1
IIT-JEE 2000 Screening
+2
-0.5
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, + $$\infty$$)
2
IIT-JEE 2000 Screening
+2
-0.5
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
$$\alpha \, < \,0 < \left| \alpha \right| < \beta$$
3
IIT-JEE 2000 Screening
+2
-0.5
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
4
IIT-JEE 1999
+2
-0.5
If the roots of the equation $${x^2} - 2ax + {a^2} + a - 3 = 0$$ are real and less than 3, then
A
$$a < 2$$
B
$$2 \le a \le 3$$
C
$$3 < a \le 4$$
D
$$a > 4$$
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