1
JEE Advanced 2024 Paper 1 Online
Numerical
+4
-0

Let $a=3 \sqrt{2}$ and $b=\frac{1}{5^{1 / 6} \sqrt{6}}$. If $x, y \in \mathbb{R}$ are such that

\begin{aligned} & 3 x+2 y=\log _a(18)^{\frac{5}{4}} \quad \text { and } \\ & 2 x-y=\log _b(\sqrt{1080}), \end{aligned}

then $4 x+5 y$ is equal to __________.

2
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 __________.
3
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 ________.
4
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 ............