1
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$2 f(x)-3 f\left(\frac{1}{x}\right)=x$$, then $$\int_\limits1^e f(x) d x=$$

A
$$-\left(\frac{2+\mathrm{e}^2}{5}\right)$$
B
$$\frac{2+e}{5}$$
C
$$\frac{2+e^2}{5}$$
D
$$\frac{2-e^2}{5}$$
2
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

Water is being poured at the rate of 36 m$$^3$$/min. into a cylindrical vessel, whose circular base is of radius 3 m. Then the wate level in the cylinder is rising at the rate of

A
$$\frac{4}{\pi}$$ m/min
B
$$4\pi$$ m/min
C
$$\frac{1}{4\pi}$$ m/min
D
$$\frac{2}{\pi}$$ m/min
3
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the equation $$3x^2-kxy-3y^2=0$$ represents the bisectors of angles between the lines $$x^2-3xy-4y^2=0$$, then value of k is

A
$$-6$$
B
$$-10$$
C
6
D
10
4
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of $$\left(x \frac{d y}{d x}-y\right) \sin \frac{y}{x}=x^3 e^x$$ is

A
$$e^x(x-1)+\cos \frac{y}{x}+c=0$$
B
$$x e^x+\cos \frac{y}{x}+c=0$$
C
$$e^x(x+1)+\cos \frac{y}{x}+c=0$$
D
$$e x^x-\cos \frac{y}{x}+c=0$$
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