IIT-JEE 2002 Screening | Quadratic Equation and Inequalities Question 32 | Mathematics

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)

-0.5

If $${a_1},{a_2}.......,{a_n}$$ are positive real numbers whose product is a fixed number c, then the minimum value of $${a_1} + {a_2} + ..... + {a_{n - 1}} + 2{a_n}$$ is

$$n{(2c)^{1/n}}$$

$$(n + 1){c^{1/n}}$$

$$2n{c^{1/n}}$$

$$(n + 1)\,{(2c)^{1/n}}$$

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)

-0.5

If $$\alpha \,\text{and}\,\beta $$ $$(\alpha \, < \,\beta )$$ are the roots of the equation $${x^2} + bx + c = 0\,$$, where $$c < 0 < b$$, then

$$0 < \alpha \, < \,\beta \,$$

$$\alpha \, < \,0 < \beta \,<\left| \alpha \right|$$

$$\alpha \, < \beta \, < 0\,$$

$$\alpha \, < \,0 < \left| \alpha \right| < \beta $$

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)

-0.5

If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) (c + d) satisfies the relation

$$0 \le M \le 1$$

$$1 \le M \le 2$$

$$2 \le M \le 3$$

$$3 \le M \le 4$$

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)

-0.5

If b > a, then the equation (x - a) (x - b) - 1 = 0 has

both roots in (a, b)

both roots in (- $$\infty $$, a)

both roots in (b, + $$\infty $$)

one root in (- $$\infty $$, a) and the other in (b, + $$\infty $$)

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