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

Sum of roots of equations f(x) - g(x)=0 is (a)0 (b) 2alpha (c) -2alpha (d) 4alpha

Let cos^-1(x/a)+cos^-1(y/b)=alpha Given equation represents and ellipse if (A) alpha=0 (B) alpha=pi/4 (C) alpha=pi/2 (D) alpha=pi

("lim")_(n vec oo)"{"(n/(n+1))^(alpha)+sin (1/n)]^n (when alpha in Q ) is equal to (a) e^(-alpha) (b) -alpha (c) e^(1-alpha) (d) e^(1+alpha)

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

The inequality sqrt(x^((log)_2sqrt(x)))geq2 is satisfied (a) by only one value of x (b) x in (0,(1/4)) (c) x in [4,oo) (d) x in (1,2)

The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 x+y+alphaz=alpha-1 and has no solution if alpha is

An ordered pair (alpha, beta) for which the system of linear equations (1+alpha)x+betay+z=2 , alphax+(1+beta)y+z=3 and alphax+betay+2z=2 has unique solution is: (a) (2,4) (b) (-3,1) (c) (-4,2) (d) (1,-3)

An ordered pair (alpha, beta) for which the system of linear equations (1+alpha)x+betay+z=2 , alphax+(1+beta)y+z=3 and alphax+betay+2z=2 has unique solution is: (a) (2,4) (b) (-3,1) (c) (-4,2) (d) (1,-3)

The inequality sqrt(x^((log)_2sqrt(x)))geq2 is satisfied by (A) only one value of x (B) x in (0,(1/4)] (C) x in [4,oo) (d) x in (1,2)

Assertion : The system of linear equations x+(sinalpha)y+(cosalpha)z=0x+(cosalpha)y+(sinalpha)z=0x-(sinalpha)y-(cos\ alpha)z=0 has a non-trivial solution for only value of alpha lying the interval (0,\ pi) Reason: The equation in\ alpha cosalphas in alpha cosalphasinalpha cosalphasinalphac osalpha-sinalpha-cosalpha|=0 has only one solution lying in the interval (-pi/4,\ pi/4)