If `lambda=sqrt((4+)sqrt((37 b-81 b^4-3)/b)) and f(x)=(x-p+5)(x-p)` where `p,lambda in R and b lt 0` then

The value of tan ^(-1) sqrt((a lambda)/(b c))+tan ^(-1) sqrt((b lambda)/(c a))+tan ^(-1) sqrt((c lambda)/(a b)) where a, b, c in R^(+) and lambda=a+b+c is equal to

If a lt b then f(x) =sqrt ((x-a)/(b-x)) is continuous on

sqrt((3+sqrt(5))/(2)),sgn(x^(2)-3x+4) and 2{[(2)/(3+x^(2))]+sin((pi)/(10))},x in R are the first three consecutive terms of G.P.and sum of its infinite terms is (lambda)/((sqrt(5)-1)^(3)), then find the value of lambda

If a lt b lt c lt d then f(x) = (x -a) (x-c)+ lambda(x-b) (x-d) has real roots

The wavelength of K_(alpha) X-rays for lead isotopes P_(b)^(208),P_(b)^(206) and P_(b)^(204) are lambda_(1),lambda_(2), and lambda_(3) , respectively. Then ...

If |{:(x+3,x+4,x+lambda),(x+4,x+5,x+mu),(x+5,x+6,x+v):}|=0 where lambda,mu,v are in A.P then prove that this is an identity in x.

The locus of the point of intersection of the lines sqrt(3)x-y-4sqrt(3)lambda=0 and sqrt(3)lambda x+lambda y-4sqrt(3)=0 is a hyperbola of eccentricity 1 b.2 c.3 d.4

If a,b,c are in A.P,then are a lambda,b lambda and c lambda in AP?

Consider int(x^(3)+3x^(2)+2x+1)/(sqrt(x^(2)+x+1))dx =(ax^(2)+bx+c)sqrt(x^(2)+x+1)+lambda int(dx)/(sqrt(x^(2)+x+1)) Now, match the following lists and then choose the correct code. Codes: {:(,a,b,c,d),((1),q,p,s,r),((2),s,p,q,r),((3),r,q,p,s),((4),q,s,p,r):}

Consider int(x^(3)+3x^(2)+2x+1)/(sqrt(x^(2)+x+1))dx =(ax^(2)+bx+c)sqrt(x^(2)+x+1)+lambda int(dx)/(sqrt(x^(2)+x+1)) Now, match the following lists and then choose the correct code. Codes: {:(,a,b,c,d),((1),q,p,s,r),((2),s,p,q,r),((3),r,q,p,s),((4),q,s,p,r):}