Javascript is required
1
JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
Let y = y(x) be the solution of the differential equation

xdy $$-$$ ydx = $$\sqrt {({x^2} - {y^2})} dx$$, x $$\ge$$ 1, with y(1) = 0. If the area bounded by the line x = 1, x = e$$\pi$$, y = 0 and y = y(x) is $$\alpha$$e2$$\pi$$ + $$\beta$$, then the value of 10($$\alpha$$ + $$\beta$$) is equal to __________.
2
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
The difference between degree and order of a differential equation that represents the family of curves given by $${y^2} = a\left( {x + {{\sqrt a } \over 2}} \right)$$, a > 0 is _________.
3
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
If y = y(x) is the solution of the equation
$${e^{\sin y}}\cos y{{dy} \over {dx}} + {e^{\sin y}}\cos x = \cos x$$, y(0) = 0; then
$$1 + y\left( {{\pi \over 6}} \right) + {{\sqrt 3 } \over 2}y\left( {{\pi \over 3}} \right) + {1 \over {\sqrt 2 }}y\left( {{\pi \over 4}} \right)$$ is equal to ____________.
If the curve, y = y(x) represented by the solution of the differential equation (2xy2 $$-$$ y)dx + xdy = 0, passes through the intersection of the lines, 2x $$-$$ 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to _________.