The least natural number a for which `x+(a)/(x^(2))>=6,AA x in(0,oo);` is

The least natural number a for which x+ax^(-2)>2AA x in(0,oo) is 1(b)2(c)5 (d) none of these

The least natural number'n' for which (n-2)x^(2)+8x+n+4>sin^(-1)(sin12)+cos^(-1)(cos12)AA x in R is

Number of integral values of 'a' for which (a-1)x^(2)+(a-1)x+1>=0AA x in R ,is ?

Show that ln(1+x)>x-(x^(2))/(2)AA x in(0,oo)

The values of 'a' for which 4^(x)-(a-4)2^(x)+(9a)/(4)<0AA x in(1,2) is

Number of integral values of m for which x^(2)-2mx+6m-41<0,AA x in(1,6], is

The set of all real numbers x for which x^(2)-|x+2|+x>0 is (-oo,-2) b.(-oo,-sqrt(2))uu(sqrt(2),oo) c.(-oo,-1)uu(1,oo) d.(sqrt(2),oo)

The number of pairs (a,b) for which a(x+1)^2+b(x^(2)-3x-2)+x+1=0 AA x in R is :

The number of pairs (a,b) for which a(x+1)^(2)+b(x^(2)-3x-2)+x+1=0AA x in R

Let f(x)=x^(2)-2x-1AA x in R , Let f,(-oo,a] to [b,oo) , where 'a' is the largest real number for which f(x) is bijective. The value of (a+b) is equal to