1

### JEE Advanced 2013 Paper 2 Offline

MCQ (More than One Correct Answer)
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
$${{2{{\log }_2}\,3} \over {2{{\log }_2}\,3 - 1}}$$
2

### IIT-JEE 1989

MCQ (More than One Correct Answer)
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
$$\alpha < \gamma < \beta$$
3

### 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.
4

### 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.

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