Da n dA C trisect each other

If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 , where a , ba n dc are the sides of a triangle ABC, then cosB is equal to 1-c/(2a) (b) 1-c/a 1+c/(c a) (d) 1+c/(3a)