WB JEE 2020 | Differential Equations Question 42 | Mathematics

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

If $$x\sin \left( {{y \over x}} \right)dy = \left[ {y\sin \left( {{y \over x}} \right) - x} \right]dx,\,x > 0$$ and $$y(1) = {\pi \over 2}$$, then the value of $$\cos \left( {{y \over x}} \right)$$ is

log x

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

The differential equation of the family of curves y = e^x (A cos x + B sin x) where, A, B are arbitrary constants is

$${{{d^2}y} \over {d{x^2}}} - 9x = 13$$

$${{{d^2}y} \over {d{x^2}}} - 2{{dy} \over {dx}} + 2y = 0$$

$${{{d^2}y} \over {d{x^2}}} + 3y = 4$$

$${\left( {{{dy} \over {dx}}} \right)^2} + {{dy} \over {dx}} - xy = 0$$

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

Let $$y = f(x) = 2{x^2} - 3x + 2$$. The differential of y when x changes from 2 to 1.99 is

0.01

0.18

$$ - $$0.05

0.07

WB JEE 2020

MCQ (Single Correct Answer)

-0.5

Let $$y = {1 \over {1 + x + lnx}}$$, then

$$x{{dy} \over {dx}} + y = x$$

$$x{{dy} \over {dx}} = y(y\ln x - 1)$$

$${x^2}{{dy} \over {dx}} = {y^2} + 1 - {x^2}$$

$$x{\left( {{{dy} \over {dx}}} \right)^2} = y - x$$

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