1
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
Let y = y(x) be the solution of the differential equation dy = e$$\alpha$$x + y dx; $$\alpha$$ $$\in$$ N. If y(loge2) = loge2 and y(0) = loge$$\left( {{1 \over 2}} \right)$$, then the value of $$\alpha$$ is equal to _____________.
2
JEE Main 2021 (Online) 27th July Morning Shift
Numerical
+4
-1
If $$y = y(x),y \in \left[ {0,{\pi \over 2}} \right)$$ is the solution of the differential equation $$\sec y{{dy} \over {dx}} - \sin (x + y) - \sin (x - y) = 0$$, with y(0) = 0, then $$5y'\left( {{\pi \over 2}} \right)$$ is equal to ______________.
3
JEE Main 2021 (Online) 25th July Evening Shift
Numerical
+4
-1
Out of Syllabus
Let a curve y = f(x) pass through the point (2, (loge2)2) and have slope $${{2y} \over {x{{\log }_e}x}}$$ for all positive real value of x. Then the value of f(e) is equal to ______________.
4
JEE Main 2021 (Online) 25th July Morning Shift
Numerical
+4
-1
Let y = y(x) be solution of the following differential equation $${e^y}{{dy} \over {dx}} - 2{e^y}\sin x + \sin x{\cos ^2}x = 0,y\left( {{\pi \over 2}} \right) = 0$$ If $$y(0) = {\log _e}(\alpha + \beta {e^{ - 2}})$$, then $$4(\alpha + \beta )$$ is equal to ______________.
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination
Medical
NEET