1
IIT-JEE 2000 Screening
+2
-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
A
$$0 \le M \le 1$$
B
$$1 \le M \le 2$$
C
$$2 \le M \le 3$$
D
$$3 \le M \le 4$$
2
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
3
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
$$\alpha \, < \,0 < \left| \alpha \right| < \beta$$
4
IIT-JEE 2000 Screening
+2
-0.5
For $$2 \le r \le n,\,\,\,\,\left( {\matrix{ n \cr r \cr } } \right) + 2\left( {\matrix{ n \cr {r - 1} \cr } } \right) + \left( {\matrix{ n \cr {r - 2} \cr } } \right) =$$
A
$$\left( {\matrix{ {n + 1} \cr {r - 1} \cr } } \right)$$
B
$$2\left( {\matrix{ {n + 1} \cr {r + 1} \cr } } \right)$$
C
$$2\left( {\matrix{ {n + 2} \cr r \cr } } \right)$$
D
$$\left( {\matrix{ {n + 2} \cr r \cr } } \right)$$
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