1
JEE Advanced 2022 Paper 2 Online
Numerical
+3
-1
The product of all positive real values of $x$ satisfying the equation

$$x^{\left(16\left(\log _{5} x\right)^{3}-68 \log _{5} x\right)}=5^{-16}$$

is __________.
2
JEE Advanced 2021 Paper 1 Online
Numerical
+4
-0
For x $$\in$$ R, the number of real roots of the equation $$3{x^2} - 4\left| {{x^2} - 1} \right| + x - 1 = 0$$ is ________.
3
JEE Advanced 2018 Paper 1 Offline
Numerical
+3
-0
Let a, b, c three non-zero real numbers such that the equation $$\sqrt 3 a\cos x + 2b\sin x = c,x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$$, has two distinct real roots $$\alpha$$ and $$\beta$$ with $$\alpha + \beta = {\pi \over 3}$$. Then, the value of $${b \over a}$$ is ............
4
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0

The value of $$6 + {\log _{3/2}}\left( {{1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}...} } } } \right)$$ is __________.

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