JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

The question given below consist of an assertion

(A)

and the reason (

R

) use the following key to choose the appropriate answer.

A: The product of the ordinates of the point of tangency to the curve

\left(1+x^2\right) y=2-x

, where the tangent makes equal intercept with coordinate axes is equal to 1 .

\mathrm{R}

: Slope of straight line making equal and same sign intercept with coordinate axes is equal to -1

View answer and explanation

Correct option: A

If both assertion and reason are correct and reason is the correct explanation of the assertion

Option C (Decreasing on

(0,1)

and increasing on

(1,2)

) is correct because the sign of the derivative changes from negative to positive at x=1, indicating a minimum.

More Questions from DIFFERENTIAL EQUATIONS

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y=y(x)

\left(3 y^{2}-5 x^{2}\right) y d x+2 x\left(x^{2}-y^{2}\right) d y=0

y(1)=1

\left|(y(2))^{3}-12 y(2)\right|

x

{x^2} + {y^2} = 1

\left( {y' = \frac{{dy}}{{dx}},y'' = \frac{{{d^2}y}}{{d{x^2}}}} \right)

x = A\cos 4t + B\sin 4t,

\frac{{{d^2}x}}{{d{t^2}}}

y=y_{1}(x)

y=y_{2}(x)

\frac{d y}{d x}=y+7

y_{1}(0)=0

y_{2}(0)=1

y=y_{1}(x)

y=y_{2}(x)

y=y(t)

\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}

\alpha>0, \beta>0

\gamma>0

\lim \limits_{{x \rightarrow \infty}} y(t)