1

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
$$\,[ - 1,{1 \over 2}]\,\,$$
2

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
3

IIT-JEE 1982

MCQ (Single Correct Answer)
The largest interval for which $${x^{12}} - {x^9} + {x^4} - x + 1 > 0$$ is
A
$$ - 4 < x \le 0$$
B
$$\,0 < x < 1$$
C
$$ - 100 < x < 100$$
D
$$ - \infty < x < \infty $$
4

IIT-JEE 1982

MCQ (Single Correct Answer)
If p, q, r are any real numbers, then
A
max (p, q) < max (p, q, r )
B
min (p, q) = $${1 \over 2}\left( {p + q - \left| {p - q} \right|} \right)$$
C
max (p, q) < min (p, q, r)
D
none of these

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