MHT CET 2025 26th April Evening Shift | Differential Equations Question 4 | Mathematics

The population of towns A and B increase at the rate proportional to their population present at that time. At the end of the year 1984, the population of both the towns was 20,000 . At the end of the year 1989, the population of town A was 25,000 and that of town B was 28,000 . The difference of populations of towns A and B at the end of 1994 was

5950

8000

7950

6950

MHT CET 2025 26th April Morning Shift

MCQ (Single Correct Answer)

-0

The general solution of the differential equation $\frac{d y}{d x}=\cot x \cdot \cot y$ is

$\cos x=\mathrm{c} \operatorname{cosec} y$, where c is the constant of integration.

$\sin x=\mathrm{c} \sec y$, where c is the constant of integration.

$\sin x=x \cos y$, where c is the constant of integration.

$\cos x=\mathrm{c} \sin y$, where c is the constant of integration.

MHT CET 2025 26th April Morning Shift

MCQ (Single Correct Answer)

-0

The equation of a curve passing through $(1,0)$ and having slope of tangent at any point $(x, y)$ of the curve as $\frac{y-1}{x^2+x}$ is

$\quad 2(y-1)+x(x+1)=0$

$\quad 2 x-(y-1)(x+1)=0$

$\quad 2 x+(x+1)(y-1)=0$

$\quad 2 x(y-1)+(x+1)=0$

MHT CET 2025 26th April Morning Shift

MCQ (Single Correct Answer)

-0

The differential equation which represents the family of curves $y=c_1 e^{c_2 x}$, where $c_1, c_2$ are arbitrary constants is

$y^{\prime \prime}=y^{\prime} y$

$y y^{\prime \prime}=y^{\prime}$

$y y^{\prime \prime}=\left(y^{\prime}\right)^2$

$y^{\prime}=y^2$

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