1
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$S$$ be the set of all non-zero real numbers $$\alpha$$ such that the quadratic equation $$\alpha {x^2} - x + \alpha = 0$$ has two distinct real roots $${x_1}$$ and $${x_2}$$ satisfying the inequality $$\left| {{x_1} - {x_2}} \right| < 1.$$ Which of the following intervals is (are) $$a$$ subset(s) os $$S$$?
A
$$\left( { - {1 \over 2} - {1 \over {\sqrt 5 }}} \right)$$
B
$$\left( { - {1 \over {\sqrt 5 }},0} \right)$$
C
$$\left( {0,{1 \over {\sqrt 5 }}} \right)$$
D
$$\left( {{1 \over {\sqrt 5 }},{1 \over 2}} \right)$$
2
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
If $${3^x}\, = \,{4^{x - 1}},$$ then $$x\, =$$
A
$${{2{{\log }_3}\,2} \over {2{{\log }_3}\,2 - 1}}$$
B
$${2 \over {2 - {{\log }_2}\,3}}$$
C
$${1 \over {1 - {{\log }_4}\,3}}$$
D
$${{2{{\log }_2}\,3} \over {2{{\log }_2}\,3 - 1}}$$
3
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.
4
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.
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