Solving Inequalities

Q. Which of the following values of x do not satisfy the inequality $x^2-3x+2>0$ at all?

1. $-5\le x\le -1$
2. $1\le x\le 2$
3. $2<x<4$
4. $5<x\le 10$

Q. The real values of 'a' for which the quadratic equation $2x^2-(a^3+8a-1)x+a^2-4a=0$ possesses roots of opposite signs are given by :

1. a > 6
2. a > 9
3. 0 < a < 4
4. a < 0

Q. The solution set of inequality |x -1| + |x + 1| < 4 is

1. $(2,\infty )$
2. $(-\infty ,-2)$
3. $(-2,2)$
4. $(-\infty ,\infty )$

Q. In what range will 'x' lie, if $x^2$ + 10x + 21 $\le$ 0?

1. $x\le -7\&x\ge -3$
2. -7 < x $\le$ -3
3. -7 $\le$ x < -3
4. $-7\le x\le -3$

Q. If x $ϵ$ R, and $\alpha =\frac{x^2}{(1+x^4)}$ then

1. $0\le \alpha \le 2$
2. $0\le \alpha \le 1$
3. $0\le \alpha \le \frac{1}{4}$
4. $0\le \alpha \le \frac{1}{2}$

Q. What is the range of m, which satisfies $3m^2$ - 21m + 30 < 0?

1. m < 2 or m > 5
2. 2 < m < 5
3. m > 2
4. m < 5

Q. If x satisfies |x - 1| + |x -2| + |x - 3| $\ge 6,$ then

1. $0\le x\le 4$
2. $x\le -2orx\ge 4$
3. $x\le 0orx\ge 4$
4. $x\le -1orx\ge 5$

Q. What is the range of x for which the expression 19x - $2x^2$ - 35 is positive?

1. x < 7
2. $x>\frac{5}{2}$
3. $\frac{5}{2}\le x\le 7$
4. $\frac{5}{2}<x<7$

Q. The inequality |2x - 3| < 1 is valid when x lies in the interval :

1. (-4, 3)
2. (-1, 2)
3. (1, 2)
4. (3, 4)

Q.

For what values of x will the following inequality hold true $3|a-1|+a^2-7>0$ ?

1. (-∞, -1) U (2, ∞)

2. (-∞, -5) U(2, ∞)

3. (-∞, -1)U (4, ∞)

4. (-∞, -5)U(4, ∞)