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

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 __________.

Your input ____
2
JEE Advanced 2022 Paper 2 Online
Numerical
+3
-1
Change Language
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 __________.
Your input ____
3
JEE Advanced 2021 Paper 1 Online
Numerical
+4
-0
Change Language
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 ________.
Your input ____
4
JEE Advanced 2018 Paper 1 Offline
Numerical
+3
-0
Change Language
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 ............
Your input ____
JEE Advanced Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12