Exercise - 2.13

Choose the correct or the most suitable answer. . If | x + | ≤ , then x belongs to ( ) ( −∞ , − ) [ − , ] ( ) ( −∞ , − ) ∪ [ , ∞ ) ( ) ( − , ) . Given that x, y and b are real numbers x < y, b > , then ( ) xb < yb xb > yb ( ) xb ≤ yb ( ) b ≥ y b . If | x − | x − ≥ , then x belongs to ( ) [ , ∞ ) ( , ∞ ) ( ) ( −∞ , ) ( ) ( − , ∞ ) . The solution of x − < and x + > − is ( ) ( , ) ( − , − ) ( ) ( − , ) ( ) ( − , ) . The solution set of the following inequality | x − | ≥| x − | is ( ) [ , ] [ , ∞ ) ( ) ( , ) ( ) ( −∞ , ) Basic Algebra . The value of log √ is ( ) ( ) ( ) . The value of log is ( ) − − ( ) − ( ) − . If log √ x . = , then the value of x is ( ) . . ( ) . ( ) . . The value of log a b log b c log c a is ( ) ( ) ( ) . If is the logarithm of , then the base is ( ) ( ) ( ) . Find a so that the sum and product of the roots of the equation x + ( a − ) x + a − = are equal is ( ) ( ) ( ) . If a and b are the roots of the equation x − kx + = and satisfy a + b = , then the value of k is ( ) − ( ) − , ( ) . The number of solutions of x + | x − | = is ( ) ( ) ( ) . The equation whose roots are numerically equal but opposite in sign to the roots of x − x − = is ( ) x − x − = x + x − = ( ) x − x + = ( ) x + x − . If and are the roots of x + ax + c = and , are the roots of x + dx + b = , then the roots of the equation x + ax + b = are ( ) , − , ( ) , ( ) − , . If a and b are the real roots of the equation x − kx + c = , then the distance between the points ( a, ) and ( b, ) is ( ) k − c k − c ( ) c − k ( ) k − c Exercise . If kx ( x + )( x − ) = x + + x − , then the value of k is ( ) ( ) ( ) . If − x + x − x =