1
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the curve passing through the point $(0,2)$ given that the sum of the ordinate and abscissa of any point exceeds the slope of the tangent to the curve at that point by 5 is

A

$y=x-4-2 \mathrm{e}^x$

B

$y=4-x-2 \mathrm{e}^x$

C

$y=4+x-2 \mathrm{e}^x$

D

$y=4-x+2 \mathrm{e}^x$

2
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let z be the complex number such that $|z|+z=3+i$ where $i=\sqrt{-1}$, then $|z|=$

A

$\frac{\sqrt{34}}{3}$

B

$\frac{5}{3}$

C

$\frac{\sqrt{41}}{4}$

D

$\frac{5}{4}$

3
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The solution of the differential equation $(1+x) \frac{\mathrm{d} y}{\mathrm{~d} x}-x y=1-x$ is

A

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

B

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

C

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

D

$y(1+x)=x$, where c is the constant of integration

4
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\mathrm{d} x}{\sin ^2 x \cos ^2 x}= $$

A

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

B

$\tan x-\cot x+\mathrm{c}$, where c is the constant of integration.

C

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

D

$\tan x-\cot 2 x+\mathrm{c}$, , where c is the constant of integration.

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