1
IIT-JEE 1989
MCQ (More than One Correct Answer)
+2
-0.5
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.
2
IIT-JEE 1989
MCQ (More than One Correct Answer)
+2
-0.5
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.
3
IIT-JEE 1989
MCQ (More than One Correct Answer)
+2
-0.5
Let a, b, c be real numbers, $$a \ne 0$$. If $$\alpha \,$$ is a root of $${a^2}{x^2} + bx + c = 0$$. $$\beta \,$$ is the root of $${a^2}{x^2} - bx - c = 0$$ and $$0 < \alpha \, < \,\beta$$, then the equation $${a^2}{x^2} + 2bx + 2c = 0$$ has a root $$\gamma$$ that always satisfies
A
$$\gamma = {{\alpha + \beta } \over 2}$$
B
$$\gamma = \alpha + {\beta \over 2}$$
C
$$\gamma = \alpha$$
D
$$\alpha < \gamma < \beta$$
4
IIT-JEE 1986
MCQ (More than One Correct Answer)
+2
-0.5
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
$$\left( {{1 \over 2},\,3} \right)\,\,\,\,$$
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