If a and b are chosen randomly from the set consisting of number 1, 2, 3, 4, 5, 6 with replacement. Then the probability that `underset(xrarr0)lim[(a^(x)+b^(x))//2]^(2//x)=6` is

If a and b are chosen randomly from the set consisting of number 1, 2, 3, 4, 5, 6 with replacement. Then the probability that lim_(x to 0)[(a^(x)+b^(x))//2]^(2//x)=6 is

Evaluate: underset(xrarr0)lim((1-x)^n-1)/(x)

Two numbers a and b are chosen at random from the set {1,2,3,4, . . .,0} with replacement. The probability that the equation x^(2)+sqrt(2)(a-b)x+b=0 has

If pa n dq are chosen randomly from the set {1,2,3,4,5,6,7,8,9, 10} with replacement, determine the probability that the roots of the equation x^2+p x+q=0 are real.

If pa n dq are chosen randomly from the set {1,2,3,4,5,6,7,8,9, 10} with replacement, determine the probability that the roots of the equation x^2+p x+q=0 are real.

If a number x is chosen at random from the numbers -2,\ -1,\ 0,\ 1,\ 2 . What is the probability that x^2<2 ?

underset(xrarr0)(lim)(sinnx)/x is equal to

lim_(xrarr0) (6^(x)-3^(x)-2^(x)+1)/(x^(2))=?

Two numbers b\ a n d\ c are chosen at random with replacement from the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9. Find the probability that x^2+b x+c >0\ for\ a l l\ x in Rdot

If a and b are randomly chosen from the set {1,2,3,4,5,6,7,8,9} , then the probability that the expression ax^(4)+bx^(3)+(a+1)x^(2)+bx+1 has positive values for all real values of x is