1
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
The equation of the plane passing through the line of intersection of the planes $x+y+z=1$ and $3 x+4 y+5 z=2$ and perpendicular to the XY- plane is
A
$2 x+y-3=0$
B
$x-2 y+3=0$
C
$x-3 y-2=0$
D
$2 x-y+6=0$
2
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-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

A
$x^2+y^2=\mathrm{k}^2$
B
$(1+\mathrm{k}) x^2+y^2=\mathrm{k}^2$
C
$x^2+\left(1+\mathrm{k}^2\right) y^2=\mathrm{k}^2$
D
$x^2+2 y^2=2 \mathrm{k}^2$
3
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\frac{(27-2 x)^{\frac{1}{3}}-3}{9-3(243+5 x)^{\frac{1}{5}}}, x \neq 0$ is continuous at $x=0$, then the value of $\mathrm{f}(0)$ is

A
$\frac{2}{3}$
B
6
C
2
D
$\frac{1}{3}$
4
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \mathop {\lim }\limits_{x \to 0} \frac{|x|}{|x|+x^2}= $$

A
0
B
1
C
-1
D
$\frac{1}{2}$

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