1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the plane, passing through the intersection of the planes $x+y+z=1$ and $2 x+3 y-z+4=0$ and parallel to $Y$-axis is

A
$x+4 z-1=0$
B
$x+4 z-7=0$
C
$x-4 z+7=0$
D
$x-4 z+1=0$
2
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(1)=1, \mathrm{f}^{\prime}(1)=3$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ is

A
12
B
9
C
15
D
33
3
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\left[\begin{array}{lll}\overline{\mathrm{a}} \times \overline{\mathrm{b}} & \overline{\mathrm{b}} \times \overline{\mathrm{c}} & \overline{\mathrm{c}} \times \overline{\mathrm{a}}\end{array}\right]=\lambda\left[\begin{array}{lll}\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}\end{array}\right]^2$, then $\lambda$ is equal to

A
3
B
0
C
1
D
2
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\lim _\limits{x \rightarrow 0}\left((\sin x)^{\frac{1}{x}}+\left(\frac{1}{x}\right)^{\sin x}\right)$, where $x>0$ is

A
0
B
$-$1
C
1
D
2
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