If `(x+1)/2=(x+2)/3` Then value of `x` is (a)2 (b)1 (c)-1 (d)0

If tan^(-1) ((x+1)/(x-1))+tan^(-1)((x-1)/x)=tan^(-1)(-7) , then the value of x is (a) 0 (b) -2 (c) 1 (d) 2

Let x ,\ y be two variables and x >0,\ \ x y=1 , then minimum value of x+y is (a) 1 (b) 2 (c) 2 1/2 (d) 3 1/3

If x-a is a factor of x^3-3x^2a+2a^2x+b , then the value of b is (a) 0 (b) 2 (c) 1 (d) 3

If x^2+x+1 is a factor of the polynomial 3x^3+8x^2+8x+3+5k , then the value of k is (a) 0 (b) 2/5 (c) 5/2 (d) -1

If x lies in the interval [0,\ 1] , then the least value of x^2+x+1 is (a) 3 (b) 3//4 (c) 1 (d) none of these

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

If (x-2)/3=(2x-1)/3-1, then x= (a) 2 (b) 4 (c) 6 (d) 8

The value of lim_(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)0 (b) -1 (c) 1 (d) 2

If x=(7+5sqrt(2))^(1/3) -1/((7+5sqrt(2))^(1/3) , then the value of x^3+3x-14 is equal to 1 (b) 0 (c) 2 (d) 4

If the equation 2^(2x)+a*2^(x+1)+a+1=0 has roots of opposite sign, then the exhaustive set of real values of a is (a)(−∞,0) (b)(−1,−2/3) (c)(−∞,−2/3) (d)(−1,∞)