1
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The vector equation of the plane through the line of intersection of the planes $x+y+z=1$ and $2 x+3 y+4 z=5$, which is perpendicular to the plane $x-y+z=0$, is

A
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{k}})=2$
B
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{k}})+2=0$
C
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{k}})=2$
D
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{k}})+2=0$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of motion of a particle is $s=a t^2+b t+c$. If the displacement after 1 second is 20 m , velocity after 2 seconds is $30 \mathrm{~m} / \mathrm{sec}$ and the acceleration is $10 \mathrm{~m} / \mathrm{sec}^2$, then

A
$\mathrm{a}+\mathrm{c}=2 \mathrm{~b}$
B
$\mathrm{a}+\mathrm{c}=\mathrm{b}$
C
$\mathrm{a}-\mathrm{c}=\mathrm{b}$
D
$\mathrm{a+c=3 b}$
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

One side and one diagonal of a parallelogram are represented by $3 \hat{i}+\hat{j}-\hat{k}$ and $2 \hat{i}+\hat{j}-2 \hat{k}$ respectively, then the area of parallelogram in square units is

A
$2 \sqrt{3}$
B
$3 \sqrt{2}$
C
$6 \sqrt{2}$
D
$4 \sqrt{3}$
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \mathrm{e}^{x^2} \cdot x^3 \mathrm{dx}=\mathrm{e}^{x^2} \mathrm{f}(x)+\mathrm{c}$ and $\mathrm{f}(1)=0$ (where c is a constant of integration), then the value of $f(x)$ is

A
$\frac{x-1}{2}$
B
$\frac{x^2+1}{2}$
C
$\frac{x+1}{2}$
D
$\frac{x^2-1}{2}$
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