1
JEE Advanced 2024 Paper 2 Online
Numerical
+4
-0
Change Language

Let the function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by

$$ f(x)=\frac{\sin x}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)}+\frac{2}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)} . $$

Then the number of solutions of $f(x)=0$ in $\mathbb{R}$ is _________.

Your input ____
2
JEE Advanced 2020 Paper 2 Offline
Numerical
+4
-0
Change Language
Let the function f : [0, 1] $$ \to $$ R be defined by

$$f(x) = {{{4^x}} \over {{4^x} + 2}}$$

Then the value of $$f\left( {{1 \over {40}}} \right) + f\left( {{2 \over {40}}} \right) + f\left( {{3 \over {40}}} \right) + ... + f\left( {{{39} \over {40}}} \right) - f\left( {{1 \over 2}} \right)$$ is ..........
Your input ____
3
JEE Advanced 2020 Paper 2 Offline
Numerical
+4
-0
Change Language
Let the function $$f:(0,\pi ) \to R$$ be defined by $$f(\theta ) = {(\sin \theta + \cos \theta )^2} + {(\sin \theta - \cos \theta )^4}$$

Suppose the function f has a local minimum at $$\theta $$ precisely when $$\theta \in \{ {\lambda _1}\pi ,....,{\lambda _r}\pi \} $$, where $$0 < {\lambda _1} < ...{\lambda _r} < 1$$. Then the value of $${\lambda _1} + ... + {\lambda _r}$$ is .............
Your input ____
4
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
Change Language
Let f : [0, 2] $$ \to $$ R be the function defined by

$$f(x) = (3 - \sin (2\pi x))\sin \left( {\pi x - {\pi \over 4}} \right) - \sin \left( {3\pi x + {\pi \over 4}} \right)$$

If $$\alpha ,\,\beta \in [0,2]$$ are such that $$\{ x \in [0,2]:f(x) \ge 0\} = [\alpha ,\beta ]$$, then the value of $$\beta - \alpha $$ 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