1
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the general solution of the differential equation $$\cos ^2 x \frac{d y}{d x}+y=\tan x$$ is $$y=\tan x-1+C e^{-\tan x}$$ satisfies $$y\left(\frac{\pi}{4}\right)=1$$, then $$C=$$

A
e
B
1
C
$$-$$1
D
$$\frac{1}{e}$$
2
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Assertion (A) Order of the differential equations of a family of circles with constant radius is two.

Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.

A
A and R are true, R is the correct explanation to A
B
A is true, R is false
C
A and R are true, R is not the correct explanation to A
D
A is false, R is true
3
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$l$$ and $$m$$ are order and degree of a differential equation of all the straight lines at constant distance of $$P$$ units from the origin, then $$l m^2+l^2 m=$$

A
2
B
6
C
12
D
30
4
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$2 x-y+C \log (|x-2 y-4|)=k$$ is the general solution of $$\frac{d y}{d x}=\frac{2 x-4 y-5}{x-2 y+2}$$, then $$C=$$

A
4
B
2
C
3
D
$$-$$4
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