1

IIT-JEE 1989

MCQ (More than One Correct Answer)
If $$\alpha $$ and $$\beta $$ are the roots of $${x^2}$$+ px + q = 0 and $${\alpha ^4},{\beta ^4}$$ are the roots of $$\,{x^2} - rx + s = 0$$, then the equation $${x^2} - 4qx + 2{q^2} - r = 0$$ has always
A
two real roots
B
two positive roots
C
two negative roots
D
one positive and one negative root.
2

IIT-JEE 1989

MCQ (More than One Correct Answer)
The equation $${x^{3/4{{\left( {{{\log }_2}\,\,x} \right)}^2} + {{\log }_2}\,\,x - 5/4}} = \sqrt 2 $$ has
A
at least one real solution
B
exactly three solutions
C
exactly one irrational solution
D
complex roots.
3

IIT-JEE 1986

MCQ (More than One Correct Answer)
If $$S$$ is the set of all real $$x$$ such that $${{2x - 1} \over {2{x^3} + 3{x^2} + x}}$$ is positive, then $$S$$ contains
A
$$\left( { - \infty ,\, - {\textstyle{3 \over 2}}} \right)$$
B
$$\left( { - {3 \over 2},\, - {1 \over 4}} \right)$$
C
$$\left( { - {1 \over 4},\,{1 \over 2}} \right)$$
D
$$\left( {{1 \over 2},\,3} \right)\,\,\,\,$$
4

IIT-JEE 1984

MCQ (More than One Correct Answer)
For real $$x$$, the function $$\,{{\left( {x - a} \right)\left( {x - b} \right)} \over {x - c}}$$ will assume all real values provided
A
$$a > b > c$$
B
$$a < b < c$$
C
$$a > c > b$$
D
$$a < c < b$$

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