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1

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)
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
A
$$n{(2c)^{1/n}}$$
B
$$(n + 1){c^{1/n}}$$
C
$$2n{c^{1/n}}$$
D
$$(n + 1)\,{(2c)^{1/n}}$$
2

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
For the equation $$3{x^2} + px + 3 = 0$$. p > 0, if one of the root is square of the other, then p is equal to
A
1/3
B
1
C
3
D
2/3
3

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
If $$\alpha \,and\,\beta $$ $$(\alpha \, < \,\beta )$$ are the roots of the equation $${x^2} + bx + c = 0\,$$, where $$c < 0 < b$$, then
A
$$0 < \alpha \, < \,\beta \,$$
B
$$\alpha \, < \,0 < \beta \,<\left| \alpha \right|$$
C
$$\alpha \, < \beta \, < 0\,$$
D
$$\alpha \, < \,0 < \left| \alpha \right| < \beta $$
4

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
If b > a, then the equation (x - a) (x - b) - 1 = 0 has
A
both roots in (a, b)
B
both roots in (- $$\infty $$, a)
C
both roots in (b, + $$\infty $$)
D
one root in (- $$\infty $$, a) and the other in (b, + $$\infty $$)

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