`f(x)=(x-1)|(x-2)(x-3)|dot` Then `f` decreases in (a)`(2-1/(sqrt(3)),2)` (b) `(2,2+1/(sqrt(3)))` (c)`(2+1/(sqrt(3)),4)` (d) `(3,oo)`

The value of ("lim")_(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

The straight line 3x+4y-12=0 meets the coordinate axes at Aa n dB . An equilateral triangle A B C is constructed. The possible coordinates of vertex C (a) (2(1-(3sqrt(3))/4),3/2(1-4/(sqrt(3)))) (b) (-2(1+sqrt(3)),3/2(1-sqrt(3))) (c) (2(1+sqrt(3)),3/2(1+sqrt(3))) (d) (2(1+(3sqrt(3))/4),3/2(1+4/(sqrt(3))))

int_(1/sqrt(3))^(sqrt(3))(dx)/(1+x^(2))

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

If f(x)="cos"(tan^(-1)x), then the value of the integral int_0^1xf^(x)dx"i s" (3-sqrt(2))/2 (b) (3+sqrt(2))/2 1 (d) 1-3/(2sqrt(2))

Which of the following is not the solution of (log)_3(x^2-2)<(log)_3(3/2|x|-1) is (a) (sqrt(2),2) (b) (-2,-sqrt(2)) (c) (-sqrt(2),2 (d) none of these

The domain of f(x)=sin^(-1)[2x^2-3],w h e r e[dot] denotes the greatest integer function, is (a) (-sqrt(3/2),sqrt(3/2)) (b) (-sqrt(3/2),-1)uu(-sqrt(5/2),sqrt(5/2)) (c) (-sqrt(5/2),sqrt(5/2)) (d) (-sqrt(5/2),-1)uu(1,sqrt(5/2))

The value of log_((9)/(4))((1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3)))))...oo) is