Consider the equation `|In x|+x=2` then (A) The equation has two solutions(B) Both solutions are positive(C) One root exceeds one and other in less than one(D) Both roots exceed one

The equation pi^(x)=-2x^(2)+6x-9 has (A) no solution (B) one solution (C) two solutions (D) infinite solutions

Consider the equation 125^(x)+45^(x)=(2)27^(x) (A) one solution is 0 (B) the equation has one solution only (C) the equation has two solutions (D) Sum of all the solutions and the number of solutions both are 1

The equation 3^(-1)x-pix-pi/2=0 has one negative solution one positive solution no solution more than one solution

The equation 3^(-1)x-pi x-(pi)/(2)=0 has one negative solution one positive solution no solution more than one solution

Let x^2 - (m - 3) x + m = 0 (m in R) be a quadratic equation, then find the values of 'm' for which both (a) the roots are greater than 2. (b) both roots are positive, ( c) one root is positive and other is negative. ( d) One root is greater than 2 and other smaller than 1 ( e) Roots are equal in magnitude and opposite in sign, ( f) both roots lie in the interval (1, 2)

Prove that the equation x 2^x= 1 has at least one positive root which is less than unity.

If both the roots of the equation x^(2)-9x+a=0 are positive and one is greater than 3 and other is less than 3, then all possible values of a is-

Let x^2-2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then find the value of 'a' for which (a) Both the roots are positive (b)Both the roots are negative (c) Both the roots are opposite in sign. (d) Both the roots are greater than 1. (e)Both the roots are smaller than 1. (f) One root is small than 1 and the other root is greater than 1.

If x^2+ax+b is an integer for every integral value of x and roots of equation x^2+ax+b=0 are rational then is (A) both roots are integers (B) one is an integer and the othe is not (C) no root is an integer (D) one root is zero and other is non zero