1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\frac{\mathrm{d}}{\mathrm{d} x} \mathrm{f}(x)=4 x^3-\frac{3}{x^4}$ such that $\mathrm{f}(2)=0$, then $\mathrm{f}(x)$ is equal to

A
$x^4+\frac{1}{x^3}+\frac{129}{8}$
B
$x^4+\frac{1}{x^3}-\frac{129}{8}$
C
$x^3+\frac{1}{x^4}+\frac{129}{8}$
D
  $x^3+\frac{1}{x^4}-\frac{129}{8}$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{x \rightarrow 0} \frac{9^x-4^x}{x\left(9^x+4^x\right)}=$$

A
$\log \left(\frac{3}{2}\right)$
B
$\frac{1}{2} \log \left(\frac{3}{2}\right)$
C
$2 \log \left(\frac{3}{2}\right)$
D
$2 \log \left(\frac{9}{4}\right)$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the length of the perpendicular to a line from the origin is $2 \sqrt{2}$ units, which makes an angle of $135^{\circ}$ with the X -axis, then the equation of line is

A
$x+y=4$
B
$x-y+4=0$
C
$x-y=4$
D
$x+y+4=0$
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is 3 mm and after 1 second it is reduced to 2 mm , then at any time t its radius is (where $0 \leq \mathrm{t}<3$)

A
$\mathrm{3+t}$
B
$3-\mathrm{t}$
C
$4-\mathrm{t}$
D
$1+\mathrm{t}$
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