1
JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
Let a curve y = y(x) be given by the solution of the differential equation $$\cos \left( {{1 \over 2}{{\cos }^{ - 1}}({e^{ - x}})} \right)dx = \sqrt {{e^{2x}} - 1} dy$$. If it intersects y-axis at y = $$-$$1, and the intersection point of the curve with x-axis is ($$\alpha$$, 0), then e$$\alpha$$ is equal to __________________.
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2
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 __________.
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 __________.
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3
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 _________.
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4
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 ____________.
$${e^{\sin y}}\cos y{{dy} \over {dx}} + {e^{\sin y}}\cos x = \cos x$$, 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 ____________.
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Questions Asked from Differential Equations (Numerical)
Number in Brackets after Paper Indicates
No. of Questions
JEE Main 2022 (Online) 27th July Morning Shift (1)
JEE Main 2022 (Online) 26th July Evening Shift (1)
JEE Main 2022 (Online) 25th July Evening Shift (2)
JEE Main 2022 (Online) 29th June Evening Shift (1)
JEE Main 2022 (Online) 29th June Morning Shift (1)
JEE Main 2022 (Online) 27th June Evening Shift (1)
JEE Main 2022 (Online) 26th June Morning Shift (2)
JEE Main 2021 (Online) 27th August Morning Shift (1)
JEE Main 2021 (Online) 27th July Evening Shift (1)
JEE Main 2021 (Online) 27th July Morning Shift (2)
JEE Main 2021 (Online) 25th July Morning Shift (1)
JEE Main 2021 (Online) 22th July Evening Shift (1)
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JEE Main 2021 (Online) 18th March Evening Shift (1)
JEE Main 2021 (Online) 26th February Morning Shift (2)
JEE Main 2021 (Online) 25th February Evening Shift (1)
JEE Main 2020 (Online) 9th January Morning Slot (1)
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