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1

IIT-JEE 1986

MCQ (Single Correct Answer)
If $$a,\,b$$ and $$c$$ are distinct positive numbers, then the expression
$$\left( {b + c - a} \right)\left( {c + a - b} \right)\left( {a + b - c} \right) - abc$$ is
A
positive
B
negative
C
non-positive
D
non-negative
2

IIT-JEE 1985

MCQ (Single Correct Answer)
If $${\log _{0.3}}\,(x\, - \,1) < {\log _{0.09}}(x - 1)$$, then x lies in the interval-
A
$$(2,\infty )$$
B
(1, 2)
C
(- 2, - 1)
D
none of these
3

IIT-JEE 1984

MCQ (Single Correct Answer)
If $$\,{a^2} + {b^2} + {c^2} = 1$$, then ab + bc + ca lies in the interval
A
$$[{1 \over 2},2]\,\,$$
B
$$[ - 1,2]$$
C
$$\,[ - {1 \over 2},1]\,$$
D
$$\,[ - 1,{1 \over 2}]\,\,$$
4

IIT-JEE 1984

MCQ (Single Correct Answer)
The equation $$x - {2 \over {x - 1}} = 1 - {2 \over {x - 1}}$$ has
A
no root
B
one root
C
two equal root
D
infinitely many roots

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