61
MCQ (Single Correct Answer)
The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is
A
an ellipse
B
parabola
C
circle
D
rectangular hyperbola
62
MCQ (Single Correct Answer)
The general solution of differential equation $\frac{d y}{d x}=e^{\frac{x^2}{2}}+x y$ is
A
$y=C e^{-x^2 / 2}$
B
$y=C e^{x^2 / 2}$
C
$y=(x+C) e^{x^{2 / 2}}$
D
$y=(C-x) e^{x^2 / 2}$
63
MCQ (Single Correct Answer)
The solution of equation $(2 y-1) d x-(2 x+3) d y=0$ is
A
$\frac{2 x-1}{2 y+3}=k$
B
$\frac{2 y+1}{2 x-3}=k$
C
$\frac{2 x+3}{2 y-1}=k$
D
$\frac{2 x-1}{2 y-1}=k$
64
MCQ (Single Correct Answer)
The differential equation for which $y=a \cos x+b \sin x$ is a solution, is
A
$\frac{d^2 y}{d x^2}+y=0$
B
$\frac{d^2 y}{d x^2}-y=0$
C
$\frac{d^2 y}{d x^2}+(a+b) y=0$
D
$\frac{d^2 y}{d x^2}+(a-b) y=0$
65
MCQ (Single Correct Answer)
The solution of $\frac{d y}{d x}+y=e^{-x}, y(0)=0$ is
A
$y=\mathrm{e}^{-x}(x-1)$
B
$y=x e^x$
C
$y=x \mathrm{e}^{-x}+1$
D
$y=x e^{-x}$