If two variates `Xa n dY` are connected by the relation `Y=(a X+b)/c ,w h e r ea ,b ,c` are constants such that `a c<0,t h e n` (a) `sigma_gamma=a/csigma_X` (b) `sigma_gamma=-a/csigma_X` (c) `sigma_gamma=a/csigma_X+b` (d) none of these

If two variates X a n d Y are connected by the relation Y=(a X+b)/c ,where a ,b ,c are constants such that a c<0,t h e n (a) sigma_gamma=a/csigma_X (b) sigma_gamma=-a/csigma_X (c) sigma_gamma=a/csigma_X+b (d) none of these

Prove that a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.

If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that the roots of the equation x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ are constants, then find the value of A+B+Cdot

Evaluate int_a^b(dx)/(sqrt(x)),w h e r ea , b > 0.

Evaluate int_a^b(dx)/(sqrt(x)),w h e r ea , b > 0.

If the sum of n terms of an A.P. is given by S_n=a+b n+c n^2, w h e r ea ,b ,c are independent of n ,t h e n (a) a=0 (b) common difference of A.P. must be 2b (c) common difference of A.P. must be 2c (d) first term of A.P. is b+c

Find the value of the determinant |b cc a a b p q r1 1 1|,w h e r ea ,b ,a n dc are respectively, the pth, qth, and rth terms of a harmonic progression.

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-a^2b-a b^2,and C=a^2c +'a c^2-b^2' c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

Find the area of the region included between the parabolas y^2=4a xa n dx^2=4a y ,w h e r ea > 0.

Find (dy)/(dx), when xa n dy are connected by the following relations (i) a x^2+2h x y+b y^2+2gx+2fy+c=0 (ii) x y+x e^(-y)+ydote^x=x^2