MHT CET 2025 19th April Evening Shift | Differential Equations Question 45 | Mathematics

The principal increases continuously in a newly opened bank at the rate of $10 \%$ per year. An amount of Rs. 2000 is deposited with this bank. How much will it become after 5 years?

$$ \left(\mathrm{e}^{0.5}=1.648\right) $$

3926

3296

3692

3269

MHT CET 2025 19th April Evening Shift

MCQ (Single Correct Answer)

-0

The solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}=(x+y)^2$ is

$\tan ^{-1}(x+y)=x+\mathrm{c}$, where c is the constant of integration

$x+y=\tan x+\mathrm{c}$, where c is the constant of integration

$x+y=\cot ^{-1} x+\mathrm{c}$, where c is the constant of integration

$x+y=\sin ^{-1}(x+y)+\mathrm{c}$, where c is the constant of integration

MHT CET 2025 19th April Evening Shift

MCQ (Single Correct Answer)

-0

A normal is drawn at a point $\mathrm{P}(x, y)$ of a curve $y=\mathrm{f}(x)$. The normal meets the $X$ axis at $Q$. $l(\mathrm{PQ})=\mathrm{k} \cdot(\mathrm{k}$ is a constant) Then equation of the curve through $(0, k)$ is

$x^2+y^2=\mathrm{k}^2$

$(1+\mathrm{k}) x^2+y^2=\mathrm{k}^2$

$x^2+\left(1+\mathrm{k}^2\right) y^2=\mathrm{k}^2$

$x^2+2 y^2=2 \mathrm{k}^2$

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

The order and degree of differential equation of all tangent lines to the parabola $x^2=4 y$ is respectively.

$1,2$

$2,2$

$3,1$

$4,1$

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