The equation `2log(x+3)="log"(alphax)` has only one solution if `alpha=12` (b) `alpha in (-oo,0)` `alpha in (0,oo)` (d) `alpha in (0,12){24}`

If the equation x^(3)+px^(2)+qx+1=0(p

If the equation x^(3)+bx^(2)+cx+1=0,quad (b

If alpha in(2,3) then number ofsolution ofthe equation int_(0)^(oo)cos(x+alpha^(2))dx=sin alpha is

Let f(x)={{:(x^(alpha)sin\ (1/x)sinpix\ \ \ ;\ \ x\ !=0),( 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ ;\ \ \ x=0):} If Rolles theorem is applicable to f(x) on [0,1] then range of alpha is (a) -oo lt alpha lt -1 (b) alpha=1 (c) -1 lt alpha lt oo (d) alpha ge 0

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

Let f(x)=ax^3+bx^2+x+d has local extrema at x=alpha and beta such that alphabetalt0 and f(alpha).f(beta)gt0 . Then the equation f(x)=0 (A) has 3 distinct real roots (B) has only one real which is positive o a.f(alpha)lt0 (C) has only one real root, which is negative a.f(beta)gt0 (D) has 3 equal roots

Find log_(24)(48) in terms of alpha if log_(12)(36)=alpha

If log_(12)18=alpha and log_(24)54=beta then the value of alpha beta+alpha-beta